Was Einstein wrong?

Gravity is the most obvious of the four forces of nature (gravity, electromagnetism, and the strong and weak nuclear forces). It’s also the first for which we had a sensible physical theory: Newton’s law of universal gravitation. Now we have sensible theories for all four of the forces, and Newton’s theory has been superseded by an even better theory, Einstein’s general relativity (GR).

GR has passed a series of experimental challenges with flying colors: the precession of Mercury, deflection of light, gravitational redshift and time delay, gravitational radiation from the binary pulsar, and the expansion rate of the early universe during the nucleosynthesis era. But it doesn’t quite fit in with the rest of physics, since the other three forces seem to be compatible with quantum mechanics in a way isn’t so obvious for gravity. So very few people really believe that general relativity is the final answer; at some point we’ll have to invent a better model (string theory being the leading candidate) that is intrinsically quantum-mechanical yet reduces to GR in the appropriate regimes.

Usually in field theory, if a model works well in a certain regime, you might expect it to break down at shorter distances or higher energies, but continue to be successful at long distances and lower energies. Nevertheless, people have begun to ask whether general relativity might be okay in the solar system but break down on much larger scales (galaxy- or universe-sized distances). The primary motivation for such suggestions is the fact we need to hypothesize dark matter and dark energy to make sense of our universe if GR is correct. It is very likely that GR is correct, and dark matter and dark energy are both for real, but since we can’t be sure we consider the possibility that our understanding of gravity is to blame.

Of course, it’s easy to say “let’s modify gravity,” much harder to come up with a good model. Indeed, it’s not even obvious what issue you’d like your model to address — the need for dark matter in galaxies, clusters, and large-scale structure; or the perplexingly small value of the cosmological constant; or the acceleration of the universe conventionally attributed to dark energy.

Modifying gravity with the goal of replacing dark matter is a long-standing project that has met with mixed success, most famously pursued by Milgrom and his friends. Milgrom has an idea called “Modified Newtonian Dynamics,” or MOND for short. For some introductions see pages by Greg Bothun or Stacy McGaugh, or this review by Sellwood and Kosowsky. The idea is to slightly increase the Newtonian gravitational acceleration when that acceleration is very small, so that slowly-moving particles feel more force than they ordinarily would, mimicking the presence of unseen matter. This idea works extremely well for individual galaxies; indeed, Milgrom made predictions for the behavior of low-surface-brightness galaxies before they were directly observed, and the predictions were later confirmed very nicely.

Unfortunately, there are problems with the MOND paradigm itself. For one thing, it’s not really a “theory”, it’s just a rule for making predictions in a very specific set of circumstances — slowly-moving particles orbiting around massive bodies. (Just as an observational matter, it doesn’t even seem to work very well for clusters of galaxies, although it does quite well for individual galaxies.) Since it’s not a full-blown theory, it’s hard to make predictions for other tests you might like to do, like deflection of light or cosmology. So people have been trying to invent an actual theory that reduces to MOND in the appropriate circumstances. In a recent proposal, Bekenstein has claimed to succeed; now people are at work putting this idea to the test, to see both if it makes sense and if it agrees with other things we know about cosmology.

In addition to the theoretical difficulties, there is at least one model-independent reason to think that no modification of gravity will ever replace the idea of dark matter: we seem to be accumulating evidence (tentatively at the moment, to be sure) for gravitational forces pointing in directions where there is no ordinary matter. The most basic such clue comes from studies of gravitational lensing of clusters of galaxies, which can be used to reconstruct the distribution of dark matter in the clusters. The upshot is that the dark matter seems to be distributed much more smoothly than the ordinary matter; see this reconstructed cluster image for an example. Less direct evidence is found in the acoustic peak structure of the temperature anisotropies in the cosmic microwave background. (For an intro, see Wayne Hu’s tutorial.) Density fluctuations in the plasma of the early universe lead to sound waves, in which regions become more dense and therefore hot, and then bounce back and become less dense, in a repeating cycle; this leads to peaks in the plot of temperature fluctuation as a function of angular scale. But fluctuations in the dark matter don’t heat up (they don’t interact with light, since they’re dark), so they only increase with time. Consequently, odd-numbered peaks have ordinary matter and dark matter in phase, and even-numbered peaks have them out of phase. The out-of-phase oscillations are suppressed, so we expect dark matter to boost the odd-numbered peaks. This is exactly what appears to happen, as this figure indicates. At least a little bit; the data need to improve before we can be sure. But it’s hard to see how a modified theory of gravity could explain this phenomenon.

Of course, perhaps a modified theory of gravity could predict gravitational forces pointing in directions other than where there is ordinary matter; you’d have to tell me the theory first before we could say for sure. MOND doesn’t, though, and such a theory is even harder to imagine than one that simply fits the galaxy data.

Tomorrow I’ll talk a little about modified gravity and the issues of vacuum energy and the accelerating universe.