Theory and Experiment in Gravitational Physics by Clifford M. Will

Theory and Experiment in Gravitational Physics* is an excellent, if old, tract on the confrontation of general relativity and experiment (I read the revised edition of 1993).  The author, C. M. Will, however, gives regular updates in the literature (the last time was 2014, to my knowledge).  The theme of the book, really, is that General Relativity works and that, for the most part, its alternatives don't.  At least not very well.

This isn't to say that Will shortchanges alternative theories.  In fact, I'd say the opposite.  Will depicts a wide array of theories of gravity, mainly of the "metric theory" variety because only metric theories of gravity seems to be consistent with experiment -- and the Einstein Equivalence Principle (he hints that the earlier edition included more, and in a few places he includes more).  A metric theory satisfies three postulates:

1. The underlying space-time structure is defined by a metric tensor field.
2. The world lines of small objects are geodesics in space.
3. The local space-time geometry approximates a Minkowski space.

If you've worked with general relativity in the past, you were working with a metric theory of gravity.  It sounds like this would be an extremely restrictive culling of theories, but it turns out that there were already a large number of such theories of gravity being explored in the 1980's.  And if you read the update, you'll find more (including the f(R) theories).  Every one of these theories needs to have a tensor metric like general relativity, but they differ in having secondary gravitational fields, sometimes of quite different character (scalar, vector, or tensor), which changes the way in which matter couples to the metric...and therefore produce measurable differences in how space-time responds to the presence of physical objects.

The tests are presented in various ways. 

There is an early description of tests of the Einstein equivalence principle (which states that a small object will follow a geodesic trajectory), since that eliminates all non-metric theories.  The most important such test is the Eoetvoes experiment, which is a Cavendish-like experiment with bodies of different compositions; if this acts just like the Cavendish experiment, then the weak equivalence principle is sound.  And that is about a third of what you need to show that the Einstein equivalence principle is sound.  The other two points are local Lorentz invariance, which is tested by the Hughes-Drever NMR experiment, and local position invariance, which is tested by gravitational red shift experiments.  These tests restrict gravity to be a metric theory.

Since only metric theories are valid, Will then discusses a parameterized post-Newtonian framework for stellar system tests of gravitational theories.  By performing perturbative expansions of the dynamical quantities in the various gravities, he creates a suite of parameters that describe how gravity changes near bodies that are just a little more massive than can be described by classical physics.  Each metric theory has a range for each of these parameters in which it is viable.  So when measurements are taken, these parameters can be calculated by the data and then used to put limits on, and in some cases disqualify, theories of gravity.  Furthermore, many of these parameters indicate symmetry and conservation laws that are valid or invalid in the theory.  So even if a theory is not ruled out by experiment, this formulation tells you if, say, the law of conservation of angular momentum holds in it.

Getting to this point is essentially the first half of the book, and the second half mainly describes how different theories fare when confronted with the physical world.

His first foray is into what he calls the classical tests of general relativity, which he modifies because the gravitational red shift experiment is really a test of the weak equivalence principle.  So he swaps that out, and uses the deflection of light, the time-delay of light, and the perihelion shift of Mercury as his tests.  He then worries about tests of the strong equivalence principle -- which is very like the Einstein equivalence principle, but self-gravitating bodies cannot react to their own effects on space.  He finishes up with tests of gravity waves (which oscillate differently in different theories of gravity), binary pulsars (whose neutron stars should be dense enough to affect their own trajectories, if such a things is possible), and a variety of cosmological tests (this was before the anisotropy of the cosmic microwave background was discovered).

And after all this, general relativity survives and most of the other theories really don't.  Theories with additional vector and tensor couplings are right out, and scalar-tensor theories looked very doubtful. This is astounding because general relativity, with no free parameters, is the most restrictive theory of the bunch, the one with the least wiggle room to respond to those occasional experiments that are likely to tell the poor theoretician that his baby isn't as beautiful as he thought. In a Popperian world, this makes Einstein's theory the strongest or the survivors, and makes the scalar-tensor theories look bad -- especially when some theorist says that it's all this doom and gloom experiment stuff is okay, because you can always play with the parameters of his theory so that it will work (as one did in one of the papers Randy and I are reading for next week's recording -- it will probably be out around March).  These experiments are very effective to be able to eliminate so many different kinds of theories, and with the exception of general relativity, those that survive only survive by being slippery.

And that was what everything looked like in 1993.  If you look at Will's 2014 update, general relativity looks even better. Again, this is a wonderful book. We were going to use this, after Quantum Paradoxes, for the second book on PhysicsFM when we were doing that, and for good reason. It is little on the technical side, but if you've gotten through an undergraduate course in gravitation you should be okay (although there are a few chapters in the middle you might feel a little bit over your head in), and I recommend it heartily.

I need to find a better way to sign off.   I still sound like a recommendation letter.

I really hope this book gets that internship.

* Links are to Amazon pages. If you buy from them, they'll give Physics Frontiers a cut.

[Edit 5/2/2020 - Removed discussion of new edition, since it's been out for two years, and added new links to Amazon, because they kicked me out of the associates program for underperformance, again, probably in 2018.]