When it comes to quantum gravity and fundamental physics more generally, there is a lot we don’t know, and many different approaches to making progress. A top-down kind of approach attempts to figure out what the ultimate laws are, and then see what they might have to say about reality; string theory is the obvious example. But you could also take a bottom-up or phenomenological approach, in which you try to figure out what kinds of physical effects might arise due to quantum gravity and then go look for them, even if you haven’t derived them from a more complete theory. Tests of Lorentz invariance provide a good example, and the subject of my recent paper. This is the paper I mentioned writing with my (former) student Eugene; he now has a follow-up paper extending our work.
Lorentz invariance is simply the idea that there is no preferred direction in spacetime. Not only do the laws of physics not care about the direction in which you are looking (invariance under spatial rotations), it also doesn’t care about the speed at which you are moving relative to other stuff in the universe (invariance under “boosts,” as physicists would say). The idea is a cornerstone of relativity, and got a big boost (pun unintended, but accepted) when the Michelson-Morley experiment showed that the speed of light seemed to be the same in all reference frames — there was no evidence for a background “aether” with respect to which you could measure your velocity. But its roots actually go back to Galileo, who first proposed that all velocities were relative; to people on the sidewalk, the road is stationary and the cars are moving, but to people in the cars, they are stationary and the road is moving, and each perspective is perfectly valid.
Actually, this violating-Lorentz-invariance stuff is not new to me. Using cosmology to test Lorentz-violating theories was the subject of my first published paper. It was a collaboration with George Field (my Ph.D. advisor) and Roman Jackiw, both very accomplished theorists in astrophysics and field theory, respectively. My role as the meek young graduate student was largely to type in the data and make plots, but that’s how you get started in this business.
The theory we considered had a fixed timelike vector field without any independent dynamics, but it was coupled to electromagnetism in a specific way that violated parity as well as Lorentz symmetry. We showed that the coupling would cause a “twist” in the polarization of light coming from distant galaxies, and George knew that for certain radio galaxies you could determine what the polarization should be without any Lorentz-violating effect, allowing us to put a very tight limit. The data I typed in came from different sources, and consisted of the polarization information plus the distance (actually, the redshift) of the different galaxies. Years later, much to our surprise, this same data appeared on the front page of the New York Times. Two researchers had used our dataset but analyzed it in a different way, trying to constrain a vector pointing in a spacelike direction rather than a timelike one. The big difference is that they claimed to actually find a nonzero effect, which they announced in a press release before they made the paper available to other experts. Unfortunately they were just mistaken, as I recount in great detail here. But it’s still worth thinking about; indeed, some candidates for dark energy in the universe could lead to a very similar effect, so it’s worth improving the present data to put much tighter constraints (or to discover dark energy!).
What Eugene and I have done is a little different. We imagine there is a vector field through spacetime that violates Lorentz invariance (since you could, in principle, measure your speed with respect to it in an absolute sense), but we worry about its gravitational effects rather than its interactions with ordinary matter and radiation. Interestingly, we find that the vector field has no effect if there is no matter lying around, but it works to alter the strength of the gravitational field caused by matter. In other words, it changes the effective value of G, Newton’s constant of gravity. This would be an unobservable effect if it just changed Newton’s constant once and for all, since we have no experimental knowledge of what the constant was before the vector field messed with it. Fortunately, it changes it in different ways in different circumstances: making the effective value of Newton’s constant larger in the Solar System, but smaller when we consider the expansion of the entire universe.
Thus, we have an observational constraint: measure the value of G in the Solar System, use that to predict something about cosmology, and compare with the data. The most straightforward example is actually the primordial abundance of light elements such as Helium and Lithium. These were created at an early time after the Big Bang (between one second and a couple of minutes) as the universe expanded and cooled, and the precise amount of different elements you get depends sensitively on the expansion rate of the universe, and thus on Newton’s constant. We find that our vector field must be less than ten percent of the Planck scale, the fundamental unit in physics where gravity and quantum mechanics come together. The Planck scale is pretty big, so it’s not a great limit, but still an interesting one.