Recommend some reading
Reverie said:
Do any theories of gravity exist other than general relativity that are capable of explaining the perihelion of mercury's orbit?
Several gtr textbooks or readable arXiv eprints discuss such alternatives, such as
- Nordstrom's gravitation theory, a conformally flat theory which fails various tests; see problems in the book by Lightman et al. and this Wikipedia article by myself,
- Watt-Misner gravitation theory, a simple "toy theory" with preferred background which nonetheless passes many (but not all) tests; see the original paper (which is very clearly written),
- Whitehead's gravitation theory, a discredited theory which some fringe figures have occasionally attempted to revive; see this Wikipedia article by myself and then this eprint,
- Brans-Dicke gravitation theory is the best known scalar-tensor theory (or rather a family of theories, with one free parameter chosen to fit observation; after this choice is made one has a specific gravitation theory); see Weinberg, Gravitation and Cosmology, Wiley, 1972, sections 7.3 and 9.9, and then various arXiv eprints which discuss various features of this theory (note that there is a running controversy about Einstein vs. Jordan frames)
- Graf's gravitation theory, which he calls "Ricci flow gravity", and which has some mathematically interesting features; see the original paper, in which the author has evidently taken pains to achieve clarity
Of these, the fifth is very new and has so far been little studied; certainly I have not verified the author's claims. The fourth does pass all the classical tests (with a sufficiently large choice of the free parameter). It has been claimed that the third passes them all, but this theory turns out to be inconsistent. The second theory was never viable (since it failed known tests when Watt and Misner proposed it as a toy possibly useful for some purposes). The first theory was never viable--- as Einstein pointed out when it was published, this theory is insufficiently rich to be have any hope of being viable, and in any case it flunks all but one of the classical tests. These problems were acknowleged by Nordstrom, who became an ardent champion of Einstein's theory, gtr.
Warning! I cited specific versions of two Wikipedia articles which I think I can vouch for (more or less; they were not in the form I intended when I quit WP due to the inefficiency of my efforts to ameliorate the promotion of crankery at WP), but you should aware that articles on alternatives to gtr (I meant alternatives once seriously proposed by physicists, but this holds true for alleged alternatives proposed by cranks) are perennial "crank magnets" at Wikipedia.
The above list is far from exhaustive; I could have mentioned
teleparallel gravity and various
higher order gravity theories which apparently also pass all the classical tests.
And ditto robphy on some good reading for "tests of gravitation" and reviews of the available evidence.
yogi said:
the tensor-scalar theory developed by Robert Dickie [has not] been subjected to falsifying type experiments
Not true, as I just explained! And the name is
Dicke. And this theory
has a coauthor, Carl H. Brans. Please try to avoid misstatements such as these which even a modest attempt at "fact-checking" would have prevented!
Reverie said:
In particular, I would like to know if a theory of gravity exists that does not impose the fact that nothing can exceed the speed of light in a vacuum.
1. By "impose" I take it you mean "imply" rather than "explicitly take as axiomatic".
2. Such a theory could not be a metric theory of gravitation, since this speed limit is built into the structure of a Lorentzian manifold, at the level of tangent spaces.
3. In metric theories, there is a distinction between "velocity" at the level of tangent spaces and in local neighborhoods. One might worry whether this enables one to work around the Lorentzian structure, e.g. in constructing hypothetical "traverseable wormholes". Be aware that while hypothetical models of spacetimes answering to such a description have been called "solutions of the EFE", this is seriously misleading in that if one starts with an arbitrary spacetime and uses the EFE to work out what the stress tensor must be, and then claims that all tensor so arrived at must be physically legitimate, one has violated the fundamental principle that a scientific theory should be falsifiable, and this is certainly not a misuse of gtr which would please most physicists (or which would have pleased Einstein).
Reverie said:
Newton's theory allows gravity to be explained without this assumption.
In this theory, the field far away from an isolated configuration of matter responds instantly to changes in the distribution of mass in the source of the field. As you may know, Newton himself stressed the physical implausibilty of this feature.
Reverie said:
Does a theory of gravity exist more accurate than Newton's theory, which is capable of explaining the perihelion of mercury's orbit without imposing a limit on the speed of light in a vacuum?
Do you mean "a theory which passes all tests so far"? Or "a theory which passes more tests than Newtonian gravity, but is ruled out by other tests"? In the second case, no physicist would be interested in such a theory unless as a "toy", if it had some feature of interest. It is not clear to me why you think that failure to impose a speed limit would be a desirable feature. How would you answer Newton's objections?
