General Relativity is Screwed Up

With Einstein's general theory of relativity, one of the theory's harshest critics was probably Einstein himself. This was partly a matter of personal discipline, and partly – like the joke about sausages – because it's sometimes easier to like a thing if you don't know the gruesome details of how it was actually made. Einstein found it easy to be sceptical about the design decisions that had gone into his general theory, because he was the guy who'd made them. It had been the best general theory that had been possible at the time, said Einstein, but with the benefit of hindsight ... perhaps its construction wasn't entirely trustworthy.
The "iffy" aspects of C20th GR are difficult to see from within the theory, because – where the lower-level design decisions have forced a fudge or bodge – from the inside, these things seem to be completely valid, derived (and quite necessary) features. It's not until we look at the structure from the outside, with a designer's eye, that we see the arbitrary design decisions and short-term fudges that went into making the theory work the way it does.

Sure, the surface math looks pretty (with no obvious free variables or adjustable parameters), but that's because, as part of the theory's development, all the ugliness necessarily got moved down to the definitional and procedural structures that sit below the math. Change those underlying structures, and the surface mathematics break and reform into a different network that looks similarly unavoidable. So even though the current system looks like the simplest possible theory when viewed from the inside, we can't invest too much significance in this, because if the shape and structure was different, that'd look like the simplest possible theory, too.

To see how the theory might have been, we need to look at the subject's protomathematics, the bones and muscles and guts of the theory that dictate its overall shape, and which don't necessarily have a polite set of matching mathematical symbols.

Here are two interlinked examples of decisions that we made in general relativity that weren't necessarily correct:

Problem #1: Gravitational dragging, velocity-dependent gravitomagnetic effects

As Fizeau demonstrated back in ~1849 with water molecules, moving bodies drag light. General relativity describes explicit gravitomagnetic dragging effects for accelerating and rotating masses, and logic pretty much then forces it to describe similar effects for relative velocity, too. When you're buffeted by the surrounding gravitational field of a passing star, the impact gives you some of the star's momentum – momentum exchange means that the interaction of the two gravitational fields acts as a sort of proxy collision, and the coupling effect speeds you up a little, and slows down the star, by a correspondingly tiny amount.

For a rotating star, GR915 also agrees you're pulled preferentially to the receding side – there's an explicit velocity component to gravitomagnetism (v-gm). Even quantum mechanics seems to agree. And we can use this effect to calculate the existence of the slingshot effect, which is not just theory, but established engineering.

But v-gm effects appear to conflict with Newton's First Law of Motion: If all the background stars dragged light according to their velocity, then as you moved at speed with respect to the background starfield, the receding stars would pull on you a little bit stronger than the others, slowing you down. There'd be a preferred state of rest, that'd correspond to the state in which the averaged background starfield was stationary (ish). This doesn't agree with experience.

So the v-gm effect gets edited out of current GR, and when we do slingshot calculations, we tend to use Newtonian mechanics and model them in the time domain, instead. We compartmentalise.

Summary:

Argument: The omission of v-gm effects from general relativity seems to be arbitrary and logically at odds with the rest of the theory, but it seems to be “required” to force agreement with reality … otherwise “moving” bodies would show anomalous deceleration.

I'd consider this a fairly blatant fudge, but GR people would tend to refer to it as essential derived behaviour (based on the condition that the theory has to agree with reality).

Problem #2: Gravitational Aberration

If signals move at a finite speed, the apparent positions of their sources get distorted by relative motion. We "see" a source to be pretty much in the direction it was when it emitted the signal, with a position and distance that's out of date, thanks to the signal timelag.

If gravitational and optical signals both move at about the same speed, "c", (ignoring nonlinear complications), then we expect to "feel" the gravitational signal of a body to be coming from the same position that the object is seen to occupy. Which is kinda helpful.

But it seems that under current GR, the apparent "gravitational" position of a body gets assigned to its instantaneous position, as if the speed of gravity was infinite. We say that the speed of gravity isn't actually infinite, but that moving bodies somehow "project" their field forwards and then sideways so that it looks infinite as far as the observer's measurements are concerned. In other words, it seems that under current GR, there's no such thing as gravitational aberration.

This is a bit like the sound of fingernails scratching down a blackboard. It means that there's no longer the concept of a body having a single observed position, and we get separate definitions of "apparent position" for EM and gravity. This badly weakens the theory, because it means that mismatches between the two that that we might normally look out for to show us that we've made a mistake somewhere, are the theory's default behaviour. We lose a method of testing or falsifying the model.

So why do we do it?

We...ell, the usual argument involves planetary orbits and the apparent position of the Sun as seen by an observer on a rotating planet. But that argument's complicated and perhaps still a bit unconvincing, so … the simpler argument is that if gravitational aberration existed, it'd again seem to screw up Newton's First Law. When an astronaut travels through the universe at high speed, the background stars appear to bunch together in front of them (e.g. Scott and van Driel, Am.J.Phys 38 971-977 (1970) ), and if the gravitational effect of all those stars was shifted to the front as well, then we'd expect the astronaut to be pulled towards the region of highest apparent mass-density … forwards … and this'd further increase their forward speed, making the aberration effect even worse, which'd then create an even stronger forward pull.

So again, we manually edit the effect out, say that it's known not to exist, and then do whatever we have to do with math and language to stop the theory contradicting us.

Summary:

Argument: Losing gravitational aberration seems to be arbitrary and logically at odds with the rest of the theory, but seems to be "required" to force agreement with reality … otherwise "moving" bodies would show anomalous acceleration.

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Put these two arguments together, and you should immediately begin to see the problem:

If we'd resisted the "urge to fudge", it looks as if our two problems would have eventually canceled each other out anyway, without our having to get involved. They seem to have the same characteristic and magnitude, but different signs. One produces anomalous acceleration, the other anomalous deceleration. Put them together and the moving astronaut doesn't accelerate or decelerate, because the stronger rearward pull of the fewer redshifted stars behind them is balanced by the increased number of stars ahead, which are blueshifted and individually weakened. Instead of our imposing N1L-compliance on general relativity as a necessary initial condition, the theory works out N1L all by itself, as an emergent property of curved spacetime.

So in these two cases, we seem to have corrupted the "deep structure" of the current general theory of relativity not once but twice, by trying to solve problems sequentially rather than letting the geometry generate the solutions for us, organically. Both "deleted" effects turn out to be necessary for a "purist" general theory … but once we'd fudged the theory once to eliminate one of them, we had to go back and fudge the theory a second time to eliminate the second effect that would otherwise have balanced it out.

And in doing that, we didn't just "double-fudge" a few details of the theory, we broke important parts of the structure that should have allowed it to expand and blossom into a larger, more tightly integrated, more strictly falsifiable system that could have embraced quantum mechanics and dealt with properly with cosmological issues. General relativity should have been a tough block of dense, totally interlocking theory, with independent multiply-redundant derivations of every feature, rather than the thing we have now.

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The fudging of these two issues also changed some of the theory's physical predictions:

Losing gravitational aberration gave us a different set of observerspace definitions that altered the behaviour of horizons. Losing v-gm meant that we got different equations of motion, once again a different behaviour for black holes, and no way of applying the theory properly to cosmology without generating further cascading layers of manual corrections reminiscent of the old epicycle approach to astronomy. It also created a statistical incompatibility with quantum mechanics.

So general relativity in its current form seems to be pretty much screwed. GR1915 was fine as an initial prototype, but it should really have been replaced half a century ago – in 2010, it's an ugly, crippled, mutated, limited form of what the theory could, and should have been by now. But because people fixate on the math rather than on the structure, they can't see the possibility of change, or the beauty of what general relativity always had the potential to become. And that's why the subject's been almost stalled for pretty much the last fifty years, it's because Einstein died, and too many of the surviving physics people who did this stuff couldn't see past the mathematical and linguistic maze that'd developed around the subject, they didn't "get" the design principles and the dependencies between the choice of initial design decisions and the characteristics of the resulting model, and they didn't appreciate the design aesthetics.

And I find that sad on so many levels.

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.