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.

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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.