Tuesday, 22 December 2015

General Relativity and MTW's Three Tests for Viability

At well over twelve hundred pages, "Gravitation" (1973, ISBN 9780716703440) by Charles Misner, Kip Thorne and John Wheeler, collectively known as "MTW" for short, is one of the thicker textbooks on general relativity.

MTW's section on gravitational testing (~p1066) suggests that there's not really much doubt over the correctness of general relativity, but that we're supposed to put up alternatives for the sake of scientific procedure, so that we can make comparisons and conclude objectively that the theory is wonderful. MTW then give three conditions that a theory has to meet in order to be considered credible enough to warrant being compared with Einstein's wonderful theory.

There are a couple of problems here: the first is that the main competitor class of theory to GR1916 seems to be the "Cliffordian" acoustic metric class which doesn't reduce to flat spacetime and special relativity, and is therefore not included in MTW's scheme before we even look at the three conditions. This means that the main class of theory that could hypothetically whup GR's arse is already excluded from the comparison, because its metric is too sophisticated to fit the "clunky" SR-based defintions that act as a foundation for a lot of work on GR. All we're supposed to compare with GR is other similar SR-reducing theories, which means, essentially, other variations on the existing GR1916/60 theme.
The assessment is basically "skewed and screwed"  before we even begin.

The second problem is that even though the three critical tests seem to have been designed to make the 1916 theory look good, GR1916 still manages to fail at least one out the three, from the perspective of someone in 2015 it fails at least two out of the three, and when we look at the original theory before its  1960 reboot, that version arguably fails all three tests.

This is not good.

MTW, page 1066:
" Not all theories of gravitation are created equal. Very few, among the multitude in the literature, are sufficiently viable to be worth comparison with general relativity or with future experiments. The "worthy" theories are those are those which satisfy three criteria for viability: self-consistency, completeness, and agreement with past experiment. "
Let's examine these criteria:


We know (and MTW presumably also knew in 1973) that Einstein's 1916 theory had already been found in 1960 to have failed the test of internal self-consistency. That's when the theory had a crisis in which it was discovered that the principle of equivalence, arguably the foundation of the theory, appeared to be fundamentally irreconcilable with special relativity. Einstein had warned in 1950 about potential issues related to his original "pragmatic" decision to include SR as a limiting case in 1916, subsequently arguing that this wasn't obviously a legitimate feature of a general theory. He died in 1955 before the 1960 crisis vindicated his concerns:

Alfred Schild, "Equivalence Principle and Red-Shift Measurements" Am. J. Phys. 28, 778 (1960):
" ... special relativity and the equivalence principle do not form a consistent theoretical system. "
If the principles of general relativity ruled out the inclusion of SR, we'd lose both major theories of relativity and have to rewrite a new single-stage general theory to replace both previous layers. Since the "total rewrite" option was considered unacceptable, we instead rejected the very idea that SR could be wrong, and declared that SR was an unavoidable part of any credible gravitational model. The principle of equivalence therefore had to be suspended every time it was about to collide with SR and crash the theory, because any process that crashed the theory was by definition, not a correct process under that theory.

So GR1916(original) never was a self-consistent theory, and the 1960 "reimagining" that tried to fix this cannot be said to be meaningfully self-consistent, because it only achieves a more limited form of consistency by setting up protocols for coping with failures in an orderly and consistent way. This is like the difference between a self-driving car that never crashes, and a car that crashes repeatedly, but comes with seatbelts and airbags and crumple zones, and instructions for when to override the autopilot. GR1960 does failure management rather than failure avoidance.


MTW's second criterion is that
" ... it must mesh with and incorporate a consistent set of laws for electromagnetism, quantum mechanics, and all other laws of physics. ... "
At the time those words were written, it probably seemed that GR1916/60 met all those requirements, but since the theoretical discovery of black hole radiation in the Seventies, we've realised that textbook GR very much does NOT mesh with quantum mechanics.

Kip Thorne, "Black Holes and Timewarps" (1994) , p237:
" ... looking at the laws of general relativity and the laws of quantum mechanics, it was obvious that one or the other or both must be changed to make them mesh logically. "
So, assuming that current QM is basically correct, GR (past and present) also currently fails MTW test number 2. We can try to  hypothesise a larger theoretical structure – a theory of quantum gravity – that somehow contains both theories, and this is what the classical physics guys have been holding out for ... but forty years later, nobody's managed to come up with one that works without modifying GR. Current GR and QM seem to have fundamentally incompatible causal structures and definitions that would make their predictions irreconcilable, so if QM is right then we'd seem to be using the wrong general theory of relativity.


This is an odd one. It's natural to ask that a theory agree with experiment (at least reasonably well) because we need it to agree with reality. So why use the word "past"? Aren't all experiments past? Do current experiments not matter?

Setting aside that one ambiguous word, GR obviously doesn't obviously agree with all current, recent gravitational experimental data. MTW mentions "the expansion of the universe" as one of the things that  gravitational theory has to get right, and textbook GR gets expansion characteristics wrong unless we invent a new thing, "dark energy", specifically to make up the shortfall between what GR predicts and what our hardware reports.

Similarly, GR currently "under-predicts" the cohesiveness of large systems such as galaxies – the rotation curve of spiral galaxies seems to be wrong, and suggests that either the gravitational attraction within a galaxy is somehow greater, or the interaction across intergalactic voids is weaker. We'd get the second effect (and a stronger expansion characteristic) if GR was the wrong theory, and the real theory was more aggressively nonlinear, so both these things are arguably "warning flags" for the theory being faulty. Instead, we prefer to explain the extra cohesiveness by inventing a whole new form of matter ("dark matter") which obeys different rules to the rest of the universe, is conveniently invisible and unreactive (except gravitationally), and which has no theoretical basis or  reason to exist other than to help us to balance the books.

With dark matter and dark energy, we can't currently say that GR agrees well with experiment because we can't currently demonstrate that these things are real and not just ad-hoc devices that let us write "blank cheques" for any mismatch between GR and reality. GR enthusiasts might interpret the situation as meaning that once dark matter and energy are added, the theory matches the data excellently ... but they can't dispute the fact that textbook GR is currently functionally indistinguishable from a theory that fails to agree with the available data. General relativity cannot be shown to pass test #3, without making so many "creative" external ad hoc adjustments that nominally "passing" the test carries no real significance.

MTW 1973:
" Among all bodies of physical law none has ever been found that is simpler or more beautiful than Einstein's geometric theory of gravity ... as experiment after experiment has been performed , Einstein's theory has stood firm. No purported inconsistency between experiment and Einstein's laws of gravity has ever surmounted the tests of time. "
We're no longer in a position to make this statement.


According to MTW, failing any one of these conditions means that a theory is to be regarded as not worth pursuing and not worth testing. A sceptic could argue that the 1916 theory technically appears to fail all three tests, and with even the most optimistic and most generous interpretation of MTW's criteria, where the theory "only" fails test #2, we'd still be obliged to write off the current general theory as not being a credible theory of gravitation.