# Testing general relativity

Some slightly-recycled content. (But it’s new to you, right?) Science writer Amanda Gefter is working on an article for Sky and Telescope about testing general relativity. (See other articles by Amanda here and here.) She emailed me to ask some general questions about the state of GR and its experimental tests; here are the questions and my answers, just off the top of my head.

What are scalar-tensor theories of gravity? In these theories, where does the extra field come from (in other words, what is it, and why is it there?) How do these theories modify GR? If a scalar-tensor theory is found to explain experimental results, does that necessarily mean that there are extra dimensions? How viable do you think these theories are?

Scalar-tensor theories are simply generalizations of GR that add a new scalar field that interacts directly with gravity (i.e., couples directly to the curvature of spacetime). A scalar field is like the electromagnetic field, except that it only has a magnitude and not a direction; it simply takes on a single numerical value at each point in spacetime. The first scalar-tensor theories proposed that the gravitational constant, which fixes the strength of gravity, could have a variable strength that depended on some scalar field; but current theories are more general.

Scalar fields can arise in different ways. Often, they are simply put there. They can also arise from extra dimensions of spacetime, or from superstring theory. But if we find a scalar field, it certainly doesn’t imply the existence of extra dimensions, as there are many other ways to get such scalars.

Scalar-tensor theories are simple and natural generalizations of GR, and it wouldn’t be surprising if one of them were true. However, many theories that are studied in the literature assume that the scalar field is very light, and therefore leads to (potentially detectable) effects at large distances. It’s much more likely that any such scalar has a significant mass, perhaps near the Planck scale, and so would remain undetectable in any conceivable experiment. However, we know little for sure, so it pays to keep an open mind.

Are there other alternatives to GR that are being explored? Any that you find particularly promising?

There are many alternatives being explored, too many to list or even catalogue. The most straightforward, and perhaps most promising, imagine that something like GR is true in extra dimensions, and lead to a modified theory at the level of our observed four-dimensional spacetime. The ways in which this theory can be modified will depend in the specific model of extra dimensions; it has been proposed that such theories can help explain the value of the cosmological constant, or explain the acceleration of the universe without any cosmological constant, or affect cosmology at very early times. It is also possible to modify GR directly in four dimensions to help do away with the need for dark energy.

Other models try to do away with the need for dark matter, by modifying gravity on the scale of galaxies. A famous example is MOND (Modification Of Newtonian Dynamics) by Milgrom, although that is more of an “idea” than a “theory” (although Bekenstein has recently tried to put it on a more sound footing). The biggest problem with such models is that they have a very hard time reproducing the many successes of the dark matter idea, for example in accounting for the perturbation spectrum of the cosmic microwave background.

Finally, there are models that don’t try to explain some specific feature of astrophysical observations, but instead simply try to see how far we can go in modifying GR. For example, there are models which violate Lorentz invariance at a fundamental level. These are interesting to explore, if only to help us understand the extent to which GR can be trusted.

Why is it important for us to test GR? Has it become more imperative in recent years?

Gravity is an important force, and GR is our best theory of gravity, so it should be tested as well as we possibly can. More specifically, cosmological observations (dark matter, dark energy, and primordial perturbations) have revealed a universe that seems very surprising to us, and our interpretations of these observations rely on extrapolating ordinary GR to scales of time and distance that are far larger than where it has been directly tested. So any new tests can give us more confidence that we have the right to make such extrapolations.

Why is our understanding of gravity so important?

See above. On the large scales characteristic of cosmology, gravity is by far the most important force. In addition, it is the only force that has thus far evaded a quantum-mechanical understanding; reconciling GR with quantum mechanics is the greatest single quest in contemporary fundamental physics, and any information we have about gravity itself could be an invaluable clue along the way.

Up to this point, is GR a well-tested theory?

It is extremely well-tested in certain regimes, less so in others. Three regimes have been especially well-tested: the Solar System, where precision measurements have tightly constrained deviations from GR; the binary pulsar, whose orbit implies exactly the amount of gravitational radiation predicted by GR; and the early universe, where observations of light elements produced by nucleosynthesis and the anisotropies of the cosmic microwave background provide good evidence for the validity of GR when the universe was seconds old and hundreds of thousands of years old, respectively.

There is still a lot we don’t know. For example, are the predictions of GR for gravitational lensing and dynamical measures of mass consistent with each other? Are there deviations at very strong curvatures, or for that matter very weak curvatures? Are there deviations at very small distances that may be probed in the laboratory? (Current best limits go down to about one tenth of a millimeter.) Are there long-range but subtle effects that still may show up in the Solar System?

As I understand it, GR has been inadequately tested in the strong field regime. Why is it important to test GR in such extreme circumstances? What kinds of tests will be helpful? In particular, how can we use black holes to test GR?

I wouldn’t say “inadequately”, but we can always do better. To be honest, I think that testing GR with black holes is interesting, but somewhat overrated. If GR is going to be modified, there are two likely ways it can happen: subtle long-range effects, and deviations that become important when the curvature of spacetime reaches a certain fixed value. In the first case, Solar System tests will usually do better than astrophysical tests, just because the precision is higher. In the second case, we would have to get extremely lucky indeed to notice any effects in black holes. The curvature outside astrophysical-sized black holes is actually not that great; the curvature radius would be measured in kilometers, while we would probably need to go to much smaller scales to observe any deviations from general relativity.

On the other hand, as already mentioned it’s important to keep an open mind. Many of our tests of GR thus far have either been in cosmology or in the quasi-static, weak-field regime of the Solar System, with the binary pulsar being the notable exception. Even if our most respectable alternative theories wouldn’t necessarily show up first in a dynamical, strong-field situation, we should certainly do as many tests in such regimes as we can, if only to make sure there are no surprises.

Is it strange to use black holes as testing grounds for GR when they them selves are consequences of the theory of GR? (in other words, if GR were wrong, would there even be black holes?)

Most respectable theories of gravity (all that I know of, to be honest) predict that there should be black holes, although their properties might be different in different models. So they are well worth investigating, keeping in mind the previous answer.

I understand you worked with Ed Guinan on DI Herculis — what are your thoughts on that problem? Do you think it points to a gap in GR, or is it an experimental anomaly? Are physicists worried about it?

It’s a very interesting system, and I don’t know what is going on. I became skeptical that gravity is to blame when I worked out that the stars in DI Her are well within the weak-field regime where Solar System tests have already tightly constrained any possible deviations from GR; it seems very hard indeed to find a theory that could explain the motion of DI Her yet remain consistent with Solar-System tests. So I suspect that some astrophysical phenomenon is causing the discrepancy, but I’m by no means certain.

Have there been any other observations that seem to violate GR?

It’s hard to say that any given observation violates GR, since there are always other assumptions that come into play. For example, the anomalous acceleration of the Pioneer spacecraft may be due to some extremely unexpected gravitational effect; more likely, however, there is some much more mundane explanation involving the spacecraft themselves. So far, there is certainly nothing we have observed that gives anything like a good reason to doubt GR.

In your opinion, what have been the most significant tests of GR?

Historically: precession of Mercury, deflection of light, gravitational redshift, and gravitational time delay. More recently: the binary pulsar and cosmological nucleosynthesis.

Any thoughts on the importance of Gravity Probe-B? Lunar laser ranging?

GPB is in a somewhat awkward position; it will either confirm the GR prediction for frame-dragging, or it will find a discrepancy and very few people will believe it. I’m not an expert, but my understanding is that the regime it is testing (in the “parameterized post-Newtonian” sense) has already been ruled out by other observations.

Lunar laser ranging is a very different story, well worth doing. There is an opportunity to greatly improve the precision of constraints on long-range deviations from GR, which is always interesting, even if there is no firm prediction from a specific model.

Will the detection of gravity waves be an important confirmation of GR?

Yes, absolutely. At this point, however, very few people doubt that gravitational waves exist, with essentially the properties predicted by GR, so they are more looking forward to learning about the astrophysical sources of the waves. If the observations are somehow inconsistent with GR, that would be an even more spectacular finding than anyone expects.

What makes general relativity such a beautiful theory?

It is extremely powerful (accounting for all gravitational phenomena ever observed), mathematically compelling (applying elegant results from differential geometry), and remarkably simple and robust (unlike, say, the Standard Model of particle physics). GR is simply the statement that “Gravitation is the curvature of spacetime”, made precise and mathematical; few theories in science are simultaneously so simple, elegant, and comprehensive.

Finally, do you think that GR will ultimately prove to be wrong (or incomplete) at some level?

Yes. Everybody (in their right mind) does. GR is a classical theory, fundamentally inconsistent with the quantum world in which we live. At the very least we will have to find a quantum version of GR; more likely, we will have to find some more profound theory that is intrinsically quantum-mechanical and reduces to GR in the appropriate circumstances. If experiments reveal deviations from GR at even the classical level, so much the better.

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