What is a good book on alternative theories of Special and/or General Relativity?
Why do you want alternatives? These are two of the most accurate and best validated theories that we have.
I'm not aware of any good BOOKS on alternate theories but the Internet is full of crackpot sites that will give you plenty of them. It won't be actual science, but if alternate theories are what you are after, there will be plenty of them.
How do I know that if I don't know the alternatives and whether they're less or more accurate than SR or GR?
That makes absolutely zero sense.
I'm re-opening with this http://en.wikipedia.org/wiki/Alternatives_to_general_relativity
There are many alternatives to relativity that aren't crackpottery. Many of those alternatives are disproven however. It is allowed to discuss these theories, but only in an historic context since their validity has been disproven. Also, GR and SR are very successful and accurate theories, questioning their validity (in the cases its applicable) is not allowed. Thank you Micromass for this post.
Just to make sure you're clear, there are no alternatives that are more accurate than either of these theories. If there were, they would be adopted.
There are also modern theories such as String Theory and Loop Quantum Gravity that aim to extend GR beyond it's domain of applicability. They don't compete with GR, but that might be what the OP is interested in.
For special relativity, there are no serious competing or alternative theories nowadays, as far as I know. There do exist "test theories" that generalize SR by including tunable parameters. One set of parameter values produces SR. Other parameter values produce variations on SR. These theories are used to analyze experiments to determine how close their results agree with SR. That is, they are tools for testing the validity of SR in a quantitative way.
Some people misunderstand the purpose of these theories, and promote them as alternatives to SR.
Reference #4 on the Wikipedia page above is a book by Zhang that discusses this sort of thing in detail. (I've never seen the book itself, but I've read about it in discussions about SR)
"GR is one of several possible covariant theories of gravity. It is only from observation and experiment that we conclude that GR is the valid theory."
An historically important alternative to GR was Nordstrom's theory of gravity, the first theory of gravity consistent with special relativity. It is not consistent with observation, because it predicts the wrong sign for the perihelion precession. Nordstrom's theory is formulated as a field in flat spacetime. Einstein and Fokker showed that Nordstrom's theory could be equivalently formulated as a curved spacetime theory. Later Einstein formulated GR, which is a different theory, but also based on curved spacetime, and which can be reformulated (under some conditions) as a field in flat spacetime.
Deviations from Lorentz invariance are discussed, including the use of alternative theories, by Mattingly http://relativity.livingreviews.org/Articles/lrr-2005-5/ [Broken] .
You can also see alternative theories to GR discussed in section 3.2 of http://relativity.livingreviews.org/Articles/lrr-2006-3/fulltext.html [Broken] .
Clifford Will has a good popular book "Was Einstein Right?".
There seems to be ignorance here surrounding what an alternative theory to GR actually is. OP if you're interested, take a look at the end of chapter 4 of "Spacetime and Geometry"-Carroll and the references given therein.
You might also be interested in GR equivalent theories such as teleparallel gravity, in which case start here: http://arxiv.org/pdf/gr-qc/0011087v1.pdf
GR is to teleparallel gravity as Newton-Cartan theory is to standard Newtonian gravitation theory.
Gauge Theory of Gravity
A major alternative to GA is the gauge theory of gravity as presented in
"Geometric Algebra for Physicts" by Doran and Lasenby
This is a first order theory including spin (there are two gauge fields) and it is formulated on flat space time. All measurable predictions (so far) agree with GA. However, if the gauge theory of gravity there are no wormholes.
Some good ones I found, which all advocate Weber's electrodynamics:
Wesley's https://archive.org/details/SelectedTopicsInAdvancedFundamentalPhysics [Broken]
Assis's Weber's Electrodynamics
Assis's Relational Mechanics or his 2014 update, Relational Mechanics and Implementation of Mach's Principle with Weber's Gravitational Force.
Weber's force law only depends on relational quantities (i.e., relative position, relative velocity, relative acceleration).
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