Friday, 2 April 2010

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.
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.

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.

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.

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.

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