The Airbus A380 cockpit

This is a cut-down still of part of the Airbus A380 cockpit, taken from airbus.com. It's from a panoramic viewer, on a page that uses Flash to let you pan and tilt and zoom in and out of a view in any direction, so that you can really explore the cabin in detail, in high-res. If you want to look out of the window, look backwards, or look up at the ceiling while it spins, you can do that. The mouse scrollwheel zooms you in and out. It's nice. The 360-360 photography is by gillesvidal.com.

The A380 is a very nice plane, with a famously-great cockpit control surface layout. It has a comfortable, relaxing, reassuring look to it (as opposed to some of the more traditional layouts with lumpy panels and dials everywhere all screaming "Look at MEEE!"). It doesn't look scary – as a newbie, you can look at this user-interface and half-kid yourself that you might actually be able to fly it.
My concern when I first heard about the Airbus' screen-based system was: what happens if a screen develops a fault, and you lose a whole bank of virtual instrumentation? Well, the A380 panels tackle that problem brilliantly – you notice how the eight main portrait-format screens all seem to be the same size? Well, they're completely interchangeable. You're supposed to be able to pop out any of the main screens and swap them round, live. There's a couple of little grey rectangles below the bottom two corners of each screen panel, presumably those are the finger-latches. And apparently you can completely change the layout, so if one panel's connection points are messed up, you can watch its data somewhere else. I like this plane.

So let's explore ...
Twin side-joysticks and QWERTY keyboards. I don't know what those two rounded plastic bulges are ... perhaps they're calming devices, for the pilots to put their hands on in moments of stress. Or maybe they're there so that if you get thrown towards the panel, you have something to grab onto that doesn't accidentally result in you pressing an Important Switch by accident.

Three spare seats at the back (for parties), and an overhead camera (so that you can remember what you did the next morning). Fun Wagon!

Note the video camera views, on the centre screen. Useful for parking, and also for reminding yourself which airport you're at. Also for checking that you still have the right number of engines, that none of them are on fire, that all your control surfaces are present and correct, and that your wheels haven't fallen off. Without cameras (or a periscope), it's not always easy to know if your wheels are really down, because planes tend not to have glass bottoms. The central panel showing the video views is the obvious "spare" section of control surface to use in flight for additional functions if further equipment is retrofitted that needs its own display space (like customised additional avionics – rocket launchers, anyone?). There's a pull-out shelf thing in front of each seat that gives the pilots additional keyboards and pop-up screens for general flight admin and map-browsing.

Very Importantly: what looks like three cup-holders per side, left and right, away from the important controls, plus another five at the back left. It's deeply important to have enough cup-holders (one for fresh coffee, one for water, and one for soup, or perhaps noodles?). That's assuming that the holes aren't for something more boring. There's a clunky laptop-py thing at the back, for system-level stuff.

I like the documentation holder on the back of the door, made out of two types of sticky tape. But what's that panel in the door, with the nasty scratch gouged in it? Is it a “people” version of a cat-flap? I also like the design of the door-hinges, with the hinge protruding inside the cabin, and the screws accessible. That means that the cabin crew can remove the door from its hinges from the inside, if it jams (say, after a crash). Someone's put a lot of thought into this.

Twin microphones (for karaoke duets? Pilot-copilot comedy banter?). Between the "emergency power" and "oxygen" switches overhead (up above the left windscreen variable-speed wiper knob), there's also an intriguing switch marked “Entertainment”. Hmm.

Rear right, there's what looks like a locked cabinet marked CDROM. Well, if the Batmobile has one, I suppose the 380 ought to have one, too.

"Escape rope" compartments on both sides. Down to the rear left, by the fire extinguisher (whose sign I initially misread as “portable fire eating”), there's a hatch set into the floor. I've seen this hatch drawn on a schematic with a ladder poking through that exits through the front wheel port. I guess this means that if you're a pilot and you have a panic attack before takeoff, you can pop down through the floor and run away across the airfield without the passengers realising that you've gone.

The seat covers have large tags facing each other saying "Pilot" and "Copilot", which might be useful for resolving cabin arguments. Point at the tag. 'Nuff said. Also handy for avoiding those embarrassing "But I thought YOU were supposed to be flying the plane!" moments.

So, a very nice vehicle.

The only design decision here that I'd query is the upholstery. Pinstripe? Hmmm. But perhaps there's a reason for that, too ... perhaps striped material doesn't show sweat stains so easily. You don't want to be settling down into your seat for a long-haul flight, and be too conscious of the big sweaty patch left by the previous pilot. Eurgh. I wonder how often they change the covers?

With the addition of deep-pile furry tiger-pattern seat covers, vibro-back-massagers built into the seats, a proper entertainment system with giant speakers, and a couple of foot spas, I'd give this cabin 10/10.

The Relativistic Ellipse

This is an especially cool diagram for relativity theory, but it's rather hard to find in print. There's a limited version of it in Moreau's 1994 "Wave front relativity" paper, and I put it in the book (chapter 8), but I can't think offhand of anywhere else you're liable to find it.

It's simply an ellipse with lines radiating from one focus and converging on the other.

Imagine that you have a point-source of light giving off pulses. Surrounding the point-source is a spherical mirror, which catches the outgoing spherical EM wavefront and bounces it directly back to the source. All parts of the reflected wavefront arrive back at the source at the exact same moment.
This tells us (a) that all parts of the surface are at 90 degrees to the source, and (b) that all parts of the surface are at the same distance from the source.


=Relativistic Aberration=

Now let's replay the same situation, but imagine how it would have looked to us if we were whizzing past the experiment in a spaceship (but not so close that we actually disturbed the light in any significant way).

Now, the geometry seems to be different. We're forced to agree that the reflected wavefront still converges on the emitter (because nothing within the experimental region has physically changed), but since the light takes a finite time to go out and come back again, as far as we're concerned, the experimental hardware has been moving while the light was out doing its thing.
For us, the light was being emitted from one position and refocused at another.

And the shape that does that is an ellipse.

If we look at the shape of the relativistic ellipse, we find that the outgoing rays are angled forwards ... they have to be in order for them to be able to keep up with the "moving" source. And if we measure the angles of these rays on the diagram, it gives us the textbook relativistic aberration formula used by special relativity (and also by Newtonian optics, old ballistic emission theory, and any other relativistic model).


=Velocity-rescaling, distance and time under Special Relativity=

The thing that's slightly counter-intuitive about the diagram is that if the radius of the sphere is half a light-second, and if it's supposed to take exactly one second for the light to return to its starting point (so that the bouncing light makes a clock that supposedly ticks every second), you might expect the distance "v" that the object moves in one second to simply be the distance between the two points. Slightly perversely, under SR, it isn't. The relative proportional velocity v/c (velocity quoted as a fraction of the speed of light) has to be the ratio between the focal point distance and the stretched, longest dimension of the ellipse. So if the distance between the focii is half the length of the ellipse, we can say that the velocity is half lightspeed
(in the diagram above, it's 0.8c).
But since the ellipse is stretched, the distance between the points (if v is defined as a particular fraction of the speed of light) is stretched, too. If we're to follow SR and say that lightspeed is a fixed global reference, then the distance between bounce-points is somewhat more than v metres.

Under special relativity, the width of the ellipse is assumed to be constant regardless of velocity, the ellipse is stretched by the Lorentz factor (calculated from our proportional velocity), and the "point-to-point" distance ends up elongated by the Lorentz factor, too.

Under special relativity we explain the extra distance by invoking Lorentz time dilation. We suggest that the particle travels further than expected in our coordinate system in one of its own seconds, for a given nominal velocity, because its clock is running slow (so for us, it travels for more than a second,and crosses more than v metres). Or we can argue that if an observer moving with the experiment sees a piece of paper with the diagram drawn on it passing by with the same proportional velocity of v, that for them, the distance between the marks is v metres, because their measurements indicate that the moving paper is Lorentz length-contracted. The ellipse looks like a giveaway that lightspeed isn't globally fixed, but if we assume that it is, and need to explain why the ellipse somehow doesn't really count as an ellipse, we end up with the traditional SR length-contraction and time-dilation explanations.

Contract the elongated ellipsoid by the magical gamma factor, and its outline turns neatly back into the original sphere.


=Doppler shifts=

The next thing that we can do is to look at the length of the lines. Turns out that, if we're doing the SR version of the exercise, each ray elongates or shrinks by precisely the right ratio for special relativity's relativistic Doppler effect. The forward and rearward distances are stretched and squashed by the ratio SQRT[(c-v)/(c+v)], and the 90-degree-aimed ray is stretched in length by SQRT[1 - vv/cc].
That's the Lorentz transverse redshift prediction of special relativity.


=Ellipses are Cool=

So this one little diagram tells you almost everything that you need to know about special relativity. Once you've drawn it with the appropriate proportions for a given velocity, all you have to do is read off the angles and distances with a protractor and ruler to find SR's physical predictions about the appearance of a moving body, as seen from any angle.

If you'd prefer not to rely on any "odd" theory-specific definitons of velocity, distance or time whenbuildign the ellipse, all you have to do is draw in two rays from a focus, with lengths rescaled by the theory's particular Doppler shift predictions, and the rest of the diagram constructs itself. Along with the Minkowski lightcone diagram, it's probably one of the most powerful diagrams in special relativity.

So why isn't it in the books?

We-ell, perhaps the problem with the diagram is that it makes people think. Which leads to troubling ponderings, because it turns out that the diagram doesn't have to be used with special relativity. It'll compute the SR relationships if we deliberately stretch the point-to-point distance by the Lorentz factor, or if we use the SR "relativistic Doppler" relationships to define the reference wavelength-distances, or if we decide that lightspeed has to be defined as globally constant for all participants ... but if we're only interested in the principle of relativity, and we're not prepared to commit to these extra SR-specific things, the ellipse also lets us plug in other assumptions, and lets us see the their consequences.

For instance, we know that old Newtonian optics was technically a "relativistic" theory (although nobody could get NO to work properly with wave theory). We know the forward and rearward wavelength changes associated with that theory, so we can draw in these two wave-distances from one of the focal points, and construct the rest of the ellipse around these maximum and minimum radii. What we end up with is an exact duplicate of the SR ellipse, with the same proportions and aberration angles, but with an additional Lorentz magnification. All the NO wavelengths are longer than their SR counterparts by a Lorentz ratio. So transverse redshifts aren't unique to special relativity.

And then you notice some other things. The SR ellipse can be compacted back into its original circular outline just by contracting it on one axis. This is analogous to tilting the diagram off the page to produce a contracted "shadow", which gets us into the subject of Minkowski spacetime, tilted planes of simultaneity, and other cool things. The SR family of ellipses actually represents constant-width tilted cross-sections through a constant Minkowski lightcone and can be visualised as projected conic sections.

The SR version of the constructed ellipse is the only one that has this special property.
This tells us that if we require spacetime to be "flat" in moving-body problems, the SR relationships are the only ones that work. We're still freetoargue argue about the correct philosophical interpretation and presentation of the theory, and about whether the interpreted contractions and clock-changes are physically real or not (and about what wemean by "physically real" in the context of SR), but the defining Doppler characteristics of the theory – the things that dictate the final physical predictions and equations ofmotion, regardless of interpretation – are set, locked and non-negotiable once we've decided that we won't be implementing curvature as part of the model. According to the ellipse, Relativity (limited to simple inertial motion) plus flat spacetime gives SR. It's airtight.

If we now go back to the enlarged Newtonian version of the ellipse, we find that the rules are different. The enlarged NO wavelengths can't be fitted back into the original sphere without distorting the centre of the ellipse out of the page. Instead of a tilted-and-rescaled cross-section through a fixed geometry (Minkowski spacetime) we end up with a geometry whose shape dynamically changes when there's relative motion between physical masses. Instead of a purely "projective" tilt, we have a real physical change of shape. The causal structure of the metric now depends on the presence and motion of physical bodies embedded with it. We end up with a gravitomagnetic theory, with a different form of lightspeed constancy to SR. And that's why nobody, including Einstein, could put together a sane-looking reference model for Newtonian optics that didn't go crazy when you tried to treat it as wave theory. Newtonian optics simply doesn't work in flat spacetime. The wavelengths don't fit.

I still think that it's a shame that they don't teach the relativistic ellipse in physics classes. It's a powerful tool, and a really handy device for demystifying special relativity. But perhaps it's too powerful, and perhaps if you're trying to convince a class that SR is the only possible answer, a tool that suggests the existence of alternative approaches spoils the narrative.

Social Media and the Gooeyverse

Some "social media" guys have taken to bitching about the term "social media". They feel that it doesn't adequately describe what they do. It doesn't make them feel sufficiently ... special.

Well, there's two ways you can go. Either you replace the term "social media" with something more specific, like "Interactive social network enablement systems", or you go the other way, and invent a brand new buzzword that's shorter, snappier, and more subversive-sounding.

In which case, I vote for "Goo".

Goo is the amorphous, gelatinous set of shifting organic interconnections and linkages that binds and connects us all together. It's not a restrictive "web" or a fixed "net"-work. It's goo.
A locus of goo, like Twitter or Facebook, becomes a gooball. The connections between gooballs, the part of the internet that deals with crosslinks between social media hubs, becomes the intergoo. The global user environment for goo becomes the Gooeysphere, the view from within is the Gooeyverse. "Intelligent" software support for goo ("web 2.0"-based automatic book recommendations, and so on) becomes smart goo. Goo generators like Blogger or Wikipedia, that let users spawn new collections of goo connections are hypergoo.

Corporate blogging and twitterring becomes Blue Goo.

It also ties in well with the idea of links between software and wetware ... and the fact that a Graphical User Interface – the thing that you look at when you use a piece of software – is referred to as a GUI (pronounced "gooey") doesn't hurt, either.

All good clean fun.

Trouble is, how are you going to explain to your mother that you have a career in goo?

"Social media" doesn't sound so bad now, does it?

Villarceau Coils, Slinkies, and Ring-packing

Computer graphics are fine, but the problem with programming a simulation of something is that often you only get out what you put in. You lose the element of surprise. So sometimes, if you you want to find out what something really does, you build one. Available technology and spare parts permitting, of course.

For the "Villarceau Coil" blogpost, I figured that it was worth making a physical model. A good hardware place nearby sells middle-sized keyring loops for 15 pence each, so I went in with a few quid and came away with a pocketful. Then it was just a question of clipping the things together.

There were a couple of things that I hadn't expected:

Thing Number One was that a "keyring Villarceau coil" is a bit like a Slinky. You put it on the palm of your band, or on a flat surface, and tilt the surface, and the thing kinda ... slinks ... downhill. It reacts to the uneven pressure on its base, rings rotate and slither past each other, the torus squirms and turns inside out, and the thing scuttles off down the slope with a slightly guilty air about it, like an octopus running along a seabed.

From a science-fiction/xenobiology point of view, the coil makes an interesting template for a possible alien lifeform. With a soft toroidal body and a hard set of spiny Villarceau rings, an animal could burrow or shred predators or food by turning itself inside out. It could start as a skinny beastie with maybe three rings, and grow more rings as it got bigger and fatter. It'd solve the problem of how to reconcile a hard exoskeleton with the ability to change size. Young could be gestated as full-size rings within the fleshy body. Giving birth would probably have to be be kinda fatal, though, unless the rings each had a notch somewhere. :(

Anyhow ... Drop the coil, and it "splashes" when it lands, then reforms back to the torus shape ... or if you've used a lot of rings, into a pair of interlinked tori. You can pop it on your finger, and pass it from hand to hand, one finger at a time, by tilting your finger to point downhill towards the destination finger, so that the v-coil slinks down the finger, turning itself inside out as it goes.

So basically, a fun executive toy. Three quid well spent.



Thing Number Two was that the rings have a natural tendency to nest (as in, "what Russian Dolls do", not "what in birds do") .... except that, in this case, the self-similar "dolls" are all made from components that are exactly the same size. Which is a slightly wierd situation.

So if you start with maybe just three rings for a skinny torus, and you add more rings to force the thing to be fatter, you find yourself using a lot more rings than you thought. They start to form nesting toroidal layers. Since every torus that you can produce using the Villarceau configuration has exactly the same major radius as a single ring, they all fit neatly inside one another.

It's kinda reminiscent of the way that electron orbits stack up around an atomic nucleus.

And since every ring in the set of nested tori has exactly the same configuration to all the others, you can reach in and pull an inner ring and with a bit of shuggling turn it into an outer ring (while one of the outer rings shuffles back inward to take its place).

This is a FUN shape. You could probably write an entire book about it.

String Theory and The Goodies

The 1990s "string theory" boom was an example of what happens when a critical mass of researchers realise how to game the system. If enough people start churning out work on the same subject, and eagerly citing each other in multi-author papers, they levitate up the scientific citation indexes together. You get a bubble. It's in most players' interests to keep inflating the bubble – the more new people they attract to the subject, the more seniority they have in a growth area of science. It becomes like a pyramid scheme. So in the 1990s we had some pretty absurd claims being made for string theory and what it was going to do for us, and when.

I wasn't unsympathetic to string theory as such - It seemed like something that needed to be researched ... just not by everybody. The talk was that string theory was The Future, and sometimes it seemed as if anyone who wasn't already committed to some other line of "mathematical physics" research was scrabbling to get onto the bandwagon. There were people doing worthy work on the subject before the boom, and once the bubble burst, those people would probably continue doing worthy work. What was wrong was the hype.

And all though this time, I kept remembering the old 1970's episode of The Goodies, where the guys use their advertising agency to promote string as the wonder product that's good for everything. Here's just the clip of the Goodies "String" song, courtesy of YouTube:



"String, string, string, string, ev'rybody needs string!"

It also seemed to me that we'd been here before. String theory was supposed to be a ToE, a "Theory of Everything", but in the 1990s, it actually seemed to be more of a ToA, a "Theory of Anything". It sounded like a great way of being able to remodel any given physical theory, but didn't seem to offer any clues as to what sort of theory we should be trying to model. It sounded was a bit like Jean Luis Borges' fictional "Library of Babel", that contained every book ever written, and every book that might ever be written - but whose total inclusivity meant that it ultimately contained no information at all.

String theory in the 1990s seemed to suffer from the same problem that aether theory had had in the 1890s - what had made aether theory lose credibility as a subject wasn't that it gave wrong answers, or that it was limited – its problem was that it was too flexible. With enough arbitrary variables, you could construct an aether model to reproduce almost any behaviour you could possibly want – we had aerodynamic aether theories, sink-and-source aether theories, Lorentzian ether theory (LET), and so many other variants that even experts started to lose track of them. Without a guiding set of principles to eliminate possibilities, generalised aether theory as a field couldn't actually make any solid falsifiable predictions.

Aether theory had degenerated into a "Theory of Anything", and if you eventually managed to isolate a set of rules to derive a single preferred set of physical relationships from some amophous theoretical soup, then the process of logical deduction that you'd used to decide on a particular set of properties for the theory, was the theory.

And the worry with string theory was that perhaps some people in the "string" community hadn't quite understood this. Some of its more enthusiastic proponents insisted that string theory was already "discovered" – string theory was fundamental truth, and "all we had to do now" was to learn how to decode it. But without the decoding process there was only a metatheory that defined a context within which an actual physical theory might later emerge. Without an extraction process we might as well be trying to divine "ultimate truth" from tealeaves or goat entrails.

It also didn't help that the "We already have the secrets of the universe in our grasp, we just need to take a few more generations to work out how to decode them" argument, the apparent nonchalance about the lack of falsifiability, and the use of "mystical" language to try to attract public support were all things that people more usually associated with the Nostradamians and Bible Code numerologists than with the physics and math communities.


There was only so long that the string theory hype could last without the subject actually making any physical predictions, and eventually the field got hit by a nasty dose of reality, with Lee Smolin and Peter Woit both publishing critical books on what had actually been achieved. There simply wasn't a physical theory yet. Just because something was pretty didn't automatically make it physics.

I was happy to criticise when the hype was underway, but I'm uncomfortable kicking a theory when it's already down. It's too easy. Good work is probably still being done with string theory, it's just not getting headlines in New Scientist every single week as it used to. Perhaps the fashionistas will drift away and find some other fad to attach themselves to, and it'll be just the hardcore guys left, who were there from the beginning, and aren't reliant on a fortnightly press release cycle. And perhaps that's an appropriate situation.

Heck, if it gets too fashionable to knock string theory I might even have to start defending it.

Meanwhile I'm going to watch the video again. "String, string, string, string ..."

Holograms at Halloween

I don't suppose that there's any reason why holograms have to be created on a flat sheet.
It's traditional to do it that way, and it probably makes the optics easier, but there doesn't seem to be an especial reason why all of the sheet has to be at the same angle. If you created a hologram on a curved sheet that surrounded an object, then as long as the sheet kept the same shape, it should presumably look as if the object is inside the volume (rather than appearing to be in front of or behind a flat "window"). There's also no obvious reason why you can't produce cheap printed lenticular holograms on curved sheets either, other than that it'd make the initial processing more difficult.

So, Halloween. Once we're set up for manufacturing curved holograms, the obvious application (at this time of year) is the creation of the world's most scary Halloween masks.

Put a hologram of a human skull onto a curved transparent sheet, use the sheet as a visor, fitted inside the cowl of a black cloak, and make the inside smoked or semi-mirrored, and you have a "Death" Halloween costume, where, if anyone gets too close and peers under the cowl though the sheet to try to see who's face is behind the visor, they get a rather nasty shock!

Okay, on reflection, maybe not such a great idea after all. :(
You don't want people dropping dead of heart attacks when they realise that "the death guy" appears to be wandering about with what seems to be a real, genuine, gaping skull on the top of his neck. I mean, realism is all very well, but to be striding around town leaving a trail of traffic accidents and screaming people and dead bodies in your wake would probably be taking authenticity a bit too far. Oh well.

The Villarceau Coil

Sometimes it's fun to try to take the most ludicrously-abstract and pointless geometrical results and to try to turn them into something useful. It's a fun game, and the more abstract the thing is, the higher the chance that nobody's actually brainstormed it properly before you. The "square-cutting" exercise ended up as a possible idea for new storage media for hydrogen-powered cars, so after uploading the "Cutting up Doughnuts" post, I was scratching my head to try to think of some real-world application for the "Villarceau Circle" result, that might turn the pastry-cutting exercise into something with actual physics applications.

The best I could come up with was a variable-geometry magnetic containment device.


If we take our two interlocking Villarceau circles, and delete one of them, we're left with a simple ring that wraps once around the torus limb and its central void. This counts as a special-case toroidal winding. We can interleave a series of these single angled rings around the torus, intersecting, without any of them clashing or colliding. If current is circulated around each ring (perhaps by "breaking" the rings and wiring them in series), you have yourself a rather unusual toroidal coil.

What's unusual about it that it has variable geometry. Each circular ring-segment can be a rigid wound coil, and by tilting the angle of these coils we can create a larger torus with arbitrary proportions (major axis radius fixed, minor axis radius variable). Okay, so there's a limit to how fat or thin we'd be able to go due to the finite thickness of the rings that we're using to construct it, but essentially, we have something that looks like a toroidal accelerator and containment device, that can actually change shape while it's running.
Provided that the "open" configurations of the resulting toroidal coil aren't too open, this might let you prototype a device without having to calculate the ideal proportions beforehand - you'd be able to adjust the torus shape while the device was actually operating.

Now, suppose for the sake of argument that you wanted a containment device that allowed you to open it out, fire high-energy particles into it in low-energy mode, then close the coils, squash the plasma density to encourage some sort of reaction, and then open the coils again to allow the reaction products to spill out into the surrounding coolant. You could have a system that "breathes", and holds different shapes for different parts of its cycle.

Okay, I'm trying not to be too glib here – because nuclear physics is NOT my specialist field – but this thing would look awfully like a cross between the "cage fusor devices" and the "tokamak" configurations that people use for nuclear fusion. When it's closed you have something that looks like a tokamak, and when it's open you have something that looks (superficially) more like a fusor cage. One of the annoyances of the tokamak designs is that once you've built them, they're usually locked into particular configuration – with a Villarceau coil, the variable geometry means that you should be able to get some pretty significant changes in internal volume and field strength without having to vary the current flow to the coils. And if the internal pressure gets too great, the thing's going to have a tendency to self-adjust by opening out like a flower-bud, reducing internal pressure and temperature, and releasing excess plasma into the surrounding coolant in a semi-controlled way (rather than being all bottled up until things go more badly wrong).

Anyhow ... bottom line is, that even if this configuration is no damned use at all for conventional nuclear fusion, it'd still look damned cool as a piece of hardware.

Designers and art directors for science fiction movies take note. Remember how cool people though the Big Scary Spinny Machine was in Contact (1997)? Well, this configuration would be a really nice thing to use next time you have to design a cool fictional device for a spaceship reactor or engine pod. Shiny silver interlocking steel circles that tilt and swivel, with a whizzy blue plasma glow inside. Mmmm.

I want to see this cool thing in a movie NOW ! :) Who's going to be first?

---

PS: I did spent the last couple of weeks seriously consider building one of these as a toy, sticking it in a small vacuum chamber and whacking a high-tension voltage into it, as a version of those plasma balls that you find in gadget shops. I figured that with that, plus a set of circular coil units, and I might have a cool little device that could spin plasma (or bits of shiny silver paper) in an amusing way. I got as far as looking up coil formers. But sanity prevailed. Plus, I think my current landlord might take a dim view of his tenants trying to build small prototype nuclear fusion reactors on the premises.

Holographic Diamonds

Back in January 2000, the Millennium Dome exhibition opened to what was supposed to be a display of the best of British achievement. Unfortunately the people in charge of setting it up didn't seem to have a clue how to run this sort of exhibition or what to put inside the dome, and it ended up as a bit of a national embarrassment.

One of the last-minute additions to the show was the Millennium Star diamond.

To see the diamond, you had to walk though an angled passageway that was completely pitch black apart from some slightly odd (monochromatic?) blue light, and there, in the middle, you'd see a case walled with bulletproof glass, containing the blue-lit diamond. You walk past it, perhaps pause, and then make your way out. No loitering, no photography.

Something struck me when I was in there. The thickness of the cabinet's glass meant that the diamond appeared be in different places, depending on which pane you viewed it through - that's completely normal, you usually see a similar effect with fishtanks. But the blue light confused me, because normally you only see blue-lit rooms when someone's trying to hide something. Okay, so it was a blue diamond, but still ...
The human eye is pretty bad at seeing sharp details in blue light, which is why Windows has traditionally had a blue-themed startup screen - the old splash screen used crude dithering to recreate the effect of a smooth variation in tone using the default 16-colour VGA pallette, and by doing this in blue, the eye was fooled into not noticing the effect too much. If Windows 3.1 had tried that trick in red or green or yellow, the result would have been bitty and grainy and would have looked awful. In blue, you can't see the fine detail that gives the trick away.

Now, the glass.
Bulletproof glass uses a "sandwich" of alternating toughened glass and shock-absorbing plastic sheets, so that even if you shatter every layer of glass, the shatter-patterns are different, and the pieces stay stuck together by the plastic. If someone had simply added an additional sheet of plastic film with a with a hologram of a diamond ... then how would you be able to tell? You couldn't look for alignment errors between the sheets on different panes, because the diamond woudl appear at differtent positions when viewed through the different panes anyway, due the the thickness of the glass.
Does a holographic diamond appear to refract light in the same way as a real diamond? I don't know, but if someone wanted to look for an "anomalous" spectrum effect that didn't correspond to real diamond, the use of monochromatic blue light might be a good way to stop them. And with single-colour light source, we'd also find it difficult to see any interference fringes due to misregistration of the holographic films. Optical theory says that to see those coloured fringes, the colours already have to be present in the original lightsource, andf in our "blue room", that light wouldn't be there.

Of course, for all this to work, de Beers would have to have their own in-house holography R&D department aligned with their security people, which sounds pretty unlikely. But in fact, deBeers do have very strong links to holographic reseach: They have laser systems for checking diamonds, and for laser-etching holographic security marks onto them, and slightly more peripherally, Lucent have been researching diamond as a potential holographic storage medium. DeBeers also have a holographic diamond passport scheme. So diamonds and security and holography research and lasers and de Beers all have a pretty strong overlap. There probably aren't that many companies that know more about certain sorts of holography than de Beers do.


So here's a fun, harmless little conspiracy theory to ponder that's worthy of Sherlock Holmes or Jonathan Creek: What if this diamond, which thieves tried to steal from the Dome in November 2000 in a ram-raid using a mechanical digger, nailguns and a getaway speedboat, was protected by the ultimate "stage magic-based" security system? What if the diamond, that perhaps many thousands of people would swear on oath to having seen in person ...
... was never actually there?

Cosmological Hawking Radiation, and the failure of Einstein's General Theory

Cosmological horizons are rather arbitrary. The cosmological limit to direct observation is at different places for different observers, and if you change position, your horizon position changes to match. In that respect, a cosmological horizon is a little bit like a planetary horizon - it's different for everyone, and every physical location can be considered as being at a horizon boundary for someone.

With a cosmological horizon, we can mark out a region of space that we reckon should be directly visible, and another region beyond that shouldn't be, and try to draw a dividing line between the two that represents the horizon. The unseen region doesn't exist in an observerspace map even as space, which (in an observerspace projection) seems to fizzle out and come to a stop at the horizon limit.
As we try to look at regions further and further away, we're seeing larger and larger cosmological redshifts, and seeing further and further back in time, until we approach a theoretical limit where the redshift is total, time doesn't appear to have moved on at all since the Big Bang, and events apparently frozen into the horizon correspond to those in the vicinity of Time Zero.
In an idealised model, trying to see any further away than this means that we'd be expecting to be seeing spacetime events that originated before the Big Bang, which – in our usual models – don't exist. So the cosmological horizon is the rough analogue of a censoring surface surrounding a notional black hole singularity under general relativity. It kinda ties into the cosmic censorship hypothesis that, if any physical singularities do exist anywhere in Nature, Nature will always make physics work nicely and politely helpfully hiding the nasty singularities from view.

HOWEVER ... with a cosmological horizon, there are logical arguments that insist that we can receive signals though it.

Suppose that we have two star systems, A and B, whose spatial positions are on different sides of our drawn cosmological horizon, a couple of hundred lightyears away from each other. Let's say that B's the closer star to us – 100 ly inside our nominal horizon – and A's 100 ly outside. In an observerspace projection, we'll eventually be able to see the formation of the nearer star B (if we wait a few bazillion years) but A is off-limits.

But the nearer star B is quite capable of seeing events generated by A, and then helpfully relaying their information on to us. If A goes supernova, we should (eventually) be able to see a cloud of gas near B being illuminated by the flash. B can pass A's signals on, just as an observer at a planetary horizon can see things beyond our horizon and describe them to us, or hold up a carefully-angled mirror to let us see for ourselves.

So technically, Star A, under QM definitions, is a virtual object. It doesn't exist for us according to direct observation, but it's real for nearby observers and we can see the secondary result of those observations. B radiates indirectly through the horizon, so not only does the supposed Big Bang singularity have a masking horizon, the horizon emits Hawking radiation. If we'd bee a bit brighter back in the 1950's, we'd have been able to predict Hawking radiation by taking the "cosmological horizon" case and generalising over to the gravitational case. What stopped us from doing this was an incompatibility with the way that GR1915 was constructed.

The cosmological horizon is an acoustic horizon. It fluctuates and jumps about in response to events both in front of it and behind it. If someone near star A lobs a baseball at star B, we'll eventually see that baseball appear, apparently from nowhere, as a Hawking radiation event. And depending on how close the thrower is to the horizon, and how hard they throw the ball, we might even get a glimpse of their shoulder, as the physical acceleration of their arm warps spacetime (accelerative gravitomagnetism, Einstein 1921) making the nominal horizon position jump backwards.

For this sort of acoustic horizon to work, the acceleration and velocity of an object has to affect local optics (if the ball had been thrown in the opposite direction, we'd never have seen it).
If the local physics at a cosmological horizon generates an acoustic horizon, then that physics is going to correspond to that of an acoustic metric. NOT a static Minkowski metric. The presence, velocity and acceleration of objects must change the local signal-carrying properties of a region. Since the operating characteristics of an acoustic metric are different to those of the Minkowski metric that defines the relationships of special relativity, the local physics then has to operate according to a different set of laws to those of special relativity – the velocity-dependent geometry of an acoustic metric makes the basic equations of motion come out differently. For cosmological horizons to work as we expect, the local light-geometry for a patch of horizon has to be something other than simple SR flat spacetime, and the local physics has to obey a different set of rules to those of special relativity.

Now, the punchline: Since our own region of spacetime will in turn lie on the horizon of some distant far-future observer, this means that if we buy into the previous arguments, our own local "baseball physics", here on Earth, shouldn't be that of special relativity either.


The good news is that if we eliminate special relativity from GR, to force cosmological horizons to make sense, GR's predictions for gravitational horizons would also change. The revised general theory would predict indirect radiation effects through gravitational horizons, bringing the theory in line with quantum mechanics. Which would be a Good Thing, because we've been trying to solve THAT problem for most of the last 35 years.

The bad news is that there doesn't seem to be any polite way to do it. Disassembling and reconstructing general relativity to address its major architectural problems involves going back to basics and starting from scratch, questioning every assumption and decision that was made the first time around, and being pretty ruthless about which parts get to stay on in the final theory.

I find this sort of work kinda fun, but apparently I'm in a minority.

Cutting up Doughnuts

A cool thing that I didn't know about doughnuts until someone pointed it out a few months back: no matter what proportions a doughnut has, there's always an angle that you can slice though it to produce a perfect pair of interlocking circles.

Someone mentioned this on sci.math, and pointed to "Doughnut Slicing", a webpage by John Banks and Jeff Brooks, and then, someone else pointed out that there was already a a Wikipedia article on it, under the name "Villarceau Circles" ... at which point I scooted off and tried to work the thing out from scratch, before reading anyone else's "spoilers". There's only a certain number of cool results like this, and if you read other people's work before you've had a crack at a problem yourself, that's an opportunity that you never get back.

Anyhow, it turns out that if a torus has major radius R (distance from central axis to centre of limb) and minor radius r (radius of solid limb), the magic angle A that you have to cut at to get to see the double-circle is simply

SIN A = r/R

Going back and looking at the other two webpages, it seems that, unless I missed it, the authors don't seem to have actually written that down explicitly anywhere (although they do seem to have included some more involved math).

So, one quickie download of GFA BASIC 32 (and some quickie trig) later, and the relationship's obviously right. One quick program run while my tea was cooking, generating a few hundred images of tori with radius ratios from zero to one, tilted by the appropriate angles, and I now have a sequence of pretty Villarceau images sitting on my harddrive that I'll probably string together as a YouTube animation at some point.


If you want to cut up a doughnut or bagel purchased at your local bakery to see the Villarceau circles, thread a thin stick or skewer all the way through through the central hole, and then tilt it to a maximum so that your pointy-stick is touching two different parts of the surface. That line gives you the plane that you need to cut along, and the two points where your stick touches the doughnut are the two points where the pair of circles intersect.

Gulliver's Travels, Isaac Newton, and Flying Saucers

Jonathan Swift (1667-1745) anonymously published his four-part novel, "Gulliver's Travels" in 1726, at the end of a visit to London.

Most people know it for the chapters set in Liliput (where Gulliver is a giant compared to the natives), and maybe also Brobdingnag (where the natives are giants, and it's Gulliver who's considered tiny). It's a scathing social and political farce, where Gulliver's visits to other societies show different systems of government and different social orders. While in Liliput, Gulliver is considered a dangerous giant, and treats the tiny locals with callous indifference. In Brobdingnag it's Gulliver who's overlooked and considered unimportant, so the extent that he's caged and treated as a pet.

But there's also a chapter (at the end) where he visits the Houyhnhnms, a race of talking horses that Gulliver considers entirely superior to humans, who regard the local ape-decended species (the "Yahoos") as loud, primitive, warlike and violent. After living with the Houyhnhnms, Gulliver comes to see all humans as Yahoos.

And for the science fiction fans, there's a chapter about a giant flying saucer.

Really, there is. The third section of the story has Gulliver being rescued by a scientifically advanced society, based on the flying island of Laputa. The city is built on a four-and-a-half-mile-wide concave circular plate topped by buildings, along with four lakes for collecting rainwater, surrounding an astronomical observatory built into a central shaft, that also includes the levitating mechanism. It is, quite literally, a "castle in the air" inhabited by scientists.

Laputa rules over a kingdom (Balnibari), whose borders are defined by the limits of a naturally-occurring geological magnetic anomaly, and the flying city is held aloft by a giant tiltable magnet, held in place by unbreakable "adamant" cage that is of a single piece with the city's baseplate. The city rises and falls and gets sideways propulsion by adjusting the alignment of the magnet.
The flying city is a local scientific superpower, and the king's response to rogue cities below is to steer the saucer above the rebel stronghold and set it down, crushing them.

Unfortunately, I'm not aware of any illustrated editions of "Gulliver's Travels" where the illustrators tackled Laputa. Perhaps the idea was just too freaky for them. If they had, they'd have probably ended up drawing something that looked like the mothership in Spielberg's 1977 "Close Encounters" film.

The other notable thing about Swift's flying city of Laputa is that although it is ordered along entirely scientific principles, its (highly quotable) math-and-music obsessed inhabitants at the Academy of Lagado are buffoons, working on crazy and expensive projects such as the extraction of sunlight from cucumbers, constantly begging for more money for their projects as the society below them decays – it's a fairly small step to suspect that Swift was taking the mickey out of the esteemed Royal Society (then headed by Isaac Newton), and it's even been claimed that Swift emphasised this by basing all of the Lagado projects on specific Royal Society papers.


This raises an intriguing question: did Swift actually meet Newton?
It seems that when Swift had been in London in 1710, he'd been visiting a woman called Catherine Barton. Barton was Newton's half-niece, and one of the few people that Newton was close to. Barton wasn't just some peripheral nominal relative of Newton, she'd actually moved to London and moved in with Newton in about 1696 (about the time he got his job at the Mint), and kept house for him.

If Catherine Barton was living with Isaac Newton and being visited by Jonathan Swift, then Isaac Newton would have cast a rather large shadow over Swift's consciousness, even if he hadn't been /the/ Isaac Newton.

And if that wasn't enough, there was also the subject of Money.
Immediately before "Gulliver's Travels", Swift's celebrity was based on his having anonymously written and published the Drapier's Letters in ~1724-25, a series of pamphlets railing against the coining of copper currency for Ireland, which led to a widespread boycott of the new coins in Ireland and their withdrawal. One of Swift's (many) objections was an allegation that the coins were of poor quality - Newton, as Master of the Mint since the mid-1690's, had to get involved and do an assay, and reported that the allegation wasn't true.
Newton was known for his tetchiness, but Swift in particular had a reputation for being gratuitously and grossly offensive. I've got an old C19th copy of "Gulliver's Travels" that describes Swift as having "more than any other man who ever wrote in English, a liking for saying nasty things", and blames this for Swift's repeated ruination of his own career prospects. Apparently Swift wanted to be a bishop, but even as a returning hero of the Irish people, when the people in charge actually met him, it became clear that this wasn't going to happen. That edition of "Gulliver's" mentions "the deadly agitations of his private life" as being something that the C19th reader might want to enquire about in later life – but whatever this unmentionable personal train wreck was, it doesn't seem to have made it as far as his Wikipedia page.

So perhaps the two wouldn't have wanted to meet each other, especially since they both cared about the same woman. Having the the brittle, acidic, reserved Newton in the same room as the extrovert, scandalous, offensive Swift might not have been a good idea, and the fact that they both had strong ideas about currency would probably just have made things worse.


The young exiled Francois Marie Arouet ("Voltaire") was also in London around this time, and seems to have been rather keen on Catherine, too.
Voltaire later went on to write "Micromegas" (1752), a short satire that appears to have been partly inspired by "Gulliver", in which a pair of giant aliens from Sirius and Saturn arrive on Earth and meet up with and ridicule a bunch of tiny Earth philosophers (with the exception of one guy who is a follower of John Locke). That's John Locke, the guy whose writings seem to have influenced the American Declaration of Independence, not John Locke, the character from "Lost" (a TV series about a strange island with a natural magnetic anomaly).

Another link between Voltaire's story and Swift's is that both throw in a little casual detail (known to the fictional Laputans and alien scientists) that the Mars was "known" to have two moons, and it seems natural to assume that Voltaire probably borrowed this detail from Swift. In fact, Mars has got two moons – Phobos and Deimos – but they didn't get discovered for real until 1877. That earned both writers an astronomical "credit": the only two named features on the smaller of the two satellites are a pair of adjacent craters, named "Voltaire" and "Swift".

After he'd given up on the brilliant Catherine and snuck back to France, Voltaire shacked up, long-term, with another brilliant woman obsessed with Newton, Émilie du Châtelet, who as well as being a serious respected researcher in her own right, translated, produced and reworked (with her comments) the French edition of Newton's Principia.

To the C18th coffee-house intelligentsia, a mix of physicists, philosophers and political theorists, this was a time of revolution and restructuring (not to mention a certain amount of fluidity over people's living arrangements). England had recently undergone a rapid turnover of rulers, flip-flopping from Monarchy to Republic, and back to Monarchy again, then Monarchy chosen by Parliament. Cromwell had kicked out Charles I, Charles II and James II had taken over from Cromwell, and the Glorious Revolution had then given Paliament the right to choose the monarch, which brought in William and Mary, and which they then exercised again in the Act of Settlement to shunt the succession to Anne, who'd then died, too. The Acts of Union in 1707 had then finally united England and Scotland as a single kingdom. In the politics of 1726 England there were various entrenched factions with specific ideas about how the country ought to be run, and by whom, but there was no guarantee that any one particular group would obtain ultimate control.

There was a sense that this was where we decided what the future was going to look like. Was it going to be run by royalists or republicans? Theologians or scientists? Committees or street campaigners? "Gulliver's Travels" tapped into an appetite for exploring possibilities, and showing how different systems failed. Voltaire's later story got a charge out of lampooning philosophers because at the time, philosophy was reckoned to matter. These guys were potentially the architects of the new society.

"Gulliver" can be seen as parody of how people brought up in different political and philosophical systems can believe that their own way of seeing the world and the correct order of things is right and proper, even when outsiders can see that it's ludicrous, and was, in a real sense, revolutionary. Together with a surrounding body of other philosophical and campaign literature, it helped to set up the context for debate that made the French Revolution and the American War of Independence seem possible to the people who risked their lives to make those things happen.

It's not just a kid's story about a shipwrecked guy being tied down with string by little tiny people.

The Michael Jackson Continuum

Here's what happens if you take three single images of Michael Jackson - one as a kid (probably some time around "Rockin' Robin"), one during his "Thriller" period, and one when he was doing odd stuff on balconies – turn each one into a FaceGen head, and then use the program's ageing and tweening settings to generate a set of intermediate heads.

The three original heads are top left, centre, and bottom right. The rest are tweened and age-tweeked extrapolations, courtesy of FaceGen.

You should be able to get much better results than this with a more representative set of photos. A more useful source picture taken between the "Jackson Five" years and "Thriller", would have been handy, but the otherwise-usable ones that I turned up on the net all seemed to be in monochrome. :(

"Bottom left" is what FaceGen extrapolates for Michael Jackson as a fifty-something-yearold with no plastic surgery, top right runs the process in reverse, working backwards from the last picture. The rest are intermediates.

Water on the Moon

In today's Times, there's a front page story saying the the Indian Chandrayaan-1 probe, carrying NASA's Moon Mineralogy Mapper has now found signs of what might be significant amounts of (presumably frozen) water on our Moon.

For anyone who wants bullet points to explain why this is potentially a game-changer, here they are:

• Water + electricity = life support
  Humans need water and air to survive (along with temperature control). With enough solar cells, the Moon's not short of electrical power – no pesky atmosphere to get in the way – but water and air are biggies. If the water's already there, we can tick one box, and using electricity to electrolyse water gives us hydrogen and oxygen. Oxygen lets us tick the second box. Normally we breath atmospheric-pressure air, with 20% oxygen and nearly 80% nitrogen, but we can use pure oxygen at a lower pressure, if we can deal with the additional fire risk associated with pure O2. It'd be nice to have a decent local supply of nitrogen, too, but not strictly necessary.
  
  
• Water + heat + rock = building materials?
  Use solar furnaces to roast moondust, or break moonrock into pulverised dust and drive off the more volatile elements, then add water ... and we might just have ourselves a form of locally-sourced readymix concrete.
  
  You know how in films where moonbases are often all shiny white metal? To start with, they'd probably look more like adobe mud huts, or holes in the ground, with all the shiny stuff on the inside (apart from the solar panels). What you'd ideally want is big thick walls at least ten or so feet thick, on all sides, to buffer the temperature changes and block some of the radiation when the sun does annoying things with solar flares. Perhaps you'd want to maximise your protection from flare radiation without tunnelling, by by building in the bottom of a deep crater, near one of the poles ... which is also where we're hoping that some of surviving "accessible" ice might be found.
  
  Our building materials don't have to be incredibly strong, or even airtight, we could build a crude hollow blocky mesa as our surface structure and inflate a pressurised mylar balloon inside or below for living quarters. But it'd be nice to be able to pour a bit of concrete around the balloon to minimise accidents, and it'd be handy to turn moondust into something more manageable. Other than that, we're stuck trying to stack up rocks and fill sandbags with dust. In a vacuum. Not good. Quite how you're supposed to work with concrete in a vacuum without the water immediately boiling off, I don't know, but I'm sure that some clever concrete technologists are working on it. Supercooling, perhaps?
  
  One problem with building at the bottom of a polar crater is that having a few kilometres of rock in a straight line between you and the Sun isn't so good for solar power. So you'd probably want an array of thin foil mirrors around set up around part of the crater rim, redirecting and focusing concentrated sunlight down onto your generators. Luckily, your mirrors can be ultra-lightweight, there's no weather to damage them, and no intervening air to soak up the transmitted energy. Using reflectors minimises the amount of heavy power cabling, and also the number of solar generators, and depending on the shape of the ice formation that you're trying to exploit, an aimable solar furnace might also be handy for mining.
  
  
• Hydrogen + Oxygen = rocket fuel
  Hydrogen and oxygen burn rather well together to turn back into water, giving a nice roaring flame. That's the reaction that drives the shuttle's main engines. Given a solar farm and enough time, it'd be nice to have a local fuel production plant on the Moon, making rocket fuel simply from local materials. We'd probably need a robotic refueller to pick up H2 + O2 from the plant, fly back to Earth orbit, find the satellite and fill up its tanks (or swap a standardised empty satellite launch tank with a nice pre-refilled one).
  
  
• H2 + O2 + fuel cell = mobile power
  Fuel cells have a capacity that's only limited by the amount of hydrogen and oxygen you have to feed them. If you're building a water-splitting plant anyway, you might want to send along a spare set of empty fuel cells.
  
  
• Water+ electricity + rock + atmosphere = food
  Sure, we can set up a hydroponics lab to grow our own veggies in space, recycle biomass, and use the plants help remove CO2 and other nasties from the air ... and in theory we can get pretty damned close to a sealed self-perpetuating system. But in practice, you need topups, and safety margins, and an awful lot of water to get the thing started (as the name "hydroponics" kinda suggests). If you're going to be growing algae or fungus or plants to eat, there's a lot of water locked up in the system while they're going through their cycle. Industrial biological reactors usually need whole tanks of the stuff, and water's actually pretty heavy. If water's costing you thousands of dollars per kilo to ship from Earth, it's not cheap stuff. It's probably not quite as expensive as gold, but with current shuttle per-kilo launch costs, it's in the ball-park.
  

With water, the moon becomes a solar-powered robotically-constructed and remotely-operated gas station and hydroponics plant, remote-controllable from the Earth, with a mild gravity penalty. It can have its own fleet of little refuelling craft, powered by locally-produced lunar rocket fuel.

Without water, its just a big chunk of rock with some handy boulders to hide behind when there's a bad solar storm.

Anyone whose job involves thinking a decade or two ahead about future lunar, manned or deep space payload missions will be watching this story very carefully.

---

see also: Ice Splat on Mars

Black Holes, Coordinate Reversals, and r=3M

Coordinate projections sometimes have a habit of going wierd when you try to project them past a gravitational horizon. Sometimes you can do it, sometimes you can't, and sometimes the attempt turns various things inside out.
A cool physical inversion that happens outside the horizon was used as the March 1993 cover story for Scientific American: Black Holes and the Centrifugal Force Paradox (by Marek Artur Abramowicz).

The effect isn't really paradoxical, but it's counter-intuitive until you think it through. Normally, if you orbit a body, you can break free of that body by firing up your spaceship's engines and going faster – too fast to be able to orbit at your current distance.
What the BHCFP says is that if you're skimming too close to a black hole event horizon, and you fire up your engines, then the faster you try to circle, the more that your trajectory is deflected inwards, towards the hole. The centrifugal forces that would normally throw you away from the body, now seem to be inverted, pointing inwards rather than outwards.

The critical threshold beyond which this effect appears is the distance r=3M, exactly one-and-a-half times the radius of the horizon surface (which is at r=2M).

It turns out that the r=3M radius is the photon orbit. It's the critical distance at which light aimed at 90 degrees to the mass will be deflected enough by gravity to perform a complete orbit and end up at its starting-point. The SciAm article has some nice computer graphics showing what a circular self-supporting scaffolding tube constructed around the hole at r=3M would look like to an observer standing inside it ... it'd appear to be straight, and if the observer pulled out a telescope and looked far enough along the tube, they'd expect to see the back of their own head.

So r=3M is special. From the perspective of the observer at r=3M who's hovering with the aid of rocket engines, or standing in our circular tube up above the hole, the universe seems to be divided into two regions. On one side they see the black hole and its immediate surroundings, and on the other, they see the starfield that represents the outside universe. Topologically, both regions can be thought of as solid spheres, with their external parallel surfaces meeting at r=3M. Both regions are trying to impose their will on the observer's local geometry, but at r=3M, a stationary observer feels the geometrical competition between the effect of the two spheres as being in balance (although in order to maintain their position hovering above the hole, they're feeling rather a strong gravitational pull!). Spin either one of the two spheres, and the observer will be pulled towards it – spin both at exactly the same rotational rate – the effect that we'd see if we passed along the tube at high speed – and the radial gravitomagnetic effects of both spheres cancel.

So if you built an electric train to run around the interior of the tube, it'd feel the black hole's conventional gravitational attraction pulling it against one side of the tube ... but that pull would seem to be exactly the same no matter how quickly it circled the hole.

The author's moral is that if you're in a spaceship close to a black hole, and you want to escape, don't just throttle up your engines, actually point your ship away from the damned thing, or you're liable to get a nasty crashy surprise.

"Observerspace" Description:

When we think about the optics of the situation, though, perhaps the hypothetical spaceship captain wouldn't be all that surprised:

See, if we imagine standing on a suspended non-orbiting platform at r=3m, we find ourselves looking along the r=3M surface in any (perpendicular) direction. The surface appears to us to be a flat plane cutting through our location. And because our view along r=3M circles around the hole indefinitely, our view along this apparent plane repeats indefinitely, too – the plane appears extend indefinitely far in all directions, showing us older and older views of the surface at greater distances, right back to the time that the black hole originally formed. So logically, anything that we see to one side of the plane corresponds to the interior of the r=3M sphere, and everything we see to the other corresponds to the contents of the "rest-of-the-universe" sphere.
The outside universe only seems to exist on one side of this plane. On the other, gravitational lensing effects make the black hole's r=2M surface beneath us appear to be opened out into a second indefinitely-repeating surface, at some distance below the 3M plane.

Once we're at the 3M surface, there are two ways that we can go.
If we slowly winch ourselves upwards away from the hole, then we see the flat 3M boundary of the outside universe curving itself back into a more normal-looking inward-facing enclosing sphere. But if we allow ourselves to be lowered further towards the black hole, to less than r=3M, then the 3M surface continues to distort past being a flat plane, to becoming a concave surface that curves above us, away from the hole. Instead of the universe surrounding the black hole, it now seems to us that the black hole (and the r=3M surface) is surrounding the universe!
The region that we know ought to be just above the 2M surface appears visually to us to be part of a concave shell, apparently wrapped around a ball representing the remaining universe. The abstract, "topological" idea that our location can affect the choice of which sphere is "really" on the inside or outside now appears to us, visually, to be concrete reality!

The further we descend (slowly) towards 2M, the more pronounced the effect becomes, the more sharply the 2M surface appears to be curved around us, and the more that the outside starfield above appears to shrink to something that looks like a little bright ball suspended somewhere above, in the enveloping black-holey gloom directly above us, like a tiny planet or star.

So if we're hovering too close to r=2M, (or flying past in a spaceship) we shouldn't really be surprised if increasing our forward speed results in our colliding with part of the hole, because that's exactly what our forward view tells us is directly in front of us (and on every side, and directly behind us). If we want to escape from the hole's influence and get back to normal space, then we have to aim our spaceship at the little shrunken blob of compacted blueshifted starfield directly above us. All other directions point at the black hole.

So the rule-of-thumb for navigating within r=3M would seem to be: forget about your ship's fancy gyroscopic navigation systems, just look out of your window and make sure that the ship's nose appears to be pointed approximately at the part of the universe that you want to go to. But don't take your eyes off the forward view, because the harder your engines fire on your way out, the the stronger those distortion effects are going to become.

My Chocolate Tree is Unhappy

I keep chocolate trees. They're not too difficult to grow (if you set up an incubator), but keeping the things alive as houseplants without a controlled environment can be tricky. They generally do okay until you have One Bad Day with light levels that are too bright, or too dim, or the humidity's too low, or the temperature is too hot or too cold, and the things panic and drop all their leaves and turn into ugly bare sticks. And when that happens, it seems to take about eight months to coax the things into producing more proper leaves, and get back into the swing of things. Maybe it's a way of outliving predators - if any beasties have eaten the last set of leaves, the tree waits until they and their offspring have all starved to death before growing any more. Dunno.

I had two gorgeous bushy indoor trees last year, sitting by the back window, and moved them to the front of the house where the light levels were slightly lower. One day later, all the leaves had gone sickly. A day or so later they all fell off. A couple of earlier trees got trashed by a few hours of unusually harsh UV light on one clear winter's morning.

After a number of house-moves, I'm now down to just one small tree, which is only about a year old. It had a nice cluster of healthy dark-green leaves. But after just one hour's car journey (on a fairly hot day), the thing had virtually turned albino. The leaves went almost white, apart from the veins, and it's been struggling ever since. Once a leaf loses its "green", it's one short step away from dying completely, and going brown and falling off, and when all the leaves fall off, you're in trouble.

So what I have to do now is coddle the thing so that the existing leaves hopefully last until the plant has decided to try cautiously growing some new ones.
Maybe I should switch to growing something less challenging. If I used a set of mirrors to catch and redirect daylight around the room, indoor climbing roses would be nice ...

Dark Stars and Hawking Radiation

Some people have trouble getting used to the idea of Hawking radiation outside the context of strict quantum mechanics. For those people, I'd suggest that they consider the mechanics of a crusty old Nineteenth-Century “Dark Star” model.

The Dark Star was the predecessor to the modern black hole, and the basic properties of the object were worked up and published by John Michell back in 1784. Michell worked out many of the “modern” Twentieth-Century black hole properties from Newtonian principles, including the r=2M event horizon radius, gravitational spectral shifts, and a method of calculating the number of these “invisible” gravitationally-cloaked objects by finding the proportion of unseen “companion stars” in binary star systems, and then using statistics to extrapolate that proportion to the larger stellar population.

The main difference between an old “dark star” and John Archibald Wheeler's 1950's-era “black hole” was that dark stars could emit faint traces of indirect radiation. In theory, signals and particles could still migrate upstream out of the dark star's gravitational trap by using local objects as accelerational stepping-stones, whereas under GR1915, this mechanism couldn't exist – objects smaller than their r=2M event horizon radius weren't just incredibly dark, but totally black. Their signals and radiation-pressure signature weren't just absurdly faint, but entirely missing. The thing really was, as Wheeler memorably described it, a truly black "hole" in the surrounding landscape.


From the perspective of the Twenty-First Century, we can describe the difference in another way: dark stars emit classical Hawking radiation and GR1915 black holes don't.
Some people will take issue with that statement. They'll say that a hypothetical dark star's radiation-pattern is about acceleration effects rather than QM, and that Hawking radiation is all about particle-pair-production, a completely different mechanism.

So here's the sanity-check exercise. Suppose that the GR1915 description of horizon behaviour was wrong, and that a more "dark-starry" description was right … but that we still believed in GR1915. More general approaches (like statistical mechanics) would have to insist that the radiation effect was real, even though GR1915 disagreed. So how would we explain the reappearance of our naughty radiation effect?

There are number of stages we'd have to go through:

1. In a thought-experiment, catch an escaped particle and measure its trajectory.
2. Extrapolate that trajectory back to the originating body as a smooth ballistic trajectory. In our "dark star" scenario, this extrapolated trajectory is wrong – the particle only escaped by being "bumped" out of the gravitational pit by interactions with other bodies or radiation – but in our GR1915 description there's no self-supporting atmosphere outside the black hole to allow this sort of acceleration mechanism, so we have to (wrongly) assume an unaccelerated path.
3. Notice that the earliest part of this (fictional!) escape-path is superluminal. In order to escape along a ballistic trajectory, a particle would have to have started out travelling at more than the speed of light (!).
4. Apply coordinate systems. Using a distant stationary observer's coordinates, we break the fictitious trajectory into two parts, an initial superluminal section, and the later, legal, sub-lightspeed part of the calculated path. The first section appears to be off-limits in our coordinate system, and an orderly transition between the two, as the particle supposedly jumps down through the lightspeed barrier seems impossible, but …
5. … then we then notice that in a very idealised description of a superluminally-approaching particle, the particle ends up described as time-reversed ("tachyonic" behaviour). If an (over-idealised) particle approaches at more than the speed of its own light (which shouldn't normally happen, but ...), we'd end up describing it as being seen to arrive before it was seen to set out. Our artificial coordinate system approach then describes the particle as being seen to originate at the nearest part of its path, and to be apparently moving away from us at sub-light speeds, as its earlier signals eventually arrive at our location in reverse order.
6. Time-reversal counts as a reversal of one dimension, which flips a left-handed object into its right-handed twin, and vice versa (chiral reversal). So if our particle was an electron, this artificial approach would describe the earlier part of its supposed path as belonging to a positron, instead.
   
7. Our final description would then say that a particle and its antiparticle both appeared to pop into existence together outside the horizon (from nowhere) and moved in opposite directions, with the "matter" particle escaping and being captured by our detector, and its "antimatter" twin moving towards the black hole to be swallowed.
   

And this is, essentially, the 1970's QM description of Hawking radiation.

The Moon, considered as a Flat Disc

Mathematics doesn't always translate directly to physics.
That statement might sound odd to a mathematician, but consider this: even if you believe that physics is nothing but mathematics, that makes physics a subset of mathematics ... which means that there'll be other mathematics that lies outside that subset, that doesn't correspond cleanly to real-world physical theory. The key (for a physicist) is to know which is which.

That's not to say that "beauty equals truth" isn't a good working assumption in mathematical physics – it is – the problem is that the aesthetics of the two subjects are different, and mathematical beauty doesn't necessarily correspond well to physical truth. The physicist's concept of beauty is often different to that of the mathematician.

The "beauty equals truth" idea is often used as an argument for special relativity. SR uses the Lorentz relationships, and to a mathematician, it can sometimes seem that these are such beautiful equations that a system of physics that incorporates them has to be correct.

But the Lorentz relationships can also appear in bad theories, as a consequence of rotten initial starting assumptions:
Our Moon is tidally locked to the rotation of the Earth, so that it always shows the same face to us, and we always see the same circular image, with the same mappable features. Now suppose that a 1600's mathematician has a funny turn and decides that it's so outrageously statistically improbable that the moon would just coincidentally just happen to have an orbit that results in it presenting the same face to us at all times, that something else is going on. Our hypothetical "crazy mathematician" might decide that since we always see the same disc-image of the Moon, that perhaps, (mis)applying Occam's Razor, it really IS a flat disc.

Our mathematician could start examining the features on the Moon's surface, and discover a trend whereby circular craters appear progressively more squashed towards the disc's perimeter. We'd say that this shows that we're looking at one half of a sphere, but our mathematician could analyse the shapes and come up with another explanation. It turns out that, in "disc-world" the distortion corresponds to an apparent radial coordinate-system contraction within the disc surface. For any feature placed at a distance r from the disc centre, where R is the disc radius, this radial contraction comes out as a ratio of 1 : SQRT[1 - rr/RR ] .

In other words, by treating the Moon as a flat disc, we'd have derived the equivalent of the Lorentz factor as a ruler-contraction effect! :)
Our crazy mathematician could then go on and use that Lorentz relationship as the basis of a slew of good results in group theory and so on. They could argue that local physics works the same way at all points on the disc surface, because the disc's inhabitants can't "see" their own contraction, because their own local reference-rulers are contracted, too. Our mathematician could arguably have advanced faster and made better progress by starting with a bad theory! So "bad physics" sometimes generates "good" math, and sometimes the worse the physics is, the prettier the results.

The reason for this is that, sometimes, real physics is a bit ... boring. If we screw physics up, the dancing pattern of recursive error corrections sometimes generates more fascinating structures than the more mundane results that we'd have gotten if we simply got the physics right in the first place.

Sometimes these errors are self-correcting and sometimes they aren't.
If we considered the Earth as flat, then, because it's possible to map a flat surface onto a sphere (the Riemann projection), it'd still be theoretically possible to come up with a complete description of physics that worked correctly in the context of an infinite rescaled Flat Earth. We'd lose the inverse square law for gravity, but we'd gain some truly beautiful results, that would allow, say, a lightbeam aimed parallel to one part of the surface to appear to veer away. We'd end up with a more subtle, more sophisticated concept of gravitation than we'd tend to get using more "sane" approaches, and all of those new insights would have to be correct. In fact, studying flat-Earth gravity might be a good idea! We'd eventually end up deriving a mathematical description that was functionally identical to the physics that we'd get by assuming a sphericial(ish) Earth ... it'd just take us longer. Once our description was sufficiently advanced, the decision whether to treat the Earth as "really" flat or "really" spherical would simply be a matter of convenience.

But with the "moon-disc" exercise, we don't have a 1:1 relationship between the physics and the dataset that we're working with, and as a result, although the moon-disc description gets a number of things exactly right, the model fails when we try to extend it, and we have to start applying additional layers of externally-derived theory to bring things back on track.
For instance, the "disc" description breaks down at (and towards) the Moon's apparent horizon. For the disc, the surface stops at a distance R from the centre, and there's a causal cutoff. Events beyond R can't affect the physics of the disk, because there's no more space for those events to happen in. The horizon represents an apparent causal limit to surface physics. But in real life, if the Moon was a busier place, we'd see things happening in the visible region that were the result of events beyond the horizon, and observers wandering about near our horizon would see things that occur outside our map. So if we were to use statistical mechanics to model Moon activity, and were to say that the event-density and event-pressure have to be uniform (after normalisation) at all parts of the surface, then statistical mechanics would force us to put back the missing trans-horizon signals by giving us "virtual" events whose density increased towards the horizon, and whose mathematical purpose was to restore the original event-density equilibrium. In disc-world, we'd have to say that the near-edge observer sees events in all directions, not because information was passing through (or around) the horizon, but because of the disc-world equivalent of Hawking radiation.

So in the disc description, the telltale sign that we're dealing with a bad model is that it generates over-idealised horizon behaviour that can't describe trans-horizon effects, and which needs an additional layer of statistical theory to make things right again. In the "moon-disc" model, we don't have a default agreement with statistical mechanics, and we have to assume that SM is correct, divide physics artificially into "classical" and "quantum" systems, and retrofit the difference between the two predictions back onto the bad classical model – as a separate QM effect, as the result of particle pair-production somewhere in front of the horizon limit – to explain how information seems to appear "from nowhere" just inside the visible edge of the disc.

Clearly, in the Moon-disc exercise this extreme level of retrofitting ought to tell our hypothetical crazy mathematician that things have gone too far, and suggest that the starting assumption of a flat surface was simply bad ...
... but in our physics, based on the early assumption of flat spacetime, and generating the same basic mathematical patterns, we ran into a version of exactly the same problem: Special relativity avoided the subject of signal transfer across velocity-horizons by arguing that the amount of velocity-space within the horizon was effectively infinite (you could never reach v=c), but when we added gravitational and cosmological layers to the theory, the "incompleteness problem" with SR-based physics showed up again. GR1915 horizons were too sharp and clean, and didn't allow outward flow of information, so to force the physics to obey more general rules, we had to reinvent an observable counterpart to old-fashioned transhorizon radiation as a separate quantum-mechanical effect.

So the result of this sanity-check exercise is a little humbling. We can demonstrate to our hypothetical 1600's "crazy mathematician" that the Moon is NOT flat, no matter how much pretty Lorentz math that generates, and we can use the horizon exercise to show them that their approach is incomplete. By assuming that their model is wrong, we correctly anticipate the corrections that they'd have to make from other theories in order to fix things up. That ability to predict where a theory fails and needs outside help is the mark of a superior system, and shows that the "Flat-Moon" exercise isn't just incomplete, it generates results that are physically wrong, and that don't self-correct. It's faulty physics.

But the same characteristic failure-pattern also shows up in our own system, based on special relativity. So have we made a similar mistake?

On Catching Rainbows

I saw a nice rainbow yesterday.

I was out to do some shopping but took a random detour, following my feet. The detour just happened to take me to a suitable road junction, at exactly the right time. By rights, I shouldn't have been there to take the picture.

But "lucky catches" aren't just about accidentally being in the right place at the right time by nothing but dumb good luck, or about preserving a certain random element in your approach (although that certainly helps). If you want to be able to catch something that other people miss, you have to expect to spend at least some of your time in places where they aren't, and looking at things that don't always seem to be immediately necessary to the job in hand.
You also have to be prepared for the possibility of success (I try to keep a camera with me, and it had just enough juice left in the batteries to fire off a few shots for the critical sixty or seventy seconds), you have to be able to recognise the preliminary signs of something interesting (I saw a faint 'bow forming, realised what was coming, and was able to fish the camera out and find something to shield it from the rain, in time) and you also have to be prepared to look stupid (standing in the rain with a plastic folder over your camera, taking photos of the sky, at an angle where most of the people who can see you have no idea what you're doing).

But the main thing is to have your eyes open. If you're absolutely sure that nothing interesting is going to happen, then on the occasions when it does happen, you're liable to miss it.

The same thing goes for theoretical physics. If you want to catch things that have eluded other people (whether it's math, or theory, or experimental research), you don't always have to be so much smarter than everyone else, or to have better equipment. Sometimes it's enough just to be prepared for the possibility of being surprised. If you're too rigid about what you're trying to find, you miss out. In my case, I was popping out for a plank of wood for some shelving, and I came back with a plank of wood and a bloggable photograph of a rainbow. If I'd been more singleminded in my shopping, I'd have only come back with the bit of wood.

M.C. Escher's "Relativity", Intransitivity, and the Pussycat Dolls

There's a nice example of intransitive geometry in the latest Pussycat Dolls video ("Hush hush").
No, really, there is. It's the bit where the girls are on four staircases attached to the sides of a cube, that each have a different local direction of "down". The "stairwell" section of the video starts at about 58 seconds in and goes on until about a minute thirty. While you're waiting for it to start you'll have to put up with the sight of Nicole Scherzinger nekked in a bathtub making "ooo, yeah" noises for nearly a minute, though. Sometimes doing research for this blog is really tough.

The video seems to be inspired by the famous "Relativity" lithograph by M. C. Escher, which had three intersecting sets of stairs and platforms set into three perpendicular walls, as a piece of "impossible" architecture (physically you could build it, but you wouldn't be able to walk on all the surfaces as the people do in the illustration).Escher's illustration was incredibly influential, and as well as the Pussycat Dolls video (!), there are some more literal tributes online, including Andrew Lipson's recreation of the scene using Lego, part of the 1986 movie Labyrinth, and a funny short video called Relativity 2.0, that has people trapped in a nightmarish Escherian shopping mall.





If you know of any other especially good ones, please add them to the end of this post as a comment!

Next, we need a Beyonce video illustrating the event horizon behavour of acoustic metrics ...

Special Relativity is an Average

Textbooks tend to present special relativity's physical predictions as if they're somehow "out on a limb", and totally distinct from the predictions of earlier models, but SR's numerical predictions aren't as different to those of Nineteenth-Century models as you might think.

One of the little nuggets of wisdom that the books usually forget to mention is that most of special relativity's raw predictions aren't just qualitatively not particularly novel, they're actually a type of mathematical average (more exactly, the geometric mean) of two earlier major sets of predictions. So, in the diagram above, if the yellow box on the left represents the set of predictions associated with the speed of light being fixed in the observer's frame (fixed, stationary aether), and the red box on the right represents the set of physical predictions for Newtonian optics (traditionally associated with ballistic emission theory), then the box in the middle represents the corresponding (intermediate) set of predictions for special relativity.

If we know the physical predictions for a simple "linear" quantity (visible frequency, apparent length, distance, time, wavelength and so on) in the two "side" boxes, then all we normally have to do to find the corresponding central "SR" prediction is to multiply the two original "flanking" predictions together and square root the result. This can be a really useful method if you're doing SR calculations and you want an independent method of double-checking your results.


This usually works with equations as well as with individual values.
F'rinstance, if the "linear" parameter that we were working with was observed frequency, and we assumed that the speed of light was fixed in our own frame ("yellow" box), we'd normally predict a recession Doppler shift due to simple propagation effects on an object of

frequency(seen) / frequency(emitted) = c / (c+v)

, whereas if we instead believed that lightspeed was fixed with reference to the emitter's frame, we'd get the "red box" result, of

frequency(seen) / frequency(emitted) = (c-v) / c

If there was really an absolute frame for the propagation of light, we could then tell how fast we were moving with respect to it by measuring these frequency-shifts.

The "geometric mean" approach eliminated this difference by replacing the two starting predictions with a single "merged" prediction that we could get by multiplying the two "parent" results together and square-rooting. This gave

frequency(seen) / frequency(emitted) = SQRT[ (c-v) / (c+v) ]

, which is what turned up in Einstein's 1905 electrodynamics paper.

The averaging technique gave us a way of generating a new prediction that "missed" both propagation-based predictions by the same ratio. Since the numbers in the "red" and "yellow" blocks already disagreed by the ratio 1: (1- vv/cc), the new intermediate, "relativised" theory diverged from both of these by the square root of that difference, SQRT[ 1 - vv/cc ]. And that's where the Fitzgerald-Lorentz factor originally came from.

---==---

Why is it important to know this?

Well, apart from the fact that it's useful to be able to calculate the same results in different ways, the "geometric mean" approach also has important implications for how we go about testing special relativity.
Our usual approach to testing SR is to compare just the the "yellow" and "orange" predictions, identify the difference, say that the resulting differential Lorentz redshift/contraction component is something unique to SR and totally separate from any propagation effects, and then set out to measure the strength of this relative redshift/contraction component, in the range "zero-to-Lorentz". Having convinced ourselves that these effects are unique to SR, we usually don't then bother to check whether the data might actually make a better match to a point somewhere to the right of the diagram.
Since the "yellow box" predictions are so awful, special relativity comes out of this comparison pretty well.

But once you know the averaging method, you'll understand that this is only half the story -- these "derivative" effects that appear under SR but not "Classical Theory" ("orange" but not "yellow") must have counterparts under Newtonian optics ("red"), and these are usually stronger than the SR versions. So any experimental procedure or calculation that appears to support the idea of time dilation or length-contraction in an object with simple constant-velocity motion under SR would also generate an apparent positive result for those effects if SR was wrong and the older "Newtonian optics" relationships were the correct set (or if some other intermediate set of relationships was in play). We can say that special relativity's concept of velocity-based time dilation didn't exist under NO, but hardware doesn't care about concepts or interpretations, only results ... and the result of performing an SR-designed test in an "NO universe" would be that the test would throw up a "false positive" result apparently supporting SR (with an overshoot that'd then have to be calibrated out).

And, actually, the situation is worse than this.
... Since the "yellow" and "red" blocks represent the two extremal predictions for theories that allow linkage between the velocity of a light-signal and the motion of a body ("yellow" = zero dependency, "red" = full dependency), they also seem to represent the cutoff-limits for a whole slew of old Nineteenth-Century "dragged aether" models, all of which would be expected to produce similar physical effects to special relativity, differing only in their scaling and strength. So typical test procedures designed to isolate the "new" SR effects should be able to generate "false positive" results with almost all of these old theories and models.

While some of special relativity's concepts might have been new, its testable numerical predictions lie right in the middle of a pre-existing range. Any time you see a claimed experimental verification of SR that forgets to take this into account, treat it with caution.

Fibonacci Kitchenware (well, almost)

I popped into Habitat yesterday, and they're selling a range of five pseudo-Fibonacci nesting trays (four smaller trays plus a bigger one to hold them). It's just a shame that they chose such and awful selection of colours for them (who the heck decided on yellow, brown and navy blue??!?).

Fun with Special Relativity

This is where I surprise everyone by saying something nice about Einstein's Special Theory of Relativity for a change. Considered as a piece of abstract geometry, special relativity (aka "SR" or "STR") is prettier than even some of its proponents give it credit for. The problems only kick in when you realise that the basic principles and geometry of SR considered as physics don't correspond well to the rules that real, physical observers and objects appear to follow in real life.

Anyhow, here's some of the pretty stuff:

It's traditional to explain Einstein's special theory of relativity as a theory that says that the speed of light is fixed (globally) in our own frame of reference, and that objects moving with respect to our frame are time-dilated and length-contracted, by the famous Lorentz factor.
And that characterisation certainly generated the appropriate predictions for special relativity, just as it did for Lorentzian Ether Theory ("LET"). But we can't verify that this time-dilation effect is physically real in cases where SR applies the principle of relativity (i.e. cases that only involve simple uniform linear motion). Thanks to its application of Lorentz-factor relationships, Special Relativity doesn't allow us to physically identify the frame that lightspeed is supposed to be constant in. When we make proper, context-appropriate calculations within SR, we have the choice of assuming that lightspeed is globally constant in our frame, or in the frame of the object we're watching, or in the frame of anybody else who has a legal inertial frame – it's usually a sensible choice to use our own frame as the reference, but really, it it doesn't matter which one we pick, and sometimes the math simplifies if we use someone else's frame as our reference (as Einstein did in section 7 of his 1905 paper).

Some people who've learnt special relativity through the usual educational sources have expressed a certain amount of disbelief (putting it mildly) when I mention that SR allows observers a free choice of inertial reference frame, so let's try a few examples, to get a feel of how special relativity really works when we step away from the older "LET" descriptions that spawned it.

Some Mathy Bits:

1: Physical prediction
Let's suppose that an object is receding from us at at a velocity of four-fifths of the speed of light, v = 0.8c
Special relativity predicts that the frequency shift that we'll see is given by

frequency(seen)/frequency(original) = SQRT[ (c-v) / (c+v) ]
= SQRT[ (1-0.8) / (1+0.8) ]
= SQRT[ 0.2/1.8 ] = SQRT[ 1/9 ]
= 1/3

, so according to SR, we should see the object's signals to have one third of their original frequency. This is special relativity's physical prediction. The object looks to us, superficially, as if it's ageing at one third of its normal rate, but we have a certain amount of freedom over how we choose to interpret this result.

2: "Motion plus time dilation"
It's usual to break this physical SR prediction into two notional components, a component due to more traditional "propagation-based" Doppler effects, calculated by assuming that lightspeed's globally constant in somebody's frame, and an additional "Lorentz factor" time dilation component based on how fast the object is moving with respect to that frame.
The "simple" recession Doppler shift that we'd calculate for v = 0.8c by assuming that lightspeed was fixed in our own frame would be

frequency(seen) / frequency(original) = c/(c+v)
= 1/1+0.8 = 1/1.8

, and the associated SR Lorentz-factor time-dilation redshift is given by

freq'/freq = SQRT[ 1 - vv/cc ]
= SQRT[ 1 - (0.8)² ] = SQRT[ 1 - 0.64 ] = SQRT[ 0.36 ]
= 0.6

Multiplying 0.6 by 1/1.8 gives

0.6/1.8 = 6/18
= 1/3

Same answer.

3: Different frame
Or, we can do it by assuming that the selected emitter's frame is the universal reference.
This gives a different propagation Doppler shift result, of

freq'/freq = (c-v)/c
= 1 - 0.8 = 0.2

We then assume that because we're time dilated (because we're moving w.r.t. the reference frame), and that because our clocks are slow, we're seeing everything to be Lorentz-blueshifted, and appearing to age faster than we'd otherwise expect, by the Lorentz factor.
The formula for this is

freq'/freq = 1/SQRT[ 1 - vv/cc ]
= 1/0.6 = 5/3

Multiplying these two components together gives a final prediction for the apparent frequency shift of

0.2× (1/0.6) = 0.2/0.6 = 2/6
= 1/3

Same answer.

So although you sometimes see physicists saying that thanks to special relativity, we know that the speed of light is globally fixed in our own frame, and we know that particles moving at constant speed down an accelerator tube are time-dilated, actually we don't. In the best-case scenario, in which we assume that SR's physical predictions are actually correct, the theory says that we're entitled to assume these things as interpretations of the data, but according to the math of special relativity, if we stick to cases in which SR is able to obey the principle of relativity, it's physically impossible to demonstrate which frame light "really" propagates in, or to prove whether an inertially-moving body is "really" time-dilated or not. It's interpretative. Regardless of whether we decide that we're moving and time-dilated or they are, the final physical predictions are precisely the same, either way. And that's the clever feature that we get by incorporating a Lorentz factor, that George Francis Fitzgerald originally spotted back in the Nineteenth Century, that Hendrik Antoon Lorentz also noticed, and that Albert Einstein then picked up on.

4: Other frames, compound shifts, no time dilation
But we're not just limited to a choice between these two reference frames: we can use any SR-legal inertial reference frame for the theory's calculations and still get the same answer.
Let's try a more ambitious example, and select a reference-frame exactly intermediate to our frame and that of the object that we're viewing. In this description, both of us are said to be moving by precisely the same amount, and could be said to be time-dilated by the same amount ... so there's no relative time dilation at all between us and the watched object. We can then go ahead and calculate the expected frequency-shift in two stages just by using the simpler pre-SR Doppler relationships, and get exactly the same answer without invoking time dilation at all!

The "wrinkle" in these calculations is that velocities under special relativity don't add and subtract like "normal" numbers (thanks to the SR "velocity addition" formula), so if we divide our recession velocity of 0.8c into two equal parts, we don't get (0.4c+ 0.4c), but (0.5c+0.5c)
(under SR, 0.5c+0.5c=0.8c – if you don't believe me, look up the formula and try it)

So, back to our final example. The receding object throws light into the intermediate reference frame while moving at 0.5c. The Doppler formula for this assumes "fixed-c" for the receiver, giving

freq'/freq = c/(c+v)
=1/1.5 = 2/3

Having been received in the intermediate frame with a redshift of f'/f = 66.66'%, the signal is then forwarded on to us. We're moving away from the signal so it's another recession redshift.
The second propagation shift is calculated assuming fixed lightspeed for the emitting frame, giving

freq'/freq = (c-v)/c
=1 - 0.5/1 = 0.5/1 = 1/2

The end result of multiplying both of these propagation shift stages together is then

2/3 × 1/2
= 1/3

Again, exactly the same result.

No matter which SR-legal inertial frame we use to peg lightspeed to, special relativity insists on generating precisely the same physical results, and this is the same for frequency, aberration, apparent changes in length, everything.

So when particle physicists say that thanks to special relativity we know for a physical fact that lightspeed is really fixed in our own frame, and that objects moving w.r.t. us are really time-dilated ... I'm sorry, but we don't. We really, really don't. We can't. If you don't trust the math and need to see it spelt out in black and white in print, try Box 3-4 of Taylor and Wheeler's "Spacetime Physics", ISBN 0716723271. IF special relativity has the correct relationships, and is the correct description of physics, then the structure of the theory prevents us from being able to make unambiguous measurements of these sorts of things on principle. We can try to test the overall final physical predictions (section 1), and we can choose to describe that prediction by dividing it up into different nominal components, but we can't physically isolate and measure those components individually, because the division is totally arbitrary and unphysical. If the special theory is correct, then there's no possible experiment that could show that an object moving with simple rectilinear motion is really time-dilated.

If you're a particle physicist and you can't accept this, go ask a mathematician.

HTML5 is Coming!

The latest (8 August 2009) draft version of the HTML5 specifications has just been published.

Some of the additions are special dedicated tags for semantic labeling. These are labels that describe the logical content of a block – what it is rather than how it displays - although with Cascading Style Sheets ("CSS"), it's also possible to set associated display parameters for just about any tag type (colours, surrounding boxes, and so on).

Microsoft (who aren't on the HTML5 panel) have queried what the point of these things is, since they don't add any new layout specification tools for the benefit of the website designer. We already have the general-purpose <div> tag that lets us mark out blocks of code, and to assign custom class names and ID names to those blocks, so that they can be displayed in particular ways using CSS. Why duplicate the same functionality in these new tags, <article>, <nav>, <section>, <aside> and so on, if these don't give the webpage designer any new functionality for how a page appears on screen or on paper that they couldn't already achieve with <div>?

Well, even if Microsoft can't quite see the point of them, there are still a number of really good reasons why the end-users and the internet in general need at least some of these new tags.

Blogging
HTML4 came out at the end of the last century (!), and since then the blog phenomenon has pretty much exploded. Blogging software now makes it really easy for authors to produce a mass of rich, mixed, auto-updated content over tens or hundreds of pages. But search engines have to try to make sense of this mess of articles, article links, widgets and addons, and it's not easy. For instance, suppose that I write and upload a blog article about "Einstein and Fish". On Google, "Einstein and fish" currently only gives one result (if it was two words, it'd count as a "Googlewhack").
But as soon as I post the article, the title "Einstein and Fish" will appear in the "recent posts" box in the sidebar of every single page of my blogspace. Point Google's "advanced search" at my blogspace to find how many articles I've written on "Einstein and fish", and instead of one, it'll report back a list of every blog entry I've ever written as apparently containing that piece of search text. It'll also probably include all the text of every widget I've used on the site (like "NASA Photo of the Day"). And this is even though I'm using Blogger, which is Google's own blogsite company.

When webpage designers and companies like Blogger start using the new tags, general-purpose search engines should find it easier to separate out blog articles and webpage content from the surrounding mess of widgets, navigation links, slogans, adverts and general decorative junk.

Client-side reformatting
Some web designers react with outrage at the idea that a browser might display their precious page with a different layout to the one that they carefully designed (to look good on their nice 19" flat-screen monitor).
But people are increasingly looking at web pages on a rangle of devices including mobile phones and ebook readers, and although website designers can in theory produce separate style sheets that allow a page to be displayed with different layouts on every size of device, in practice there's an awful lot who don't bother (including me! :) ). If we use a dedicated blog site, we maybe hope that the site's engineering people will do all that for us, automatically. With CSS-based layouts, some designers tend to go for absolute pixel widths, and frankly, we don't know what devices and screen sizes might be most important a year from now.

Semantic labeling allows dedicated browsers built into these devices to have a good attempt as reformatting and reflowing pages to fit their own tiny screens, by being able to tell which blocks of HTML are the important page content, and which blocks are just there for decoration or navigation.

New Navigation Tools
One of the results of these new tags is that we can expect to see mini-browsers starting to sprout some new navigation buttons. If you have a long page with several sections that takes several sheets to print out, with a figure or two, an inset box with supplementary material, and a navigation bar, then the layout designed for a large screen is going to be hopeless on an iPhone. So what would be cool on an Android mobile phone browser or iPhone would be a function that scans for <section> tags, and then provides additional [<section][section>] buttons that let you skip forwards or backwards through a page. Inset panels with additional info that the designer has "artily" set into the side of the article could be identified by their HTML5 <aside> tag and stripped out and made available on a separate button as [info]. Similarly, if the author produced a number of figures that are referred to in the text, and marked them with the <figure> tag, it'd be handy if the browser could scan for these when the page is loaded, and provide a [figure] button if it finds one, and [<figure][figure>] navigation buttons if it finds several. And it'd also be really handy on a small screen to be able to strip out the navigation bar and put that onto a separate [nav] button, too.
In fact, if this caught on, it'd also be great to be able to jump around a page using these buttons on a conventional "full-size" browser, too.

Accessibility
Finally, if you think that it's difficult navigating a modern "fancy" webpage on a mobile phone, imagine how frustrating it must be if you're sight-impaired, and are using an automated text reader. If you're navigating a page "by ear", it could be useful to be able to find your place again by skipping backwards and forwards a section at a time, until you find a title or intro paragraph that you recognise ... or to be able to jump back and forth between a current reading position and the navigation options, no matter where the designer has put those navigation buttons on the page, or where they happen to appear in the webpage's source code.

One of the problems with CSS, wonderful though it is, is that it allows the designer to place any element in any part of the HTML file, onto any part of the page. This means that the sequential order of chunks of HTML in the field don't necessarily correspond to the order that they have on the screen. A navigation bar that appears at the top of the screen might appear at the bottom of the code. By labelling the sections logically, in a standardised way, it gives audio navigation software the chance of finding key sections of a page and treating them appropriately. For companies and government departments that have disability access policies (and requirements!), adopting HTML5 tags and using them consistently on new projects would be a good initiative both for supporting future standards and for potentially improving long-term disability access.

Misconstructing Fibonacci

The Fibonacci Series sequence mesmerises people. There's something about the idea that a deterministic trail of integers can mysteriously converge on a strange, fundamental, irrational number, the infamous Golden Ratio, or Golden Section, 1.61803 ..... , "phi" – which, like "pi", can't be expressed as any exact ratio between two whole numbers, or written down on paper as a complete series of digits using any conventional number system.

Some people get obsessed with the numbers, and seem to think that if they stare long enough at the simple sequence with its maddening simplicity, that the secret buried inside the integers might reveal itself.

I'm here to give you the answer – the numbers are empty. The secret's not in the numbers at all, it's set one layer back behind the numbers, in the process used to generate them.

If you want to understand how the Fibonacci sequence generates phi, it can be useful to throw away the integers and look at the shapes:
With a conventional square-tiled version of the Fibonacci sequence, we start with a single "fat" rectangle, of nominal side "1×1" (a square), and then we add an additional square to the longest side (in this case, they're all equal, so any side will do), which gives us a "long" rectangle, of dimensions "2×1". Adding another square to one of it's longest sides produces another "fattish" rectangle of size "3×2", although this obviously can't be as fat as the 1×1 square (which was already as fat as you can get). Adding a further square to one of the new longest sides then makes the shape thin-nish again, with size "5×3", although, again, it's not quite as thin as the earlier "2×1" rectangle. As we keep adding squares we get the sequence of ratios 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. and so on.


And this alternating pattern of overshoots and undershoots repeats forever.
For a rectangle that's already precisely proportioned according to the Golden Section, these sorts of square-adding or square-subtracting processes produce rectangular offspring with precisely the same proportions as their parent. But anything more elongated than the "Golden Rectangle" always produces something "fatter" than phi, and anything more dumpy than a Golden Rectangle is guaranted to produce a rectangle that's "skinnier" than phi.
If we apply the process by lopping off squares, then for a "non-phi" rectangle the proportions swing back and forth more and more wildly, getting further and further away from phi each time we remove a square, and if we do it by adding squares, the process takes us closer and closer to phi each time ... and this gives us the usual tiling construction for phi using the Fibonacci Series, shown above, that you should be able to find in a lot of books.

But this specific sequence of numbers 1, 1, 2, 3, 5, 8, 13, 24, 34, 55, 89, 144, ... isn't required for the trick to work – the method generates alternating "fat" and "thin" rectangles that converge on phi, when we start with any two numbers whatsoever. They don't even have to be integers.

Example:
Suppose that instead of 1, 1, we start with a couple of random-ish numbers, taken from say, the date of the Moon landing, 16.07 & 1969. This gives us a very skinny rectangle (with proportions around ~123 : 1). Adding a square to the longest side gives something that's almost square (very "fat", ratio ~1.008), the next pairing will be on the "skinny" side (ratio~1.99), and already we're looking at ratios close to those of the the "1, 2" entries in the standard sequence. The process then chunters on and converges on phi as before.

16.07, 1969, 1985.07, 3954.07, 5939.14, 9893.21, 15832.35, 25725.56, 41557.91, ...

If we stop there, and divide the last number by it's neighbour, we get
41557.91/25725.56 = ~1.6154

add another couple of stages and we get
108841.38/67283.47 = 1.61765..

So in just those few stages, we've already gone from a start ratio of about 123:1 to something close to the golden section value of ~1.618... , correct to three decimal places.

It really doesn't matter whether the initial ratio is 1:1, or 2:1, or a zillion to the square root of three. Any two numbers whatsoever, processed using the method, give a sequence that will lurch back and forth around the Golden Section, always overshooting and undershooting, but always getting closer and closer, guaranteed.

So the Fibonacci sequence, in this regard, is really nothing special. You can plug in any two start numbers, taken from anywhere, apply the Fibonacci method, and the trick will still work.

--===--

What the usual Fibonacci Series does have going for it is simplicity. It's probably the simplest integer example of this process, and it's been argued that perhaps if we want to approximate phi with a pair of integers, that for any given number range, the standard Fibonacci sequence "owns" the pair that get closest (although I haven't actually checked this for myself). We can also derive the "standard" sequence from tiling and quantisation exercises, and when it comes to dealing with sunflowers and pinecones and the like, where we're dealing with structures that branch recursively (like the core of a pinecone) or are the result of cell division in two dimensions, plus time (giving branching over time), then yes, it's not surprising that Fibonacci sequence integers are a recurring theme. Cell division and branching are quantised processes, like the graph of Fibonacci's rabbits.

But the "music" of the Fibonacci series isn't in the integers, its in the rhythm of the of the underlying processes that generate them. It's those underlying processes that carry the magic, not the integers themselves.

Fibonacci Rose, Alternative Tiling

Actually, this is the same arrangement of shapes as in the "double-spiral" version of the Fibonacci Rose, but coloured differently.
As before, each triangle of a given colour has sides that are the sum of the sides of the next two triangles down, giving the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...

And as before, if we zoom out arbitrarily far, the figure becomes indistinguishable from the "golden section" version, in which each triangle's sides are related to the next size up or down by the ratio phi, ~1.618034 ... .

Computers Don't Work

Computers don't work.

This is because, with a few notable exceptions related to applications in scientific and mathematical number-crunching (like computer modelling and rocket science), when a computer system does work, we usually stop calling it a computer. When small numerical calculating computers became reliable and cheap and mass-produced, we stopped calling them "computers" and started calling them "pocket calculators". When personal computers became mainstream and stopped being niche toys for geeks, we started calling them "PCs" or "Macs", without really caring what "PeeCee" stood for.

In offices where the IT system works well, people tend to refer to the things on their desks as "workstations" or "terminals". These are things that you just switch on and start working at. They're functioning business tools.

So, once all the general-purpose systems that work are taken out of the equation, what we're left with is the bespoke systems, and all the systems that don't quite work, aren't quite finished yet, or need a lot of technical support and hand-holding. These are the scary, technical, sometimes-malfunctioning things that we still refer to as computers.

It's interesting to watch this change in naming happening with products as a market sector becomes mature. Home weather monitoring systems drifted from being marketed as "weather computers" to "weather stations", and in-car navigation systems shifted from initially being referred to reverentially as "in-car computers" to being casually referred to as "GPSes". Once the novelty factor has worn off, and people know that a product is reliable, useful and worthwhile, the "computer" tag gets dropped.

So as far as retail products are concerned, "computers", almost by definition, are the remaining gadgets that are either too new to be judged yet, or that don't work properly without a certain amount of expert hand-holding.

This also gives us a handy way of quickly assessing how good a company's IT infrastructure is. If you're visiting an office, and the general office staff refer to their "computers", then the chances are that either the staff aren't very computer-literate, or the office has just been undergoing a painful IT transition, or ... their IT systems simply suck. Try it.

Kew Gardens is Nice

Visited Kew Gardens on Thursday with the family, to scatter our Mum's ashes.

Kew Gardens is cool. It's a 121-hectare site, with a collection of plants and habitats from around the world, and various public greenhouses with their own microhabitats (one of which has its own multicoloured lizard running wild). It's been going in various forms for about 250 years, and it's been a national botanical garden for about the last 170. In some ways it's the forerunner of the Eden Project, and it's the only site that I know of in the UK, other than my place, that has chocolate trees.

As well as the on-site research stations, there's now also now a satellite site at Wakehurst Place, where they do more of the Millennium Seed Bank Project stuff.

Mum wanted to be a tree surgeon when she was a kid, so she was really into Kew, and was a paid-up member. She even had an old (legitimately acquired!) Kew Gardens sign in her garden.

So it was kindofa a nice day.

Xenotransplantation and Swine Flu

Trying to solve the organ transplant shortage using pig organs was both a really good idea and a really bad idea. It was good because a pig's body is reasonably close to ours in terms of size, biology and organ-loading (and because pigs are omnivores, like us) ... and bad because of the virus problem that some people didn't like talking about.

There are three main reservoirs of "foreign" viruses that sometimes cross over into the human population and catch our immune systems unawares - other primates, livestock, and birds. Primates tend to be blamed for origins of the the AIDS virus, the 1918 "Spanish Flu" outbreak that killed between fifty and a hundred million people is sometimes reckoned to have crossed over from birds, and when mammalian livestock is concerned, the culprit is usually assumed to be pigs.

When a disease like this crosses over from a pig or a chicken, we sometimes get a bit disgruntled in the West and mutter that these poor agricultural communities really shouldn't be living in such close proximity to their animals, but for years we've been planning on going one better. Transplanting pig organs into people means that living pig tissue is in as intimate contact with human tissue as its possible to be - actually snuggled up together subdermally and sharing a common blood supply. In Darwinian terms, if you wanted to encourage pig viruses to evolve so that they could thrive in a human environment, this is exactly how you'd do it, and if you were a genocidal mad scientist intent on "accidentally" killing millions of people in a cost-effective manner, without actually hiring weapons research specialists and running the risk of being spotted, then this'd be a great way to do it.

Now, you might think that we could breed a "special" population of guaranteed "disease-free" oinkers in laboratory conditions, to ensure that any transplant organs are kept squeaky-clean, and to minimise the risk as long as the organ recipients were then kept well away from any live pigs (to protect both the human and pig populations) – some researchers were supposed to be setting up special facilities for breeding "special" pigs, perhaps with a bit of gene-manipulation to make the immune-system rejection problems less severe.

Snag is, it turns out that you can't breed "clean" pigs.
Normally, the DNA in your cell nucleii codes for proteins that get used within the cell, and for RNA that moves out of the cell nucleus to do Very Useful Things in other parts of the cell. DNA also copies itself during cell division. Viruses are often RNA-based, and usually insert themselves into a cell, where they tell the cell to make more RNA-based viruses.
But RNA retroviruses run the cell's usual DNA-RNA mechanism backwards – they write DNA versions of themselves into the cell nucleus ("reverse transcription"), and from that point onwards, the cell's own nucleus generates new viral RNA.
If a retrovirus infects a mammalian egg cell or a sperm-producing cell, and those cells produce viable offspring, then those offspring inherit the virus as part of their genome - it's been written into the DNA of every one of their cells.

Sometimes the inherited virus isn't active, or is corrupted so that it does nothing, or ends up mutating again to do something that's actually useful to the host. If it's active, the individuals who have it will presumably have gene-repression systems and a primed immune system that can deal with it, otherwise they'd not survive long enough to be born. So pigs can carry a payload of porcine viruses in their DNA, and still be perfectly healthy. And they do – it turns out that as farm animals, pigs have been so intensively interbred that it now doesn't seem possible to find a pig that doesn't have a library of piggy viruses already written into their DNA. To encourage those viruses to learn how to infect human cells, all you'd have to do is transplant some living virus-bearing pig tissue into a human, and give that human immunosuppressant drugs to damp their immune system long enough to give the fledgeling viruses a change to get in a good few generations of useful mutation, and – bingo! – you've got yourself a new "alien" human-compatible virus that most human immune systems won't yet recognise.

The xenotransplanation research community were always playing with fire. Getting funding for research that might eventually save thousands or tens of thousands of people's lives (including sick kiddies) is good ... but getting funding for a large-scale xenotransplantation programme that might end up being implicated years later in the deaths of tens of millions would be ... not quite so good. So the ethics watchdogs within the community said that it was important that society as a whole understood the risks and decided consensually to go for xenotransplantation, but when it came to lobbying for funds, the TV news would tend to show pictures of dying children with tubes stuck in them, and impassioned researchers saying that this was necessary to stop people dying ... but forget to mention the risk of a potential associated death toll on the scale of that of World War 2.

So the current swine flu outbreak has probably saved the xenotransplanation community from having to wake up in ten years time and find that their work had been responsible for killin a hell of a lot of people. Their funding bodies probably now know rather more about pig viruses, and will now tend to ask the right questions when someone suggests stitching pig tissue into human recipients. Such as: "But isn't that an insanely irresponsible thing to do?". Since the 2009 outbreak, researchers can no longer pooh-pooh safety concerns by pointing out that nobody on the board has heard of anyone who's actually been hurt by swine flu. Conventional live pig-organ xenotransplanation is probably (hopefully) now a dead field.

Good work can still be done. There are some people now looking at taking pig hearts and dissolving away all the tissue to leave a cartilage skeleton on which human stem cells can be grown, to create a working human-tissue heart. That sounds like a much more sensible idea.

There's just one last question we need to answer. The sites where US researchers were keeping their pigs tended to be secret, to avoid protester sabotage and industrial espionage, and to try to make sure that the pigs were kept free from external contamination of pig or human pathogens. It'd be useful to have a full list of all such sites, to see if any of them had been set up conveniently across the border in Mexico. If there's genuinely not a link between xenotransplantation research and the current swine flu outbreak, then the xenotransplantation community can consider themselves lucky – they dodged a bullet.

Remembering Emil Rupp

In the "impossible diamond" post, when I was talking about the impression given by C20th physicists had that fraud didn't happen in their profession, I forgot about Emil Rupp. Then again, almost everyone tends to forget about Emil Rupp.

Emil Rupp (1898-1979) studied under Nobel-prizewinning experimenter Philipp Lenard, and was considered by some to be one of the most exciting experimenters of his time. He did a series of experiments related to effects like electron diffraction that caught the imaginations of a number of key theoretical physicists, and his work was sometimes credited with being one of the most important influences on the development of quantum mechanics.

Rupp's work was central to some key questions in quantum mechanics. What is reality? is light really a wave or a particle? Is it emitted continuously or instantaneously? Can a state that is said not to exist still influence the outcome of an experiment?

Ironically, it then turned out that Rupp's own experiments, which had been so influential, didn't seem to have existed either. The thing supposedly came to light when some of his colleagues visited the lab where Rupp was working and confronted Rupp – he'd been describing experiments with 500kV electrons, but wasn't in possession of an accelerator that went up to 500kV. He'd been making up his experimental results.

Why did Rupp do it? Well, like Bernie Madhoff, for a while he was getting away with it, and was having a very, very good time. He was identifying problems that the physics community wanted solving, and solving them (albeit with fake experimental writeups). He was an enabler, and people (other than the fellow experimenters that he kept leapfrogging) liked him for it. Great names in theoretical physics would seek him out and cite him. Einstein spent quality time corresponding with Rupp in 1926, working through issues with wave-particle duality, and trying to work out what should happen in certain experiments ... and trying to come up with explanations for how it was that some of Rupp's experiments had come out so well, given some of the difficulties that he should have come up against. The collaboration was reasonably well-known, and people started referring to the "Einstein-Rupp experiments".

When the game was up, Rupp found that he'd now given the physics community a new headache. He'd shown that peer review didn't work as an efficient way of identifying "friendly" fraud within the system. If you had the right background, and you worked out which results people wanted and published those results, your paper tended to pass peer review unless the referees were so convinced that you couldn't possibly have gotten those results that they called you on it. And if an experiment produced the expected result, it was difficult for a referee to insist that an experiment was too successful. Results that don't agree with current thinking can be summarily rejected by peer review on the grounds that getting a "wrong" answer amounts to apparent evidence of error, but rejecting results that give the "right" answer is more awkward.
The lesson seemed to be that if you wanted a career as a scientific fraudster, the way to succeed was to agree with whichever theories were currently in vogue. So the physics community was now facing a potential upheaval – how would they assess how many other key papers by respected researchers might have been unreliable, or even outright fakes?

Rupp solved that problem for them with another piece of documentation. He sent a retraction of his five key papers, along with a letter from his doctor stating that Rupp had been in a "dreamlike" mental state when he'd written them.
It was a tidy conclusion – Rupp exited physics without there having to be a nasty inquiry, the community got to draw a line under the affair, quickly, and thanks to Rupp's explanation, they got to write off the matter not as an extended period of fraud lasting nine or ten years, but as the unfortunate actions of a guy who was having some mental health issues. That let the community off the hook – if Rupp hadn't been completely sane at the time, then we could still tell ourselves that physics was a special "fraud-free" field of science, and that no sane physicist would ever commit fraud. So everything was okay again.

Was Rupp's doctor's letter genuine? We didn't really care. We had the result that we wanted.

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Refs:

• Jeroen van Dongen, "Emil Rupp, Albert Einstein and the canal ray experiments on wave-particle duality: Scientific fraud and theoretical bias",Historical Studies in the Physical and Biological Sciences, 37 Supplement (2007), 73-120 [arXiv:0709.3099v1]
• Jeroen van Dongen, "The interpretation of the Einstein-Rupp experiments and their influence on the history of quantum mechanics", Historical Studies in the Physical and Biological Sciences 37 Supplement (2007) 121-131 [arXiv:0709.3226v1]

Projective Cosmology, and the topological failure of Einstein's General Theory

The graphic above is from my old, defunct, 1990s website, and I also borrowed it for chapter 12 of the book.

It shows a rather fun observerspace projection: if we assume that the universe is (hyper-) spherical, but we colour it in as it's seen to be rather than how we deduce it to be, expansion and Hubble shift result in a description in which things are more redshifted towards the universe's farside. Free-falling objects recede from us faster towards the apparent farside-point, as if they were falling towards some hugely massive object at the opposite end of the universe, and as if there was a corresponding gravitational field centred on the farside. At a certain distance between us and where this (apparent) gravitational field would be expected to go singular, there's a horizon (the cosmological horizon) censoring the extrapolated Big Bang singularity from view, and that looks gravitational, too.

And, funnily, enough, this "warped" worldview turns out to be defensible (as an observer-specific description) using the available optical evidence. Since we reckon that the universe is expanding, and we're seeing older epochs of the universe's history as we look further away, we're seeing those distant objects as they were in the distant past, when the universe was smaller and denser and the background gravitational field-density was greater than it is now.

Our perspective view is showing us an angled slice through space and time that really does include a gravitational gradient – between "there-and-then" and "here-and-now". The apparent gravitational differential is physically real within our observerspace projection, and viewed end-on, the projection describes a globular universe with a great big black hole at the opposite end to wherever the observer happens to be.

This projection is fascinating: it means that we end up describing cosmological-curvature effects with gravitational-curvature language, and it cuts down on the number of separate things that our universe model has to contain. If we take this topological projection seriously, some physics descriptions need to be unified. If we can agree on a single definition of relative velocity, the projection means that cosmological shifts (as a function of cosmological recession velocity) have to follow the same law as gravitational shifts (as a function of gravitational terminal velocity) ... and then, since gravitational shifts can be calculated from their associated terminal velocities as conventional motion shifts, we have have three different effects (cosmological, gravitational and velocity shifts) all demanding to be topologically transformed into one another, and all needing to obey the same laws.

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This all sounds great, and at this point someone who hasn't done advanced gravitational physics will probably be anticipating the punchline – that when we work out what this unified set of laws would have to be, we find that they're the set given by Einstein's special and general theories, QED.

Except that they aren't. We don't believe that cosmological shifts obey the relationship between recession velocity and redshift supplied by special relativity.

We dealt with this by ignoring the offending geometry. Since cosmological horizons had to be leaky, and GR1915 told us (wrongly) that gravitational horizons had to give off zero radiation, we figured that these had to be two physically-irreconcilable cases, and that any approach that unified the two descriptions was therefore misguided. Since a topological re-projection couldn't be "wrong", it had to be "inappropriate". Instead of listening to the geometry and going for unification, we stuck with the current implementation of general relativity, and suspended the usual rules of topology to force a fit.

But then Stephen Hawking used quantum mechanics to argue that gravitational horizons should emit indirect radiation after all, as the projection predicts. So we'd broken geometrical laws (in a geometrical theory!) to protect an unverified physical outcome that turned out to be wrong. Where we should have been able to predict Hawking radiation across a gravitational horizon from simple topological arguments in maybe the 1930's, by using the closed-universe model and topology, we instead stuck with existing theory and had to wait until the 1970's for QM to tap us on the shoulder and point out that statistical mechanics said that we'd screwed up somewhere.

If we look at this projection, and consider the consequences, it suggests that the structure of current general relativity theory, when applied to a closed universe, doesn't give a geometrically consistent theory ... or at least, that the current theory is only "consistent" if we use the condition of internal consistency to demand that any logical or geometrical arguments that would otherwise crash the theory be suspended (making the concept almost worthless).
It basically tells us that current classical theory is a screw-up. And that's why you probably won't see this projection given in a C20th textbook on general relativity.

The Riemann Projection and General Relativity

The Riemann projection is associated with the mathematician Bernhard Riemann (1826-1866), and gives a method of projecting the contents of a finite spherical surface onto an infinite flat plane.

We place the sphere onto the plane, so that its South Pole is touching the surface, and then we draw lines from the North Pole to the plane. After leaving N, each line intersects one (and only one) point on the spherical surface, and one (and only one) point on the spherical plane. Every point on one on one of the two surfaces has its corresponding point on the other. As long as we don't mind making a vanishingly-small pinprick in the spherical surface at its North Pole, the two surfaces are topologically identical … we can take our pin-mark, stretch it to a finite-sized hole, and then stretch the resulting bowl-shaped surface to cover the full infinite plane.

We can also imagine this as a simple optical projection – if the sphere is a hollow transparent surface and we place a lightsource at N, then anything drawn on the sphere will project shadows onto the plane.

Einstein used the projection in his "Geometry and Experience" lecture, as an aid to visualising the idea of a closed finite universe:There's also a nice Riemann Sphere animation on YouTube, courtesy of the American Mathematical Society, and a nice image at Encyclopaedia Britannica.

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Now although we don't usually want to make this sort of projection (unless we're working on something a bit abstract, like Moebius transformations), the "Riemann Sphere" projection was psychologically important for physics, because the thing was fairly easy to visualise, and because it had such far-reaching implications for geometrical physics.

Thanks to the projection, we know that any physics described in sphereland has to have an exact counterpart description in flatland, as long as we scale all our definitions to match. When we lay rulers over the surface of the sphere, rulers near the North Pole have projections onto the plane that tend towards becoming infinitely large, so the plane's surface appears (to its occupants) to be finite, just like the sphere. Similarly, a constant-speed light-pulse travelling around the sphere has a "shadow" on the plane whose speed tends to infinity as the corresponding position on the sphere approaches N . If we take objects and structures whose internal equilibrium is maintained by signals travelling at the speed of light, then as we move these objects away from S, they enlarge. So it takes us the same number of tiles to pave the infinite plane as the sphere. And to the plane's inhabitants, there's no obvious way of telling which tile is the central tile – the internal physics of the plane and sphere are precisely the same.

But the intrinsic geometry of a blank plane, on its own, is not the same as that of a sphere. We need to add something – a density-map. In order to recreate the sphere's properties , we need to either project a helpful scaling grid from the sphere onto the plane to describe how scalings need to vary across the plane's surface, or attach a value to each point on on the plane to describe the local scaling. This "density" parameter varies smoothly over the surface, so we're entitled to describe it as a field. We can then say that it's this density-field that deflects light and matter in the plane towards the region of highest density (S), by Huygens' principle. But as Newton and Einstein both pointed out, a variation in the density of an underlying medium, and the associated variation in the speed of light, can both be considered as expressions of the action of a gravitational field.

As a crude first approximation, we can say that the unscaled plane description includes a gravitational field that doesn't exist in the sphere description – and yet both descriptions are equivalent.

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So ... the implication of the Riemann projection is that gravitational fields aren't absolute. We can take a physical description that works, and stretch and squash our reference-grid in weird and silly ways, and as long as we invent compensating gravitational fields that vary in sympathy with our fictitious distortions (causing space's contents to nominally stretch and squash and distort to fill exactly the same region as before), the final predictions should be identical, regardless of which grid we use.
Within a space defined by that grid, these fields are physically real. And, said Einstein, we could also run the process backwards. We can place an observer in a genuine gravitational field, and allow them freefall acceleration, and for them, that field will no longer exist in their local physics ("a freefalling observer feels no gravity"). If Eötvös' Principle (that everything falls at the same rate in a gravitational field) was right, and gravity affected everything equally, then we had to be able to produce a geometrical description of gravitational effects ... and by allowing space to be warped, we could then eliminate gravitational fields from our description as a separate effect. The background gravitational field was simply space(-time), and what we normally thought of as conventional gravity was simply the result of curvature, and of curvature-related variations in projected density.

In practice, things were a little more difficult than this: Riemann and co couldn't get their curved-space models to work using curvature in just three dimensions, so a geometrical theory of gravity had to wait until Einstein had noticed the argument for gravitational time dilation, and that it led to curvature in four dimensions.
Einstein also decided to use a "frame-based" approach, which led to some simplified geometries being cross-mapped and projected that sometimes didn't correspond to actual physics, or to the shapes that more general principles said ought to be there.

I'll deal with the topological failure of the current default version of the general theory of relativity in a future post (or two). If anyone can't wait, it's in the book.

Physics Fraud, and the Impossible Diamond

Physicists used to tell me was that physics was a special subject, because you never had to worry about the possibility of fraud. Their reasoning was that You Can't Fake Physics. If you make up an experimental result that isn't right, you're doomed to be found out when other people try the same experiment and can't replicate your result. It's a dumb thing to do, and no physicist would ever be stupid enough to try.

However, it might be more accurate to say that perhaps no sane physicist would try to fake a result that they believed to be wrong. Faking a correct result may be cheating, but doesn't carry the same risk. It's much more difficult to spot a fake result when it agrees with everyone else's results and with what everybody expects to happen.

We can sometimes spot a "false positive" when a theoretical prediction that is successfully verified later turns out to be wrong, or when an experimental technique later turns out to be impossible, or impossible to conduct to the claimed accuracy. When this happens in an experiment that contradicts current theory, we usually rip the person responsible to shreds, and accusations start flying of scientific fraud. When it happens in an experiment that agrees with current theory, we're usually more charitable, and tend to say that perhaps the experimenter was simply mistaken, or overcome with a little too much enthusiasm. There's such a large grey area for honest mistakes, or the unconscious selection of "good" data (or simple wishful thinking) that a certain amount of bad science probably slips under the radar without being spotted, and it's not often that we find a "bad" result supporting a "good" outcome that's really so profoundly impossible that people are forced to consider using the "f" word.

One candidate case happened in 1955.
Researchers had been wanting to create artificial diamonds since at least as far back as Nineteenth Century. When H.G. Wells published his short story "The Diamond Maker" in 1894, a number of researchers had already been trying approaches with varying degrees of optimism and claiming positive results, including James Ballantyne Hannay in 1880, and Nobel Prize-winner Henri Moissan (also in 1894). One of the wildest attempts to create artificial diamond was carried out by John Logie Baird, who briefly blacked out of part of Glasgow when he deliberately short-circuited an electricity substation's power terminals across a graphite rod embedded in reinforced concrete (the story goes that he couldn't work out how to get the thing open afterwards, and it ended up at the bottom of a river, unexamined).

The potential financial payoff for anyone able to create artificial diamonds on demand was obvious, and by the 1950's there had been more reported (but often disputed) successes, and competing researchers were trying desperately hard to be the first people to produce a proper, replicable, accepted process that definitely did produce diamonds. One team in particular figured that they were on the edge of actually achieving it. They had the theory right, they had the equipment right ... the only problem was that their pressure-vessel obstinately refused to cough up any diamonds.
It was desperately unfair. They'd done all the work correctly, and the experiment refused to come out the way it was supposed to. They needed a diamond to get further funding. From their perspective, they probably reckoned that they deserved a diamond. It was necessary for their future research. Science needed a diamond!

And a diamond dutifully appeared. They got new funding, bought new equipment and replicated the result, others managed the same thing, and everyone was happy.

Except that ... someone went back and checked the calibration on the original pressure reactor and found that its readings had been significantly "off". The pressure-vessel had been running at too low a pressure for diamond to form. With hindsight, their original artificial diamond seemed to have been a physical impossibility. So how did it get there?

Three of the four original team members put their names to a letter to Nature in 1993, explaining that subsequent spectral analysis of the "run 151" diamond years later had shown that it appeared to have the characteristics of a natural gemstone rather than those of an artificial rock. The experimenters had carried a small stock of natural diamonds for research purposes, and it seemed that one of those had somehow found its way into the pressure vessel during setup, and been "fortuitously" discovered after the experiment.

It's quite a nicely- and elegantly-written letter, but the authors must have been acutely aware that to most people, the idea that one might "accidentally" lose a real diamond inside an apparatus designed to create artificial diamond, in such a way that it could then be rediscovered and used to get further desperately-needed money ... if this happened in any other field, we'd tend to assume deliberate fraud.

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Another thing that might surprise some outsiders is that although the announcement that the experiment had been a success was made in 1955, the retraction didn't happen until 1993, nearly forty years later. For Twentieth-Century experimental physics, this wasn't actually all that unusual – there seemed to be an unspoken "gentlemen's agreement" that if someone had claimed a "correct" result that they shouldn't have, that the community would hold off making too many pointed suggestions in print until some time after the person concerned was safely dead. This was probably a great way of avoiding public controversies, but it also meant that we never really got to the bottom of what had happened in many of these cases. If you weren't supposed to go public while someone was still alive, but you couldn't suggest fraud after they were dead (because it was unfair to level that sort of accusation at someone when they couldn't defend themselves), then it meant that anyone who did get up to no good had a decent chance of not being publicly outed, in print, ever. By the time a critical report could be written, the people with first-hand knowledge of what had really happened might have all died off.

By avoiding investigating these cases until after it was too late to reach a conclusion, the physics community probably did manage to achieve a nominal "no confirmed mainstream fraud" result. But that result was itself not especially honest.

Things are now looking up. Berkeley recently went public very quickly about problems with the work of two physicists (in two separate cases) who seemed to have been almost routinely fabricating data to get their "world-class" results (Victor Ninov and Jan Hendrik Schön), and there've now been a few more speedy "outings" of scientists caught misbehaving. So from now onwards, the more temptation-prone members of the physics community know that if they gain fame and fortune by faking data, universities and comissioning bodies won't necessarily hush the thing up for them.

But for research published before 2000 (or perhaps before ~2005) ... be more careful. A certain number of the "jewels" in physics history aren't quite what they appear to be.

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• "Errors in Diamond Synthesis", Nature 365 2nd Sept 1993, p.19

Fibonacci Series Tiling, with Triangles

With the conventional Fibonacci Series, there are two standard ways of constructing the series with interlocking squares.

In the version on the left, we put two squares side by side, add another square to the longest side, and repeat, darting from left to right as we decide where to put the next square. In the version on the right, we constantly circle the block to find the next addition site, and end up with a spiral pattern.

You might think that these are the only two flat tiling solutions, but there's also a third version, which uses equilateral triangles to form a double-spiral:



Finally, here's a "quad-spiral" version of the tiled squares.

Einstein (1950) - Special Relativity is Not Fundamental

Albert Einstein, 1950 (Scientific American):

"[re: the general principle of relativity] ... without this ... it would be practically impossible for anybody to hit on the gravitational equations, not even by using the principle of special relativity ...

... This is why all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning. This situation makes it difficult for us to use our empirical knowledge, however comprehensive, in looking for the fundamental concepts and relations of physics, and it forces us to apply free speculation to a much greater extent than is presently assumed by most physicists.

I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: what would physics look like without gravitation? "

Some people really don't like the implications of what Einstein seemed to be saying here about his own theories. Some online physics people in the past have insisted that Einstein couldn't possibly have said such a thing, but I've checked paperback reprints and the original 1950 SciAm publication and there it is, in black and white. That's what he said.

Einstein's point is entirely logical, and supported by the historical record. If we look at the background to the development of relativity theory, notably the Newtonian Catastrophe, we find that the version of general relativity that we ended up with, with special relativity providing an underlying flat-spacetime layer, was not just not inevitable, it actually seemed to depend on a rather unlikely-looking chain of historical accidents. Probablistically, it really shouldn't have happened like this.
We should have understood that gravity slowed time a century before Einstein eventually noticed, shortly after John Michell had predicted gravitational shifts way back in 1783. With the benefit of that missing piece of information, Gauss and Riemann and Clifford and friends ought to have been able to complete their curved-space projects (allowing curvature in four dimensions rather than just three) and should have been able to produce a general theory of relativity in the Nineteenth Century, before special relativity had been thought of. Einstein's special theory was partly a reaction against the aether models that dominated in the absence of a proper curvature-based description, and when Einstein went on to try derive his more ambitious general theory a few years later, he naturally wanted it to incorporate his earlier theory.

But special relativity assumed inertia without gravity, and energy-concentration without curvature. Its founding geometrical principles are fundamentally incompatible with key results that arise from the general principle of relativity. Like Einstein said, historically understandable, but not objectively justifiable with the benefit of hindsight.

Training a Brick Wall

After writing the last (rather hand-wavy) post on the idea of using fields to grow exotic conductor structures, I found a paper on someone doing this sort of thing for real, using silver nanowires:

• "A technique for controlling the alignment of silver nanowires with an electric field"
  Yang Cao et al 2006 Nanotechnology 17 2378-2380 doi: 10.1088/0957-4484/17/9/050
  

There's also an article (and a larger version of the above image) at www.physorg.com

• "Electric field can align silver nanowires"
  PhysOrg.com May 17th, 2006

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Brick walls can learn

Another (slightly random) example of materials "memorising" and recreating the effect of an applied potential is what happens to an external house-wall when your guttering is leaky.

Suppose that rainwater runs down the outside of your house and creates a bit of a damp patch on the inside wall. If the patch is bad, it's tempting to try to dry this out quickly from the inside by training a blow heater on the offending splodge. You evaporate the water at the surface, more water moves in from within the wall to take its place by capillary action, and you hope that at some point, the process will stop. You hope that you'll dry out the surface deeply enough that the rest of the water will stay put, somewhere deep within the wall, and perhaps dissipate. Some of it might work its way to the inside surface over a larger area and evaporate slowly and less intrusively, and some of it might eventually find its way back to the outside, the same way it got in. You hope.

But damp spots on walls are pesky creatures ... if you remove the surface water from one place too "aggressively", you're encouraging moisture directly below that section of surface to seep in to take its place faster than the usual seepage rate. In the worst-case scenario, instead of water slowly spreading through the wall in all directions, you're creating a faster directional flow within the wall, with water from a wider region of brickwork and plaster all converging on the extraction point where your heater is trained ... and as it moves, it dissolves salts and minerals from the wall and deposits them where the water is being driven off. If you see a crusty surface deposit forming, you're in trouble – it means that all that material has been dissolved out of the wall, possibly from around the points of greatest proportional resistance to the directional flow that you've created. You've etched a series of tiny micro-channels into the wall that converge on your extraction point, as a microscopic three-dimensional counterpart of how rivers carve channels into their landscape.
There might also be a concentration of those salts and minerals within the wall, towards the extraction point. If that happens, then the water-loving salts have created an absorbency gradient within the wall that represents the original flow, and once that piece of wall has dried out, if the dried region butts up against a damper region, the more "salty" part of the wall will draw water into it preferentially. The water will continue moving preferentially towards the most absorbent neighbouring region, following the original gradient ... straight back to your dried-out patch. So what you've done is (1) optimised the wall microstructure to collect water from a large area and direct it towards your extraction point, and (2) created an absorbency gradient in the wall to attract and hold the moisture and recreate the original damp patch. You've trained the wall to take water from the outside and carry it to the exact point on the inside where you didn't want it!

Materials that Learn

Suppose that we have a suspension of long electrically-conductive particles (such as metal filings or buckytubes) suspended in an insulating liquid resin. If we then try to force the liquid to conduct electricity in a particular direction, the particles will tend to self-organise to make that outcome achievable more efficiently.

A physicist will say that what actually happens is that when we apply a high voltage across the material in an attempt to force it to conduct, the particles become charge-polarised, and line up "lengthwise" in the electric field ... then the oppositely-charged "heads" and "tails" of adjacent particles tend to link up, and pretty soon you have lines of conducting threads running through the material linking the two electrical contact points. If your insulating resin's electrical resistance breaks down over small distances (above a given threshold voltage between a pair of particles), and if the sides of your particles can be persuaded to repel each other, to prevent the formation of additional conductive paths at right angles to your applied voltage, then, if you allow the resin to set, you should have a new type of material whose electrical conductivity depends on direction.

In itself, this doesn't sound particularly interesting: after all, we can already produce a solid directionally-conducting block by mechanically glueing or fusing a stack of insulated wires together and then machining the block to the desired shape. The advantage of using self-organising materials is that we can use them to build conduction patterns into films or coatings, or to build more exotic structures into solid blocks. You might want to tailor the electrical response of the paint on an aircraft or satellite to produce certain effects when it's hit by an incoming EM wave (say, to deflect radar or focus an incoming signal), or you might want to produce solid waveguides or field guides for electrical engineering, without laboriously building them from layers of laminated conductors, or winding them as coils.

The idea of self-organising materials isn't new. We use the idea dynamically with liquid crystal displays, and we've recently spent a lot of R&D money coming up with a "freezable" counterpart to LCDs, "electronic paper" (as used in the Amazon Kindle). But the idea of being able to "print" field structures into or onto materials, in a way that automatically self-corrects for any structural defects or variations in the material, is rather interesting. You could use superconducting grains to build exotic superconducting structures in two or three dimensions, or you could use a resin that's conductive when liquid, and freeze it from one end while the applied field is varied, to grow field structures that would be impossible to achieve by other means. You could even try coupling the process with 3D printer technology to produce independent conduction-alignment of each point within a structure to produce extremely ornate conductor structures. Then we have the interesting idea of field holography: if we create a complex external field around a device, and "freeze" the critical regions into superconducting blocks, then when those blocks are milled and reassembled, will Nature tend to recreate the original field by "joining the dots" between the separated blocks? What if we have a containment field with complex external field junctions that tend to destabilise under load – if we could freeze that field junction topology into a set of surrounding superconducting blocks, would they tend to stabilise the field?

We might be able to use expensive hardware to set up, say, a toroidal containment field, place a container of "smart resin" in the field, and "freeze" the external EM image of the device into the external block. If this was a useful component to have, we'd have a method of mass-producing them for use as as field guides or field stabilising devices.
With a number of interconnected connected and energised surrounding blocks, and the original device removed and replaced with a container of "smart resin", you might also be able to use the process in reverse, to recreate a rough electromagnetic approximation of the internal structure of the original device (crudely analogous to the old stereotype process originally used by printers to preserve and recreate the shape of blocks of moveable type).

Admittedly most of the potential applications for this sort of process don't exist yet. We're not mass-producing cage-confinement fusion reactors, and the LHC's magnets don't need miniaturisation. Fusion-powered vehicles are still some way off. But it's nice to know that there are still some fabrication tricks that we might be able to use that don't require laborious hand-tooling and impossible levels of molecular-level precision.

Jitter

Jitter is a fascinating concept, with applications in digital imagery and quantum mechanics. The word is a corruption of the scotticism "chitter", which is an omomatopoeic rendering of the noise that your teeth make when you shiver (another offshoot is "chatter"). So jittering is a jerky jumping between positions that surround a central averaged point, and "having the jitters" means being nervously jumpy, or having the shakes for some other reason (e.g. drug or alcohol withdrawal, see also the origins of the word jitterbug). In digital measuring systems, it's the tendency for background noise to make measurements jump about between adjacent states when the real signal value is close to a quantisation threshold.

At first sight, jitter looks like an engineering annoyance. If you feed a slowly-changing analogue signal into a digitiser you might expect the correct result to be a "simple" stepped waveform, but if the signal is noisy, and the signal level happens to be near a digital crossing-point, then that noise can make the output "jitter" back and forth between the two nearest states. A small amount of noise well below the quantisation threshold can be amplified and generate 1-bit noise on the digital data stream, as the output "jitters" between the two closest states.

So early audio engineers would try to filter this sort of noise out of the signal before quantisation. However, they later realised that the effect was useful, and that the jittering actually carried valuable additional information. If you had an digitiser that could only output a stream of eight-bit numbers, and you needed that stream to run at a certain rate, you could run the hardware at a multiple of the required rate, and deliberately inject low-level, high-frequency noise into the signal, causing the lowest bit to dance around at the higher clockrate. If the original signal level lay exactly between two digital levels, the random jitter would tend to make the output jump between those two levels with a ratio of about ~50:50. If the signal voltage was slightly higher, then additional system noise would tend to make the sampling process flip to the "higher" state more often than the "lower state. If the original input signal was lower than the 50:50 mark, the noise wouldn't reach the higher threshold quite so often, and the "jittered" datastream would have more low bits than high bits. So the ratio between "high" and "low" bit-noise told us approximately where the original signal level lay, with sub-bit accuracy.

This generated the apparently paradoxical result that we could make more accurate measurements by adding random noise to the signal that we wanted to measure! Although each individual sample would tend to be less reliable than it would have been if the noise source wasn't there, when a group of adjacent samples were averaged together, they'd conspire to recreate a statistical approximation of the original signal voltage, at a higher resolution than the physical bit-resolution of the sampling device. All you had to do was to run the sampling process at a higher rate than you actually wanted, then smooth the data to create a datastream at the right frequency, and the averaging process would give you extra digits of resolution after the "point".
So if you sampled a "jittery" DC signal, and measured "9, 10, 9, 10, 10, 9, 10, 10", then your averaged value for the eight samples would be 9.625, and you'd evaluate the original signal to have had a value of somewhere just over nine-and-a-half.

Jitter allowed us to squeeze more data through a given quantised information gateway by using spare bandwidth, and passing the additional information as statistical trends carried on the back of an overlaid noise signal. It was transferring the additional resolution information through the gateway by shunting it out of the "resolution" domain and into a statistical domain. You didn't have to use random noise to "tickle" the sampling hardware – with more sophisticated electronics you could use a high-frequency rampwave signal to make the process a little more orderly - but noise worked, too.

So jitter lets us make measurements that at first sight appear to break the laws of physics. No laws are really being broken (because we aren't exceeding the total information bandwidth of the gateway), but there are some useful similarities here with parts of quantum mechanics – we're dealing with a counterintuitive effect, where apparently random and unpredictable individual events and fluctuations in our measurements somehow manage to combine to recreate a more classical-looking signal at larger scales. Even with a theoretically-random noise source with a polite statistical distribution tickling the detector thresholds, the resulting noise in the digitised signal still manages to carry statistical correlations that carry real and useful information about what's happening under the quantisation threshold.

Once you know a little bit about digital audio processing tricks, some of the supposedly "spooky" aspects of quantum mechanics start to look a little more familiar.

General Relativity and Nonlinearity

One of the difficulties set up by the structure of Einstein's general theory of relativity is the tension between GR's requirement that there be no prior geometry, and the assumption that the geometry must necessarily reduce to the flat fixed geometry of special relativity's Minkowski metric as a limiting case over small regions.

Although it's not news that GR shouldn't presume a prior geometry (GR's fields are not superimposed on a background metric, they define the metric), this is one of those irritating principles that's easier to agree with in principle than it is to actually implement.
It's only human nature when attacking a problem to want to start off with some sort of fixed point or known property that everything else can be defined in relation to. It's like starting a jigsaw by identifying the four corner pieces first. We tend to start off by imagining the shape of the environment and then imagining placing a test object within it ... but the act of placing an observer itself modifies the shape and characteristics of the metric, and means that the signals that the observer intercepts might have different characteristics to those that we might otherwise expect to have passed though the particle's track, if the particle hadn't actually been there, or if it had been moving differently. Although the basic concept of a perfect "test particle" isn't especially valid under relativity theory, we like to assume that the shape of spacetime is largely fixed by large background masses, and that the tiny contribution of our observer-particle won't change things all that much (we like to assume that our solutions are insensitive to small linear "perturbations" of the background field).

Unfortunately, this assumption isn't always valid. Even though the distortion caused by adding (say) a single atom with a particular state of motion to a solar system may well be vanishingly small, and limited to a vanishingly-tiny region of spacetime compared to the larger region being looked at, every observation that the atom and solar system make of each other will be based on the properties of exchanged signals that all have to pass through that teensy-weensy distorted region. So if we build a theory on mutual observation and the principle of relativity, even a particle-distortion or gravitomagnetic distortion that's only significant in over a vanishingly small speck of spacetime surrounding the atom still has the potential to dramatically change what the atom sees, and how outsiders see the atom. It changes the properties of how they interact, and by doing that, it also changes the characteristics of the physics. Although a star isn't going to care much whether an individual distant atom makes a tiny distortion in spacetime or not, our decision as to whether to model that distortion or not can change the functional characteristics of our theory, and change the way that we end up modelling the star, and some of the predictions that we make for it. It also has the potential to wreck the validity of the frame-based approach that people often use with general relativity – if we take nonlinearity seriously, we should probably be talking about the relativity of object views, rather than the relativity of "frames".

Field components aren't always guaranteed to combine linearly, they can twist and impact and writhe around each other in fascinating ways, and generate new classes of effect that didn't exist in any of the individual components. For instance, if we take a bowling ball and a trampoline, and place the ball on the trampoline, their combined height is less than the sum of the two individual heights, and the trampoline geometry has some new properties that aren't compatible with its original Euclidean surface. The surface distorts and the rules change. [Ball+ Trampoline] <> [Ball] + [Trampoline].
Or, place a single bowling ball on an infinite trampoline surface and it settles down and then stays put. But place two bowling balls on the surface, reasonably near to each other, and the elastic surface will push them towards each other in an attempt to minimise its stresses and surface area, producing relative motion. A one-ball model is static, a two-ball model is dynamic, so the rules just changed again.
The result of assuming a background field and simply overlaying particles isn't guaranteed to be the same as a more realistic model in which the particles are intrinsically part of the background field. Nonlinear behaviour generates effects that often can't be generated by simple overlay superimpositions.

Einstein's special theory of relativity rejects the idea of any such interaction between a particle and its surrounding spacetime, so this class of nonlinear effect is incompatible at the particle level with our current general theory of relativity (which is engineered to reduce to SR). While we understand that perhaps a fully integrated model of physics can't be broken up into self-consistent self-contained pieces that can be modelled individually and then assembled into a whole, we try it anyway, because it's easier to tackle smaller bite-size theories than to try to create the full Theory of Everything from scratch. And when we work on these isolated theories, and try to make them internally consistent without taking into account external factors, we end up with a series of theoretical building blocks built on different principles that don't fit together properly.

For Einstein's general theory of relativity, we say that the theory must reduce to the flat-spacetime physics of special relativity over small regions, which makes the theory pretty much incompatible with attempts to model particle-particle interactions as curvature effects. But if what we understand as "physics" is the result of particle-observers communicating through an intermediate medium, and the geometrical properties of those particles on the metric is an intrinsic part of how they interact – if physics is about nonlinear interactions between geometrical features – then by committing to special relativity as a full subset of GR, we might have guaranteed that our general theory can never describe the problem correctly, because any solution with a chance of being right will be ruled out for being in conflict with special relativity. Since deep nonlinearity (which GR1915 doesn't have) seems to be the key to reproducing QM behaviour in a classically-based model, it's not surprising that serious attempts to try to find a way to combine GR and QM have tended to run into the nonlinearity issue:

Albert Einstein, 1954

at the present time the opinion prevails that a field theory must first, by "quantization", be transformed into a statistical theory of field probabilities ... I see in this method only an attempt to describe relationships of an essentially nonlinear character by linear methods.

Roger Penrose, 1976, quoted by Ashtekar:

... if we remove life from Einstein's beautiful theory by steam-rollering it first to flatness and linearity, then we shall learn nothing from attempting to wave the magic wand of quantum theory over the resulting corpse.

Some GR researchers did try to move general relativity beyond a reliance on a fixed initial geometry and dimensionality (see John Wheeler's work on pregeometry), but the QM guys were better at analysing where their "perturbative" and "nonperturbative" approaches differed than the GR guys were at identifying the artefacts that special relativity might have introduced into their model.

In order to work out what parts of current GR might be artefacts of our approach, it's helpful to look at non-SR solutions to the general principle of relativity, and compare the results with those of the usual SR-based version.
The two approaches give two different sorts of metric. If we embrace nonlinearity, we get a relativistic acoustic metric and a general theory that supports Hawking radiation, classically. The second approach (where we start by assuming that a particle's own distortion is negligible and doesn't play a role in what the particle sees) gives us standard classical theory, Minkowski spacetime, the current version of general relativity, and a deep incompatibility with Hawking radiation and quantum mechanics.

So I'd suggest that perhaps we shouldn't be trying to reconcile "current GR" with quantum theory ... we should instead be trying to replace our current crippled version of general relativity with something more serious, that didn't rely on that additional SR layer. There seem to have been two different routes available to us to construct a general theory of relativity, and it's possible that we might have chosen the wrong one.

The Principle of Relativity

The principle of relativity is pretty straightforward: it's essentially that "nothing is nailed down" The locations and properties of our universe's contents are defined by their relationships to other things in the same universe: there is no absolute sheet of "universal graph-paper" that's overlaid on the universe from outside that defines where everything "really" is, and which dictates the laws of physics in some occult manner.

If we think about the problem logically, we find that there's another aspect to the idea: if there were such a sheet of universal graphpaper, and that sheet did force physics to operate in such a way that we could identify an objects absolute motion relative to it, then that hypothetical sheet of graphpaper would (in a sense) have to exist within our universe, and the motion of bodies could once again be described using the principle of relativity, by treating our absolute frame as another (rather special) physical "thing". But it's perhaps slightly perverse to decide that the universe exactly one of these special things, with nothing else like it, so Occam's Razor pretty much demands that we reject the idea of a single absolute reference frame, unless there's compelling supporting evidence for it.

A more serious problem with the idea of an absolute, inviolable aetheric medium is that such a thing would appear to break some basic principles concerning cause and effect. Normally we assume that when a thing acts, it knows that it's acted ... that is, that there is a back-reaction for every reaction. We assume that if Object A exerts power over Object B, that A's ability to influence is somehow reduced, or at least altered in some way. There is no “something from nothing”, no expenditure of influence without a corresponding lessening of the bank account, and no free lunch. If A's ability to affect B was absolute and without consequence for A, then we could say that A's stock of influence appeared to be infinitely large. And if we are talking about an identifiable physical and quantifiable influence, it leads to some nasty mathematical results if we say that anything has an infinite quantity of a real physical thing. A further problem with these infinities is that they break accounting rules and the chain of causality. When asked where this influence comes from, we can't reverse the sequence of events and extrapolate any further back than the dictatorial rulings of our infinitely-strong metric, which then acts as a limit for any further logical analysis. It becomes a prior cause, a thing that can't be politely incorporated into a larger, fluid, mutually self-contained logical structure, but has its own separate anchor-point that doesnt relate to anthing else inside the structure, and allows it to dictate terms to everything else without retribution.

This sort of “absolute aether” is a way of saying that things simply happen in a certain way because they do, with no further analysis possible, and from a theoretical-analytical point of view, it's a dead end.

It was partly Einstein's appreciation of this problem that led him to the conviction that spacetime itself had to be a stressable, flexible, malleable thing. The “medium” of Einstein's general theory was the background gravitational field (which also defined distances and times), but the assumed properties of this field were no longer absolute, but were affected by the properties of the physics that played out within it. Spacetime was an interactive, integrated part of physics. The “fabric of spacetime” deformed gravitomagnetically as objects passed through it, and spacetime itself was the medium by which masses communicated with and connected causally to other masses. There was an interplay between the properties of spacetime and the properties of matter and energy – as John Wheeler put it, “Matter tells space how to bend, space tells matter how to move”.

The more static, "fixed" spacetime of special relativity, Einstein later decided, was a somewhat distasteful creature. Certainly special relativity had done away with the idea of there being any absolute reference for location, and even for absolute independent values of distance and time, but the overall spacetime structure still had an “absolute” quality to it, in that the geometry of Minkowski spacetime was meant to control and define inertial physics, without its own properties being in any way affected (a slightly abstract version of "action without reaction"). Minkowski spacetime was still "absolute" in the geometrical sense.

To quote Einstein ("The Meaning of Relativity", Princeton University Press):

... from the standpoint of the special theory of relativity we must say, continuum spatii et temporis est absolutum. In this latter statement absolutum means not only "physically real", but also "independent in its physical properties, having a physical effect, but not itself influenced by physical conditions".
...

It is contrary to the mode of thinking in science to conceive of a thing (the space-time continuum) which acts itself, but which cannot be acted upon. This is the reason why E. Mach was led to make the attempt to eliminate space as an active cause in the system of mechanics. According to him, a material particle does not move in unaccelerated motion relatively to space, but relatively to the centre of all the other masses in the universe; in this way the series of causes of mechanical phenomena was closed, in contrast to the mechanics of Newton and Galileo. In order to develop this idea within the limits of the modern theory of action through a medium, the properties of the space-time continuum which determine inertia must be regarded as field properties of space, analogous to the electromagnetic field.
...
... the gravitational field influences and even determines the metrical laws of the space-time continuum."

Because the word "relativity" is often equated with the predictions of specific theoretical implementations of the principle, it comes with a certain amount of historical baggage that isn't always useful when one wants to discuss a problem more generally. Sometimes it's more convenient to start from scratch and use a different form of words when trying to explain a relativistic principle without getting bogged down in historical implementational specifics. John Wheeler used the term "democratic principle" to refer to the idea that there's no single overriding cause that determines the forces on a particle, and another way of describing it might be to refer to the principle of mutuality, in that everything in the universe might be expected to not only have a vote in influencing anything that happens (subject to signal-propagation times), but also to be influenced itself in return.

So really, the principle of relativity in its broadest sense is just about going back to classical first principles: there's no action without origin and/or consequences, causality is A Good Idea, and nothing happens for no reason. These are somewhat pragmatic assumptions if we want to analyse the pattern of rules that the universe obeys – the first step is to assume that there IS a pattern.

There are, of course, more specific definitions of what the principle of relativity "says", which are tailored to the contexts of specific theories (usually Einstein's special and general theories). But we aren't obliged to use those existing definitions, and if we want a chance of discovering broader and deeper theories, we probably shouldn't.

All Physics as Curvature?

William Kingdon Clifford (1845-1879) was an Nineteenth Century mathematician and geometer commemorated by modern mathematicians by having Clifford algebra named after him. He was also a fellow of the Royal Society and The Metaphysical Society, wrote a children's book, and made the occasional cutting remark about the inadvisability of trusting the opinions of groups of experts (unless one knew for a fact that at least one of the group had personal first-hand knowledge of the thing that they were talking about).

Amongst relativists, Clifford is remembered as having been one of the first people to come out unambiguously in favour of the idea that physics could (and should) be modelled as a problem involving curved space.

In 1870, Clifford addressed the Cambridge Philosophical Society ("On the Space-theory of Matter" *), declaring:

"...
I hold in fact,

1. That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them.
2. That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave.
3. That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial.
4. That in the physical world nothing else takes place but this variation subject (possibly) to the law of continuity.
   

... "

In other words, according to Clifford, matter was simply a persistent local curvature in space. While some other well-known theorists of the time (such as Oliver Lodge) were were interested in the idea of describing matter as a sort of condensation of a presumed aetherial medium, and using ideas from fluid dynamics as a shorthand for the properties of space, Clifford considered the mathematical curvature-based descriptions as more than just a means of expressing the variation in field-effect properties associated with density-variations and distortions of an underlying medium: for Clifford, the physics was simply the geometrical curvature itself.

Clifford was one of a number of C19th mathematicians working on geometrical descriptions of physics considered as a curved-space problem, a loose association of broadly similar-minded researchers whose presentations were sometimes propagated in lectures rather than in published journal papers (and who were memorably referred to by James Clerk Maxwell as the "space-crumplers".

Clifford's view was influential, but his vision arguably wasn't quite implemented by Einstein's general theory of relativity – although GR1915 implemented curvature-based descriptions of gravitation, rotation and acceleration effects, it still fell back on an underlying flat-spacetime layer when it came to describing inertial mechanics (that layer being special relativity).

This seems to be fixable, but we're not there yet.

* "William Kingdon Clifford, Mathematical Papers", (1882) pp.21-22

Cyclamate Sweeteners Shrivel Your Testicles

Sometimes I notice details that don't quite seem to connect, and it bugs the hell out of me until I eventually find out why.

Some years back, I saw an episode of a detective show (perhaps "Columbo"?), whose resolution hinged on the idea that there was a particular artificial sweetener used in soft drinks in the 1960's that then got withdrawn. That was a bit before my time, but it puzzled me that the writers seemed to assume that the viewer knew about this, but somehow I hadn't heard of it. So I thought I'd look the thing up to see if it was true.
Apparently it was – according to the literature, cyclamate sweeteners appeared in mainstream products before being banned by the FDA in 1969. But a substance doesn't just get banned from food production without kicking up a bit of media discussion, and I was arrogant enough to figure that if I hadn't come across any such discussion then ... there was probably more to this subject than met the eye. My antennae started twitching. Something smelled wrong.

So I looked deeper. The listed reason why cyclamates were withdrawn, according to the first wave of usual sources, was a possible "slightly elevated cancer risk". Again, this didn't smell right – I'd heard a lot over the years about the similar alleged (small, supposed) risk of bladder cancer associated with saccharine, which wasn't banned in most countries, so where had the corresponding discussion about cyclamates gone? There was an cultural anomaly here – the public discussions that ought to have happened seemed to be missing, and I now badly wanted to find out why.

This was long before the days of Google, so in about 1990 I found myself at an outpost of the British Library, crouched over an old green-screen text terminal that had basic online subscription access to a medical research database, and there I found the obvious answer to why industry people didn't discuss cyclamate side-effects. A distinctive three-word medical term, that once heard and explained, you don't tend to forget.

Cyclamates are associated with ITA.

ITA stands for Irreversable Testicular Atrophy.

=:0

Yes, you read that correctly. It seems that if you're a primate, and male, cyclamate sweeteners can cause your balls to progressively shrivel and wither away. Permanently. Researchers don't know why.

So that was it. That was why nobody told the public what they'd discovered, and why the product was taken off the market, using the iffy "cancer" argument as an excuse. It wasn't in the interests of the drinks companies to mention that they'd probably been chemically castrating some of the guys who drank their cola, it wasn't in the interests of the FDA to admit that they'd approved a substance for mainstream use that had been permanently shrivelling the Male American Public's manly bits. It probably also wasn't in the interests of the research community to go around telling outsiders about their part in a major public health boo-boo that many of those outsiders would find difficult to forgive, if they knew about it. But if you bypassed the commentaries and looked up the original research papers, there it was, in stark black-and-white. ITA.

Cyclamate Returns

The story's moved on since then. Some companies really liked using cyclamate as an ingredient – it was cheap, people preferred the taste to saccharine, and it avoided the later nasty public-relations mess associated with Nutrasweet and product safety. And the biochemical/food industry did some digging of their own, and realised that actually, organisations like the FDA might not be allowed to ban cyclamates.

See, the FDA's remit is public health, and the industry lobbyists started arguing that that having permanently shrunken testicles doesn't actually count as a health problem (no matter how angry the owners of those testicles might be if they found out why). It isn't traditionally associated with work disability (unless you're a porn star), and there's no obvious associated reduction in life expectancy, unless you start to guess at factors like depression and impotence-related suicides.

A product that damages the testicles of male customers doesn't obviously kill anybody. In fact (the industry argued), the associated reduction in testosterone in guys with withered testes might even be associated with a statistical reduction in the frequency of certain testosterone-related cancer deaths (for instance, high testosterone is supposed to exacerbate prostate cancer). Since castrati were generally reckoned to have a greater life expectancy than "intact" blokes, there was an argument that the use of their sweetener product might actually extend average male lifespans rather than reduce them. So (the industry argued) not only were the FDA not allowed to use the ITA argument as a reason for banning the product, they couldn't use the weaker "bladder cancer" argument either, unless they could show that the hypothetical life-expectancy reduction due to increased incidence of bladder cancer was expected to be greater than the corresponding LE extension due to reduced male hormone levels. Cyclamates probably weren't "harmful" if you judged "harmfulness" by a number based on medical life expectancy.
A further argument was that if the potential sexual-function-impairment aspects of cyclamates were outside the FDA's remit, then the FDA was not supposed to tell anyone about them in their reports, because it wasn't the job of a government department to use state funding to "bad-mouth" a product by mentioning negative aspects of that product that weren't anything to do with them. The FDA were supposed to shut up.

So now cyclamates are finding their way back into food, and for a few years now, industry groups have been more bullish about lobbying for the FDA ban to be removed. As a page on the National Cancer Institute website delicately puts it:

" A food additive petition is currently filed with FDA for the reapproval of cyclamate. The FDA's concerns about cyclamate are not cancer related. "

---==--

One last point: if you're reading this and feeling smug because you're female ... well, don't.
See, we don't yet know the mechanism by which cyclamates appear to damage and kill off seminal frond tissue, and it may well be that cyclamates might be doing do something similar to the female reproductive system, unnoticed. Atrophied ovarian tissue is going to be more difficult to spot in the lab than atrophied testicles, simply because its not as easy to do a "before and after" weighing comparison with internal organs. We also don't know whether cyclamate's attack on the germ cells might be associated with heritable genetic or epigenetic damage to the reproductive cells that survive. If your guy's taking cyclamate sweeteners, is it damaging his sperm, and affecting any kids that you might have with him, from that sperm? And what happens if you're pregnant with a male child while ingesting a lot of cyclamate? Does the reproductive-tissue-shrinkage effect in adult males have a counterpart that affects the growth and development of that tissue in the fetus?

There are some genuinely nasty possibilities here.

Moviemaking

One of my mates is a filmmaker, and currently has one of his short films ("The Cost of Living") featured on the BBC Film Network site.
[Sept 09 update: it's now also on MiShorts]

When they made it, I came down for a few days (along with a bunch of other people) to watch the filming and help out. They basically took a two-storey flat and remodelled some of the insides for the shoot. The flat had full-height sliding windows along one wall, which were blocked off with some arty alcoved false walls, and upstairs provided a perfect vantage point for setting up the lighting and sound.

It's quite impressive to watch something like this happening. It's like a military operation, they go in, remodel, redecorate, install all the gear (including those great big trolley things on rails for doing tracking shots), shoot everything, then disassemble and make good, and go home.

The tv screens in the film were my LCD computer monitors that I loaned them, disassembled and fitted with new temporary surrounds by the production designer, Fabrice Spelta ... although they obviously aren't recognisable on-film. Fabrice also designed and installed the arty interior remodelling, which I thought (in conjunction with the lighting) gave the final film a really wierd surreal feel, a bit like Andrei Tarkovski's "Solaris". When those curved interior features line up right, they conspire to produce an "eye" shape, which fits in well with the film's creepy theme of subliminal messaging and constant monitoring. Natasha Collymore did the animated "shopping site" screen graphics.

Albert Einstein, Tea, and the Wall of Death

You may have noticed that when you stir a mug of tea, the tea leaves at the bottom congregate in the middle.

This is potentially disturbing behaviour – see, when you stir the tea, centrifugal forces throw the tea and the tea leaves against the outer wall of the mug, as if there's an outward-pointing gravitational field (the "wall of death" effect) [*]. If the tea leaves were denser than the tea, we'd expect them to be thrown harder and to "sink outwards" and collect at the outer wall, while if the the leaves were lighter than the tea, we'd expect them to be floating around at the top of the mug, rather than sitting at the bottom. So our two main options for where the tea leaves ought to end up, based on density, seem to be either "bottom of mug, around the edge", or "top of mug". In real life, the tea leaves decide to do something else.

So what gives?

Albert Einstein published the answer in a paper entitled "The cause of the formation of meanders in the courses of rivers and of the so-called Baer's Law" in 1926, which was published in Die Naturwissenschaften, complete with a diagram of a cross-section of a cup of tea.

What's happening here (said Einstein) is that the tea leaves are sinking because they are denser than the surrounding tea, but they're also being swept to the centre of the mug by a vortex circulation pattern.
The stirred tea doesn't just rotate within the mug as a simple solid cylinder. There's frictional dragging associated with the sides of the mug, and with the bottom of the mug. The side-wall dragging effect is almost the same at all heights in the tea [**], but the base-dragging effect means that as the stirred tea slows through friction with the mug, the tea at the bottom has always lost a little more speed, because of the additional source of friction. It's always rotating a little more slowly than the rest of the tea. So the centrifugal forces in the "slower" layer of tea at the bottom of the mug push outwards less strongly than those in the faster-rotating tea at the top, and as a result, the tea at the top of the mug "wins the battle" and pushes the tea at the bottom of the mug back on itself, inwards to the centre.

So the rotational speed differential induces a vortex circulation pattern in the tea. The rotating tea at the top surface moves outwards to the edge of the mug, and then crawls down the side-walls in a spiral until it reaches the bottom. Then it moves inwards towards the centre, and finally forms a rising column of tea in the centre of the mug until it returns to its starting point, and does the whole thing all over again (since the average rotation speed has slowed even more since the last circulation cycle).

The current is usually powerful enough to scrape the tea leaves inwards towards the centre of the mug, but its usually not quite strong enough to lift them back up to the surface, so the leaves tend to collect as a little curve-sided cone-shaped pile in the centre. Which you can see if you have a glass mug, and don't add milk.

Tea, Einstein, vortex. Problem solved.

---==---

* If we're doing this as a Newtonian calculation we say that the tea is riding up the sides of the mug because it's attempting to move in a straight line and is being thwarted by the crockery wall, whereas if we apply Mach's Principle, and/or the general principle of relativity, it's equally legitimate to say that the tea itself isn't rotating, but the outside universe rotating around it creates a special sort of radial gravitational field that draws the tea outwards from the rotation axis. In the first calculation the tea pushes outwards against the walls because of its inertial mass, in the second the outward effect is gravitational, and the tea is drawn outward by the effect of its gravitational mass. So under a general theory of relativity, the inertial and gravitational masses of a body can't be separated, because the inertial and gravitational descriptions are interchangeable.

** Okay, so the side-wall dragging effect is different at different heights too, because the base-dragging effect gives the tea different rotational velocities at different heights. This often happens in physics, we define two variables that're supposed to be independent, and then we find that in practice they interact and cross-breed and twist and twirl around each other in exotic ways that're much more difficult to model. We often try to ignore these additional levels of complexity in the hope that they won't upset our final results too much. Sometimes we're right.

Google Analytics, and World Domination

Every mad scientist should have a big world map on the rear wall or their Secret Lair, with pins or lights on it. It's traditional, and I always had a nagging feeling that I was somehow letting the side down by not doing it.

Google to the rescue! They have a thing called Google Analytics, that generates code that you then embed in all of the web-pages that you want tracked. Google get to sneakily snoop on your site's traffic, and in return, you get to call up breakdowns of traffic sources and search terms and so on for your site(s). And one of the features is the Big World Map, automatically coloured in according to the number of visitors. Bwa ha ha!

Unfortunately, like most online real-time statistics, it gets a bit addictive. Why has nobody from "Serbia and Montenegro" visited my website in the last three months? Everywhere else in mainland Europe has visited, so why not them? It's a little white void in an otherwise green chunk of map. Noth Dakota was another holdout that was bugging me a few months ago, but someone's finally visited, so this quarter's stats have the US totally coloured in (yaay!). Greenland not visiting I can forgive (almost nobody lives there), but what about Iceland? I seem to be missing six Central and South American states this quarter, including Bolivia, Paraguay and Venezuela - the Dominican Republic visited, but not Cuba. Are Cuba's visits logged? African coverage is a bit patchy, but improving around the edges. Iran's dropped off the map this quarter, but Iraq's still hanging on in there.

In the Far East, the last quarter's stats are missing Cambodia, Papua New Guinea, North Korea and Myanmar, and slightly to the West, I have a gap comprising Turkmenistan and the surrounding countries (including Iran). Nobody's visited from Madagascar this year. And Antarctica doesn't appear on the map. Other than that, just about everyone's visited in the last quarter, apart from Mongolia.

Mongolia in particular is beginning to bug me. It's a big white splodge on the map between Russia and China, and it sticks out something rotten. Clearly not enough people in Mongolia feel that my site is worth visiting. I am trying to not feel the wound too deeply ... perhaps I have not paid enough attention to the needs of the Mongolian theoretical physics community. Mongolia, I shall endeavour to do better. Thou shalt be mine!

Trigonometric Julia Set Images

The usual Julia Set images are generated by repeatedly running the formula z→ z² + c.
But there are other things that we can do to generate variations, like trying different powers of z.
One of the cooler variations is to replace the usual Julia formula with z→ c× f(z), where f(z) is a trig function. This was the method I used to create the (TAN-based) cellular and (SIN-based) circley fractals in the 1st March and 9th February blog posts.

Thanks to Pythagoras' Theorem, trig functions include z² terms, so there's a certain amount of crossover between the "conventional" z² and "sine" Julia sets.

Web-wise, priority seems to go to Paul Bourke and Tim Meehan for putting up a webpage on "Julia set of sin(z)" nearly ten years ago.

For those who want to see more, there are some more "sine Julia" and other "trig Julia" images on the relativitybook.com website on three new pages, here, here and here. The third page shows how more complex and more strongly repeating versions of the more familiar Julia Set images (example above) appear within the "sine Julia" parameter set.

Some of the pictures are cool.

Fibonacci and the Baker's Dozen

Last year I did some typesetting for a 1970's book by Martin Hutchinson, on archaeology and the Fibonacci Series.

A couple of things stuck in my head that I hadn't come across before. One was the idea that the ribbed stonework of North-European Gothic cathedrals might have been inspired by the ribbing in Northern European longboats. The other was that the Fibonacci Series may once have been used as the basis of an international prehistoric system of weights and measures (which kinda overlaps with Alexander Thom's work on the existence of a possible standardised "megalithic yard").

At first sight, this second idea looks a bit anachronistic ... surely the Fibonacci Series is a comparatively recent invention, with perhaps a few obscure older precedents in ancient texts, and could only have been of interest to a very limited number of people in ancient times?
Well, if you think of the Fibonacci Series as a mathematical thing, sure ... but if you've ever worked on a delicatessen stall, it should strike you that actually, the qualities of the Fibonacci Series make it an ideal system for quickly measuring out and bagging standardised quantities of food and other measurables, if your customers (or staff!) aren't especially numerate.

If you've ever used an old-style kitchen counterweight balance with weights that go up in powers of two, then you'll already be used to the idea of using binary for a weights and measures system. The binary system lets you measure out any integer quantity of something, but it's a bit fiddly. If you run a busy market stall, you don't want to be carefully measuring out whatever weights a customer might ask for. You want a simple set of pre-packaged sizes.

The binary series is the first member of a family of additive systems that form an Extended Fibionacci Series. But as a trader, we don't want to be only supplying our product in quantities that are powers of two - that's not customer friendly. We want a system that does 1, 2, 3 ... and then has units where each step is somewhere in the vicinity on one-and-a-half times the previous size. And that's where the next member of our Extended Fibonacci Series comes in. This second member of the family is the usual Fibonacci Series. It's the basis of an ideal weights-and-measures system for people who can't multiply or divide, and maybe don't even have a strong grasp of number. You can present them with a set of pre-set sizes that you can name, that can be created by stacking rods or blocks together, and the simplicity of the system means that they can easily check for themselves that you aren't cheating them. All they have to do is learn and recognise how the units stack together.

Traditional pre-metric weights and measures (such as the old Imperial system) tended to be based on multiples of threes and fours and sixes and twelves, with a few fives and tens thrown in for good measure. There seems to be a strong influence here from ancient Sumerian mathematics, with its emphasis on base-60 (which allows a large number of convenient integer divisions with integer results). The Sumerians get credited with the decision to use a factor of 360 for the number of degrees in a circle, and for using sixty divisions for minutes into degrees (measuring angles) or minutes into hours (measuring time).

But one of the odd features of many pre-metric (ie non-decimal) systems was the appearance of "thirteen" in some of the definitions of units.
Thirteen has no right to exist in any multiplicative system of weights and measures. It's a prime number! And it's so close to twelve (which divides so nicely into 2, 3, 4 and 6), that there's no obvious reason why we'd want to use multiples of thirteen in a system instead of multiples of twelve.

Except that twelve doesn't appear in the Fibonacci Series, and thirteen does. So all those thirteens in the old archaic weights and measures systems might be leftovers from a more primitive tradition of weighing and measuring, where people created larger sizes by clumping one each of the two smaller sizes together. They might have been the last echoes of an old pre-Sumerian tradition.

Habits and traditions are sometimes passed down through human societies long after the original meanings have been lost, as a kind of behavioural fossil. If Hutchinson's hypothesis is correct, this may be one of the oldest.

'Hyperbolic Planar Tesselations', by Don Hatch

John Baez's "This week's finds in Mathematical Physics" page often has links to math goodies. I haven't visited it for a while (where "a while" is probably measured in years), but I had a peek today, and it had a link to a site containing a whole collection of these beasties:

It's a page by Don Hatch called Hyperbolic Planar Tesselations, and it's full of links to larger versions of the pretty pictures. The image selected on the Baez page is especially nice, because it shows the tiling that you can achieve in negatively-curved space by replacing the usual flat-spacetime hexagonal tiling with heptagons. These regular tilings don't work in a flat plane. If we extrude a flat plane in one direction, then the amount of space per unit area, as judged within the plane, is less than we'd expect. If we extrude in two opposing directions (to produce a "saddle" or "pringle" shape), then as we draw larger shapes on the surface, they include progressively more area that we'd normally expect, thanks to all the folds and crinkles, and the resulting hyperbolic plane allows things like regular heptagonal tiling.

Okay, so I'm probably a sucker for tables of blue, black, and white geometrical figures, but even so, the "Don Hatch" page is really very nice. Some of the figures are reminiscent of Appollonian Net diagrams, which I'm quite fond of as fractal tiling systems, and which also in turn tend to correspond to maps of fractal-faceted solids with an infinite number of circular faces that you can achieve by continually grinding maximally-sized flat circular facets into the remaining curved surface of a truncated sphere:

I put a quick illustrative connection map of heptagonal space on p.27 of the book ("3: Curved Space and Time"), but it was really just a crude sketch. So while my first reaction to the Hatch page was "Wow! Cool!", my second was, "Damn, I wish I'd done that".

They did exactly what we paid them to do

Some economics commentators have recently been getting worked up over why it is that the clever people who work at major financial institutions somehow always seem to end up creating boom-bust cycles.

Those people get paid big bonuses during a boom
They don't have to pay those bonuses back when there's a crash.

It's that simple.

Special Relativity is not Compulsory

One of the foundations of Twentieth Century relativity theory was the idea that Einstein's early "special-case" theory of relativity ("Special Relativity", or "SR") had to appear as a complete subset of any larger and more sophisticated models.

At first glance, this seemed unavoidable.

Einstein's later and more sophisticated general theory was at its heart a geometrical theory of curved spacetime... it described gravitational fields in terms of how they warp lightbeam geometry, and then used the principle of equivalence to argue that the effects associated with accelerations and rotations must also follow the same set of rules. We could then model all three classes of effect as an exercise in curved-spacetime geometry, and go on to extend the model to include more sophisticated gravitomagnetic effects.

But Einstein's general theory didn't attempt to apply these new curvature principles to simpler problems involving basic relative motion, because his earlier special theory had already dealt with those cases by assuming flat spacetime. Instead of going over the same ground a second time, Einstein simply said that, just as classically-curved surfaces reduced over sufficiently small regions to apparent flatness, so the geometry and physics of general relativity, if we zoomed in sufficiently far, ought to reduce to flat spacetime and the "flat-spacetime" version of physics described by the special theory.

There were good pragmatic reasons for Einstein's adoption of special relativity as a foundation for GR, but geometrical necessity wasn't one of them. Here's why:
... It's true that if we zoom in on a GR-type model sufficiently far, we end up with effectively-flat spacetime, but this doesn't automatically mean that we then have flat-spacetime physics. It might instead mean that we've zoomed in so far that there's no longer any meaningful classical physics to be had. We have to accept at least the logical possibility that real physical particles (and their interactions) might be unavoidably associated with spacetime curvature, and in that scenario, we can't derive their relationships by presuming absolutely flat spacetime, because that condition would only be met if our particles didn't physically exist.

Allow any form of velocity-dependent curvature at all around moving particles, and SR's flat-spacetime derivations fracture and fail. This is especially unfortunate since the experimental evidence suggests that moving particles do seem to disturb the surrounding lightbeam geometry, just as we'd expect if curvature effects were a fundamental part of physics, and if the flat-spacetime basis of special relativity was wrong.

---==---

This suggestion that "all physics is curvature" was put forward at the end of the Nineteenth Century by a mathematician called William Kingdon Clifford, who's usually remembered for having his name on Clifford Algebra. The critical thing about a "Cliffordian" model in this context is that when we implement the principle of relativity within it, we find that the resulting physics doesn't reduce to special relativity and the relationships of Minkowski spacetime. Instead of a Minkowski metric, it reduces in the presence of moving particles to something that looks more like a relativistic acoustic metric, and which appears to be much more compatible with quantum mechanics than our current classical models.

So the perfect, unbreakable geometrical proofs of SR's inevitability as physics aren't complete. In order to complete them, we have to be able to show that Cliffordian models can't work ... and that seems to be difficult, because the results of taking a Cliffordian approach seem to be pretty damned good.

To date, nobody seems to have been able to come up with a convincing disproof of this class of curvature-based solution, and until that happens we have to accept the possibility that special relativity might not be a part of our final system of physics.

Relativity Book, Errata

There were a few issues that didn't get sorted (or spotted) before "Relativity in Curved Spacetime" went to press.

1. The concept of universes spawning other universes via the formation of black holes (pages 241-242, Fig 17.9). I didn't get to find who ought to be credited with the idea in time for publication, so I had to leave the discussion and attribution a bit vague. The idea seems to have been Lee Smolin's. Sorry about that, Lee. :(
   
   
2. I'd really wanted to track down the old textbook reference that I'd had for the electromagnetic analogue of of Mach's Principle, applied to rotation. If you place an electron inside a hollow charged sphere, the field cancels, and the electron doesn't "see" the background field. But if you then spin the charged sphere, the electron is supposed to feel a radial force acting at right angles to the rotation axis, and also a sideways dragging force, analogous to the outward and sideways forces that matter feels when the mass of the outside universe is spun around it (blamed on apparent "centrifugal" and "Corioilis" fields experienced within the rotating frame). Didn't manage to find the reference in time.
   
   
3. Missing reference. The Harwell group produced a controversial paper on centrifuge redshifts in 1960, which caused a bit of a stir. The dispute was documented in a paper by Alfred Schild, which is mentioned at the top of page 158 ("the Schild rebuttal"). Schild should have been listed in the bibliography on page 366, between the 1960 references for Hay, Schiffer et.al., and L.I. Schiff:
   

   1960 | Alfred Schild " Equivalence Principle and red-shift measurements" Am.J.Phys 28 778-780
   - rebuttal paper

   But the entry was accidentally deleted and the "rebuttal paper" comment ended up attached to the following "Schiff" reference.
   This got corrected in the hardback edition.
   
   
4. There were also a handful of minor typesetting mistakes (typically missing or misplaced "s"-es) in the first half of the book that snuck past the spell-checker, but nothing serious. Those have been corrected for the hardback.
   

And as far as I know, that's it.

Cell Fractal

Here's a nice example of a "cell" fractal that I've been staring at, off and on, for the last week or so:


I probably didn't have to zoom in quite so far to demonstrate the thing, but I thought, what the hell, let's just leave the Eee Box running until the zoom calculations hit the 32-bit floating-point limit.

The zoom doubles in size every second, and does that for about 47 seconds.

At some point there'll be a web page to go with this, but it's not quite finished yet.

Isaac Newton and E=mc²

The history of the idea of mass-energy conversion is a slightly murky one. Textbooks and lecturers find it convenient to say that Albert Einstein was the first person to suggest that mass and energy were interchangeable, but really ... he wasn't. That's a handy piece of educational fiction. It ain't so.

By 1905, a number of researchers were reckoned to be close to the E=mc² result. The basic argument went something like this: imagine a mirrored cavity embedded in a piece of material, containing a trapped light-complex, in equilibrium with its container. The radiation pressure of the trapped light within the container is the same in all directions. But if the container and its trapped electromagnetic (EM) energy are now viewed by a different observer who reckons that the container is "moving", then that observer will assign different Doppler-shifted energies and radiation pressures to different parts of the light-complex: The forward-aimed components now get assigned greater energy and momentum than the rearward-aimed components, and the overall momentum of the complex no longer cancels out - the container's nominal motion gives the trapped light an overall momentum that points in the direction of motion.
So the EM contents of the moving container appear to contribute additional momentum to it, as if it contains a speck of matter rather than EM energy. If we aren't allowed to look inside the container, we might not be able to tell whether it contained EM energy or real matter, and by working out how much energy it takes to reproduce the external effects associated with a given amount of mass, we end up with a very short equation for the conversion factor between rest mass and rest energy. That (if we calculate it correctly) is E=mc².

However, it seems that Einstein's competitors either didn't calculate the conversion ratio properly, or failed to come out and suggest in print that this wasn't merely an apparent conversion of mass and energy, but The Real Thing. Einstein did both, and earned the credit.

--===--

If we want to go back further, to find an older example of the idea of "interconvertibility" in a major English-language physics text by a famous author, all we have to do is open a copy of Isaac Newton's "Opticks" [Babson archives]/[1717 edition.pdf], and flip to the "Queries" section at the back. The relevant section is Query 30:

Qu.30: Are not gross Bodies and Light convertible into one another, and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?...
The changing of Bodies into Light, and Light into Bodies, is very conformable to the Course of Nature, which seems delighted with Transmutations.

I've quoted this at the start of Chapter 2 of the "Relativity..." book ("Gravity, Energy and Mass"), which goes through some of these arguments in more detail (with the help of some pictures).

Traditionally, at this point in the discussion, a physicist will interrupt and say something like,

"Okay, perhaps Newton had the idea, but we weren't able to calculate the specific relationship until we had special relativity. Einstein used Lorentz's relationships in his calculations rather than Newtonian physics, so so E=mc² is clearly specific to Einstein's physics."

But that's not true either. It's correct that Einstein originally presented E=mc² in the context of his new "special" theory, but if he'd done the momentum calculations with the same degree of care using "olde" Newtonian emission theory, he'd have gotten the same result (with slightly less working). In fact, we can construct a continuum of hypothetical theories whose relationships differ by Lorentzlike ratios, and all of them generate E=mc². Turns out, E=mc² is a general result. I've put the details of the "Newtonian optics" argument into the book's "Appendices" section, as "Calculations 2"

So, while some physics histories present Einstein's discovery of E=mc² in 1905 as a triumph of the scientific method, the reality seems to be that the equation's discovery is marked by a sequence of earlier human failures going back two hundred years.
To start with, Newton couldn't calculate E=mc² because he'd gotten the relationship between energy and frequency upside down, and assumed (reasonably but wrongly) that the "bigger", redder wavelengths of light carried more energy and momentum for a given amplitude, rather than less ("The Newtonian Catastrophe", chapter 3). Newton lived 'til 1727, and then his his successors still couldn't calculate E=mc², because they trusted Newton to have gotten it right. If you were an English physicist, suggesting that Newton might have made a mistake was heresy. Towards the end of the century (1783), John Michell used Newton's arguments to calculate the gravitational wavelength-shifting of light, but he was still citing Newton's writing and using the old bad "inverted" relationships. Defending Newton from criticism was now a matter of national pride, and in 1772, Joseph Priestley's History of Optics had been cheerfully ridiculing the mental capacity of those poor retards in Europe who were so behind the times that they actually still thought that light was a wave! Antagonism between the two sets of researchers meant that the Newtonian group couldn't admit the possibility of major error.

The next couple of decades saw Europe shaken up by the French Revolution, and then Continental physics really began to hit its stride. Newton's mistake had generated a bad prediction that light should travel more quickly through glass than air, and when Continental experimenters started using new technology to measure lightspeeds, they were able to show, quite conclusively (and perhaps slightly gleefully), that this wasn't the case. As we got to the mid-C19th, work by Christian Doppler and others meant that we were now quite sure how to calculate the effect of velocity on light for any given model, but instead of going back and correcting Newton's error, Newton's supporters slunk off with their tails between their legs, and did their best to rewrite physics history so that later English-speaking physics students hopefully wouldn't realise just how dumb they'd been.

The latter part of the C19th was then "lost", too. Although we now had plenty of expert wave theorists, lightwaves were now generally reckoned to propagate through some sort of aetheric medium, and there was no agreed set of governing principles defining what that medium's properties ought to be. The credibility of the older Newtonian principles concerning the behaviour of light (such as the idea that the behaviour of matter and light ought to obey a single set of underlying rules) were now widely considered to be "damaged goods", and the proliferation of aether models meant that we now had a bewildering array of competing predictions for exactly how the properties of light ought to be affected by motion. There were just too many damned versions for us to be able to do these sorts of calculations confidently, and be sure that our results meant anything.

That state of affairs lasted until the early Twentieth Century.

This is where Einstein came onto the scene. Einstein had three advantages over most other contemporary theorists when it came to deriving E=mc² - he was a fan of the idea that the principle of relativity should apply to light, he was definite about the set of equations that he wanted to use, and he was (apparently) blissfully unaware of almost all of the previous two centuries of political bickering on the subject (probably helped in part by his habit, as a student, of not bothering to turn up for lectures). So Einstein was able to come to the problem "fresh", without a lot of preconceptions. He'd already tinkered with emission theory, recognised some of the problems, and had then latched onto Lorentzian electrodynamics, and decided that this was The Future.

In 1905, he published his "reimagining" of Lorentzian electrodynamics , which took the characteristics of Lorentz's relativistic aether and deleted the "physical medium" aspect as unnecessary. According to Einstein in 1905, aether was irrelevant to the problem - all that was required to generate the Lorentzian relationships was the principle of relativity and an assumption about lightspeeds. These two postulates were then sufficient to generate all of Lorentz's important math.

And then (as a very short followup paper) ... if the Lorentzian relationships in the previous paper were correct, internal energy imparted mass to bodies, according to the relationship E=mc².
At this point, Einstein was on a roll, and he was looking forwards rather than backwards ... he didn't really have much motivation to point out that, if the relationships in his earlier paper were wrong, and we reverted to the previous relativistic calculations for light, we still got E=mc². Pointing that out was a job for peer review and outside commentators, but almost no-one noticed.

We then coasted though another century, without much to suggest that anyone had connected the dots and understood the broader context for what Einstein had done and how it really related to Newton's earlier work. Right into the 1990s, students were still being told that E=mc² was unique to special relativity, and that the fact that atom bombs worked was ample evidence that no other system of equations could be right. Those claims weren't scientifically or mathematically correct, and weren't researched, but everyone seemed to believe them. Some people wrote research papers and entire books on the history of E=mc², and still somehow managed not to mention the Newtonian connection.

--===--

Not everybody missed it. The Sandman series by Neil Gaiman quotes and cites the key section in "Opticks" and points out its its significance. But Sandman isn't a book on theoretical physics, it's an illustrated fantasy graphic novel. So what we appear to have here is a subject where some people who write university textbooks seem to be doing rather less background research and fact-checking than some people who write comicbooks.

I feel that this is an unhappy situation. But it seems to explain a lot about why theoretical physics is in its current state.

John Milton, 'Paradise Lost', and General Relativity

John Milton (1608-1674) was a linguist, pamphleteer and poet, nowadays best remembered for having written Paradise Lost, first published in 1667.

England in 1667 had been experiencing decades of social upheaval, and an accelerating succession of crises. Oliver Cromwell's side had won the civil war, abolishing the monarchy and executing Charles I in 1649, but Cromwell had then died in 1658, and without Cromwell as a driving force, Parliament had decided to restore the Monarchy, with Charles II being appointed the new king in 1660. Milton had campaigned for religious reform, written campaign material for Cromwell and the Republic, and had held a post in the new regime before going blind. With the Restoration, Milton briefly became a wanted man, and his books were publicly burnt. As England was coming to terms with the abrupt political reversion, it got hit first by the Great Plague of 1665, and then by the Great Fire of London [*] [*] in 1666.

These were, as the saying goes, interesting times.



Paradise Lost, Milton's masterwork, was an epic poem, originally in ten sections, that outlined the rebellion and fall of Lucifer and the subsequent fall of Adam and Eve, in the contemporary poetic equivalent of high-definition widescreen. Milton had something of a talent for visual imagery and a good turn of phrase, and some commentators later ruefully pointed out that Milton seemed to have been influenced by his experiences with the ill-fated English revolution, and not only made the rebellious Lucifer a sympathetic character, but given him some of the the best lines. "Better to reign in hell than serve in heaven", indeed!

The mind is its own place, and in itself
Can make a heaven of hell, a hell of heaven

There are some great phrases in the poem – when we talk about "the fabric" of spacetime, we're arguably borrowing from Milton – but to a physicist, one of the most surprising sections (along with his name-dropping of Galileo) is the bit where Milton writes :

... whether heavn move or earth
Imports not, it thou reckon right.

To a historian, those lines might be taken as an assertation of independence, and a rejection of the notion of centralised supreme power. There's no single authority that decides what is really "moving" and what isn't. No church, no Pope, no religious leader, no monarch.

But to a physicist, they set out the general principle of relativity. When the Earth spins on its axis and loops along its orbit around the Sun, it's convenient to think of the Earth as moving and the background starfield as fixed. But in reality, there's no "special" status accorded to those stars. They're just stars, each following their own line of least resistance as they drift in the wash of their own individual surrounding gravitational tides and currents. It doesn't matter whether we say that the Earth rotates beneath Heaven, or that Heaven rotates around the Earth. If you calculate properly, (said Milton), the answers should be the same in either case.

And if they're not, you've done it wrong.

--===--

While Milton was getting his piece finalised and published in 1665-67, the plague had other consequences. Cambridge University sent its students home in the fall of '65, and one these, a previously unremarkable and undistinguished student, chose to make use of the two years of enforced comparative isolation back at his family's farm in the village of Woolsthorpe to work through some ideas on gravity, optics and mathematics. His name was Isaac Newton.

My Favourite 3D Fractal

It's this one:

It reduces to the Mandelbrot Set on one plane, and to the "Tricorn" or "Mandelbar" fractal on another. And there's a stream of self-similar solids emanating from the main pointy bit.

I don't only like this fractal because I don't know of anyone else having found it before me ... okay, perhaps that is a contributing factor ("It's MY fractal, Miiiiiine!"), but there are other fractal solids in the same series and I don't like those nearly so much. And according to my YouTube stats, neither do other people.

Now, if only I had access to a high-resolution 3D printer ...

Edible 3D Fractals

If you're into fractals, you've probably already heard of the Romanescu.

It's a relative of the cauliflower, and it produces a spiralling cone made up of smaller spiralling cones, which in turn are made of of smaller ... well, you get the idea. Imagine a pinecone, where each segment is a protruding mini-pinecone, composed of segments that are also mini-mini-pinecones, and you have some idea of what a romanscu looks like, up-close.
Oh, and they're a livid shade of green.

If M.C. Escher had designed a vegetable, this would be it.

You might now be tempted to track down lots of awfully pretty artsy photos of romanescu on the net. I'd advise you not to bother. Instead take a trip to your local chi-chi supermarket and buy some, for real.
I got a pair for about one pound fifty, at the local Waitrose. They're awfully cute, they're much more fun to stare at in real life than someone else's photo, and when you eventually get bored with them, you can eat them!

Steam them, or wet them, cover them and shove them in the microwave for a couple of minutes.
They taste a little like cauliflower. Cheese sauce is optional.

Summer Glau

Here's an odd thing. I added a "Summer Glau" head to the collection at relativitybook.com, and it struck me ... if anyone runs this software, their PC will be pretending to be an actress, who is pretending to be a robot, which is pretending to be a human.

You know that you've reached a certain level of technology when things start to get this complicated ...

Curvature is Important

Curvature allows us to comprehend views of reality that can't otherwise be seen, or appreciated without an understanding of a few basic principles. Curvature allows connections and interrelationships and juxtapositions that you may find it impossible to see if you don't have the necessary mind-set.

This doesn't just apply to theoretical physics, mathematics and abstract logical structures. it also applies to real life.

Let's suppose that we're signwriters, and we have a famous department store as a client. They'd like an impressive curved sign over their main entrance, proudly displaying their name. Wouldn't it be awful if we neglected to take into account how that curved set of letters looked from different angles, and accidentally built a sign that said a Very Rude Word?

At this point you're probably remembering the fictional Great Big Sign in Douglas Adams' "Hitchhiker" series ... the one built by Sirius Cybernetics that when collapsed to half its original size, spelt out the message "Go stick your head in a pig" ... you're probably thinking that I'm about to describe some tortured hypothetical example that would never really happen in real life ... some crazy laboured combination of store name and typeface and sign geometry that would be so improbable that it'd never ever happen.

And so, sceptical reader, I invite you to examine this real-life department store sign:

It's for a store called T J Hughes. Naturally, above the store's entrance we see the words T J HUGHES proudly displayed, in large red capitals. It's on a corner, and the letter sequence follows the curve.

If we turn the corner, cross the road, and look back at the sign, we still see the final “S” facing us, and to its right we see in white, slightly shrunken by perspective, the reversed white backsides of the letters H, J and T. Unfortunately, the letter J is very narrow, and the curved base of the letter is out of sight. So the J looks like an I, and although the H and T are seen reversed, they're symmetrical and still look like a perfectly normal H and T.

At this point you should be able to take a wild guess at the problem.

Here's the photo:

That's right. Seen from the right, the sign above their storefront really does say

Unfortunate, no?

This isn't a doctored photograph. The shop is real, and the sign has been there for an awfully long time. Here's the store's website, its location on Google Maps and their wikipedia entry. This really happened.

Like the title says, curvature is important. Ignore it at your peril.

Cool Circley Fractal!

While playing about with some Mandelbrottish code, I've managed to find a fractal that looks like it's entirely made out of circles:


Instead of having Mandelbrots that spawn "mini-Mandelbrots", it's got circles spawning "mini-circles".

Yaaay Me!

I may have to adopt a version of this as my new logo ...

Mathematics, Certainty, and the Mathematical Impossibility of the Saturn V

Back in the early Twentieth century, after Konstantin Tsiolkovsky had initially tried to get people interested in the idea of liquid-fuelled rocketry, the story goes that an elite mathematical society decided to study the problem, and decided that LFRs were impractical. They didn't just decide that LFRs were unlikely to to be useful to launching payloads into space, they proved mathematically that such a device wasn't workable. Or so they thought.

The argument was nice. It said, to launch a rocketship to any given height requires a certain amount of fuel, and with an LFR, a certain amount of additional infrastructure (fuel tanks, pumps, piping, the rocket engine itself, etc.). The more infrastructure you have, the more weight you have to carry, and the more “dead weight” you end up with at the end. If you want to get higher, you have to carry more fuel, which means that you start with more weight, which in turn means that you have to carry even more fuel to compensate.


Solid-fuelled rockets were simpler. They were basically big fireworks, and when you used solid fuel, the “fuel problem” wasn't intractable. If you calculated “weight of fuel required plus weight of payload” for a given height, it was solvable. It helped that the weight of the fuel being carried was constantly reducing as the flight progressed. With a solid rocket, you might start off with a monstrous amount of rocket propellant on the launchpad, but by the time you got into space you had something much more lightweight.

With a liquid-fuelled spaceship (it was argued) the equation was different. Once again, the higher you wanted to go, the greater the amount of fuel you had to carry ... but with a liquid-fuelled craft, all that propellant had to be carried in tanks, and fed through pipes. Although the tankwork became more efficient as you built larger tanks, the total weight of tankange and pipage was always greater for a larger craft, and since this weight had to be subtracted from the final payload weight, you found that beyond a certain height, your payload was effectively 100% infrastructure.
If you wanted to lift a person into space, with accompanying life-support, liquid rocketry obviously wasn't the way to go. It was an impractical idea, and funding liquid fuelled rocket research was clearly a waste of time.

A few decades later, when we landed on the moon, we got there using LFRs.

Where Things Went Wrong

When Apollo 11 went to the Moon, NASA didn't attempt to lift the entire Saturn V rocket into space. That would have been silly. They took a rocket that could lift a heavy payload pretty high, and instead of enlarging it, they then sat a second rocket on top of it. The payload for the first rocket was another rocket. Rocket #2 was smaller, was launched from the new height (with a good starting velocity), and didn't have to carry the dead weight of rocket #1, which simply fell back and crashed into the sea. The Saturn V had multiple stages, with only the last stage(s) leaving Earth with their final payload.

---

The mathematicians would probably say that they didn't do anything wrong. Their calculations were exactly correct for the problem that they were given. The problem was that the question wasn't asked carefully enough ... or rather, that they'd asked a version of the question that was too careful, phrased in such a way as to be easily solvable and to give a definite answer.
And by doing that, they got an answer that was simple, straightforward, provably correct ... and physically wrong.

There are three main lessons here:

1. The "test particle" fallacy

Firstly, the physical behaviour of compound systems is sometimes quantatively or even qualitatively different to the results that we predict from simply studying individual components in isolation. The limits of a two-rocket system aren't the same those of a one-rocket system. If we take a “test particle” approach to physics, and derive a set of laws based on the idealised behaviour of single non-interacting idealised objects, and then turn those predictions into elegant mathematics and beautiful self-contained geometrical models, it doesn't mean that the answers given by those models are going to be correct. We can have beautiful, rigorously-derived geometry and mathematics that allows just one solution, and that provably has zero errors in any of its derivations, and creates breathtakingly elegant resonances across multiple fields of mathematical theory ... and physically, it it can still be quite wrong.

This isn't always appreciated.

2. Physics vs. mathematics

Secondly, mathematics is not physics. It might well be that "all physics is mathematics", but that can mean that physics is a subset of mathematics, rather than the thing itself ... physics is obliged to correspond to reality, while mathematics is not, so the two disciplines aren't automatically interchangeable. Modern physics is now so strongly math-based that researchers can spend their lives learning to manipulate the textbook mathematical machinery, without necessarily realising that the resulting answers aren't guaranteed to be physically meaningful. These guys are liable to tell you that "You can't argue with the math", but sometimes, if you're a physicist, your ability to argue with (and occasionally overturn) mathematically-proven results is what makes you worth your salary and your job title. There are situations where not understanding the importance of disputing math, regardless of the apparent strength of the proofs, means that perhaps you haven't really understood the idea of physics at all.

3. Proof vs Certainty

Thirdly, in physics, there's a sometimes a tradeoff between calculability and correctness. Sometimes the things that you do to a problem to make it well-defined and easily modellable destroy delicate-but-critical characteristics of the original problem. Instead of a "correctly vague" answer to an "indistinct" problem, you then end up with an unambiguous answer to a well-defined problem .. that doesn't actually correspond to the thing that you're trying to model.

In a worst-case scenario, a desire to be able to definitively solve a problem can, if your tools aren't up to the job, lead to a process of successive approximation that converges more and more definitely on an answer that's emphatically wrong. In everyday situations a physicist will use common sense to ignore answers that obviously aren't right, but when we're working at the edge of known theory, the selection process becomes more dangerous.

If we're not careful, all we end up doing is generating mathematically rigorous retrospective justifications for whatever it is that we already happen to believe. But what what we believe is based on our cumulative experiences to date. Our current belief system is a logically-perfect inverse projection of an imperfect dataset, designed to recreate the particular set of rules that we inherited from the generation before us.

And it's wrong

Putting Periscopes on Airplanes

One the subject of airplanes, a wacky idea I had about twenty years ago was designing aircraft cockpits to include periscopes.

A dumb idea? Not necessarily.

See, one of the problems with large aircraft is taxi-ing. Aircraft are designed to fly. They aren't really designed to be driven. So if you're in the cockpit of a 747, and you want to park it somewhere, you can't really see what you're doing. You're high up, your visibility sucks, and you have this nose-cone thing sticking out in front of you, guaranteeing that you have no chance of seeing what's just in front of your wheels. Consequently, expensive aircraft get trashed from time to time while they're still on the ground, while somebody is simply trying to find somewhere to park them.

What you need in this situation is a periscope – not to look up, but to see how things look from beneath the aircraft. You want to be able to pull a lever, and have a chunk of optics pop out of the bottom of the aircraft giving you a 180-degree or 270-degree view, relayed up to the cabin and perhaps projected onto a curved mirrored trim just below the windscreen. Worried about debris on the runway? Check the periscope. Trying to park? Check the periscope. Coming in to land, and not sure if your landing gear is deployed? Check the periscope. Unsure if one of your engines has just flamed out? ... you get the idea.

Consider the case of Concorde. One of the most difficult engineering tasks in designing Concorde was supposedly the design of the nose. Concorde has a looong nose, and it needs to be pointy and smoothly tapered for efficient supersonic flight. But when Concorde comes in to land, it glides in at an angle with its nose in the air, and the pilots can't see where they're landing. To get around this the engineers developed a "droop snoot" for the plane – an entire nose section that could swivel to point downwards when the plane landed, to give the pilots a fighting chance of seeing what they were doing. This was a difficult bit of engineering, with double windshields and so on.

Wouldn't a pop-down periscope system have been simpler?

Okay, so nowadays the idea's probably becoming a bit redundant. With recent aircraft, with their instrumentation displayed on LCD panels, it's probably easier to embed reliable cameras into key positions in the airframe and allow the copilot to switch one of their screens to camera view. The data networks are probably already in place, and the instrumentation panels are now flexible and modular. We're probably approaching the point where a pilot will trust a set of cameras more than a set of odd additional direct optics.

But for the last few decades, large planes probably really should have all had periscopes.

Computer-generated 3D faces, FaceBank, FaceGen

I initially added the FaceGen page to the relativitybook.com website as a bit of fun, but it's quickly become the most popular page on the website. It seems that - strangely enough - a lot of people out there find Angelina Jolie to be rather more interesting than gravitomagnetic field theory.

So I've spent some time adding more sample 3D faces. There are now more than fifty of them, and I've put up a separate "face bank" page for browsing them, http://www.relativitybook.com/CoolStuff/facebank.html . There's also some jerky video on the ErkDemon YouTube channel.

Some of the sharper-eyed visitors will have noticed that apart from Albert Einstein and Barack Obama, all the faces are female. Personal preference. I suppose that I really ought to grudgingly do a few more male faces at some point, just to make thing look more balanced. One or two. Maybe.

If anyone wants to leave any feedback or comments, you can do it here, on this blog page.

Now, see if you can work out which slider to move to make Barack Obama's ears waggle ...

Fear of Doors

If you ask most people what the single most dicey bit of equipment is on an airplane, you'll get a range of answers.
The obvious answer is the wings. But actually, wings are pretty stable things. They don't flap or do anything fancy, and the airframe is fitted to them pretty solidly. Wings tend not to fall off. Okay, so the control surfaces sometimes do fall off (some years back, a large flap landed in Richmond golf course that no airline wanted to claim), but this isn't as big a deal as you might think. The tailfin is important for stability, and you certainly don't want to lose that, but they're usually overengineered, too. Wheels are handy if you're planning on landing, but as long as you know that your undercarriage has failed, you can take appropriate steps. So maybe the little undercarriage warning light is one of the most important pieces of kit on the plane.

Engines are another matter. Jet engines are beautiful pieces of kit, but they're somewhat exposed. You have delicately-engineered compressor blades whose outer tips shear a helical scream through the air at more than the speed of sound, and they operate without safety covers. They're damned strong, but they're only designed to cut and chop air at supersonic speeds. Not water. Or ice. Or large items of poultry.

Try to convince a cruising jet engine that it ought to suddenly try being a food processor and attempt to make some albatross pate, and it gets unhappy. Blades can break and fly off. Control lines can get severed, and fuel tanks punctured. If you're lucky, when the engine tries to inhale a flock of geese, it'll just stop.

So bird strikes are dangerous. But they happen far more often than most people think, often to freight aircraft, where the incidental loss of an engine or an altered flightplan doesn't result in any scared passengers or a news story. Airliners have multiple engines, and unless you lose all of them, the pilot can usually try to do something with what's left.

If you're an airliner passenger, perhaps you should be rather more worried about geese than about the idea that the wings might fall off the plane.

So-o ... back to engineering. What's the most dangerous bit of equipment that the passenger is allowed to see? Perhaps it might actually be the aircraft's doors.
People don't think of doors as being dangerous. Doors are not supposed to be difficult pieces of engineering. But airliner doors are slightly different. See, there's no “safe failure mode” for an airliner door. If you need it to open in an emergency, it HAS to open, but while airborne, the door mustn't fly open when someone trips over and accidentally falls against it. It has to be really easy to open (or everyone dies), but not too easy (or everyone dies).

The door and its housing also have to operate under extremes of temperature, when the plane is parked in baking Saudi desert heat, or on a frozen Moscow runway with maybe a quarter-inch of ice on the seals. It has to cope elegantly with thermal expansion and contraction. If the door sticks, you do NOT want to damage the mechanism by forcing it too hard. If it's damaged, you can't fly.

Added to this was the problem that in older aircraft designs, the doors were liable to be one of the last things to be designed. And in the older “tapered” planes, you couldn't necessarily design a door in advance and place it anywhere you wanted ... oooooh no, the fuselage curvature was different all over the plane, sometimes a door designed for one part of the plane simply wouldn't fit anywhere else. And what happened to this mission-critical component whose failure could bring down a plane? It got slammed. It got shoved. People banged their luggage against it.

On recent airliners these things are better. Passenger doors now tend to be inward-opening, with a “bath-plug” taper to their cross-section that means that even if the locks fail, the internal air-pressure pushes the door tightly against it's frame. The doors are relatively small, rigid, and thick, and the higher you fly, the harder the doors are pushed into their mounts by the pressure-differential. The Airbus range (and the later Boeings) also have noticeably cylindrical fuselages, and while this may sometimes look like an ugly design cop-out, it helps with some aspects of the engineering. A “cylindrical” plane can be produced more easily in a range of “stretched” or “squashed” versions by adjusting the number of standard prefabricated sections. And it means that ... magically ... the doors work better. A door can start to be be designed and extensively tested as soon as the aircraft dimensions are decided, and then the resulting design can be deployed and duplicated at any point along the cylindrical section of the fuselage.

But for cargo-bay doors, things aren't so great. Cargo doors have to be big for loading, and while passenger doors can be designed with a “plug” taper so that they can't be forced open by air pressure when unlocked, cargo doors often open outwards. They also have a larger surface-area-to-edge ratio, so they're less rigid. They flex more. And the guys who load are using motorised equipment to move multi-ton pallets about, so you might expect the occasional accidental prang. And they aren't necessarily experts in aircraft safety.

As a result, serious cargo door failures in airliners do happen from time to time, sometimes leading to some of the passengers experiencing an unscheduled exit from the plane. In the worst-case scenario, in a pressurised aircraft at high altitude, the resulting explosive decompression can rip apart the plane's innards, destroying the control systems and bringing down the aircraft.

http://www.absoluteastronomy.com/topics/Turkish_Airlines_Flight_981
http://www.absoluteastronomy.com/topics/United_Airlines_Flight_811

See, people just don't RESPECT doors.

Happy flying!

Ten Things that an LHC manager doesn't want to hear

1. “Can you smell burning?”
   
   
2. “There's a guy here from Health and Safety, says he wants to talk about mini black holes and strangelets.”
   
   
3. “Well, you see, the problem is, what you have here is a perfect environment for rats ...”
   
   
4. “That's not the budget, that's the electricity bill.”
   
   
5. “So, as far as the site's environmental footprint is concerned, how much work did it take to make this place carbon-neutral?”
   
   
6. “I'm sorry, I'm here to represent the contractor, and the specifications definitely said un-insulated copper wire.”
   
   
7. “Quick, come see, someone's using the main magnets to levitate and crush a beer can!”
   
   
8. “So the installation is now finally finished! Dave, the champagne if you please? Er, Dave, mind where you point that bottle. You know, the cork ... You don't want the cork going ... (pop) ... Nooooo!”
   
   
9. “Wow, this technology is incredible! This has to be one of the greatest achievements of the human race! So, roughly how much power do you reckon this thing is going to generate when it finally comes online?
   
   
10. Hey, what happened to the Sun?