In this illustration, one photon (purple) carries a million times the energy of another (yellow). Some theorists predict travel delays for higher-energy photons, which interact more strongly with the proposed frothy nature of space-time. Yet Fermi data on two photons from a gamma-ray burst fail to show this effect, eliminating some approaches to a new theory of gravity. Click for an animation that shows the delay scientists had expected to observe. Credit: NASA/Sonoma State University/Aurore Simonnet
Sometimes a single photon can tell us a lot. Especially when it comes barreling toward us with extremely high energy from a gamma-ray burst billions of light-years away. If you catch just the right photon in just the right way, it might even tell you something about the fundamental structure of space-time and provide guidance toward unifying gravity and quantum physics.
In a paper first published on the arXiv on August 13, and then published in Nature today, the Fermi Gamma-ray Space Telescope team presents a reconstruction of the gamma-ray burst GRB090510, observed on May 10, 2009. The burst included a 31 GeV photon, one of the highest-energy photons ever observed from a gamma-ray burst. Although no grand sweeping statements can be made, this observation does place some limits on the kinds of theories physicists can develop about the nature of space-time.
This burst and photon have already received a lot of attention over the past few months and will get a lot more in the coming days, probably with a series of arguments and claims about how this kills or doesn’t kill various theories of quantum gravity. Based on what has already happened on the Web, the discussion is likely to become pretty rancorous with a small re-inflammation of the string wars on the way. But behind all the shouting, there is a lot of interesting science going on here and the real potential to increase understanding of astrophysics and provide some guidance for the future of quantum gravity theories.
What quantum gravity says about space-time
To set the scene, we need to know a little about quantum gravity. At this time, there is no complete theory of quantum gravity, but there are various frameworks for trying to understand the problem. String theory and loop quantum gravity are probably the best known of these, but there are many other attempts to build quantum physics and gravity into one theory.
Without going into details of specific frameworks, many quantum gravity frameworks adopt the idea that space-time itself might be quantized, or made up of some kind of fundamental unit or grainy structure, down on the level of billionths of billionths of the size of an atom’s nucleus. If that is indeed the case, there are many reasons to think that light moving through that quantized space-time might “feel” the quanta as it travels. One consequence could be that light of different energies would travel at different speeds.
The biggest problem is that no frameworks of quantum gravity really make concrete predictions of anything much. Instead, much of this research is phenomenology, a realm that sits somewhere in between fundamental theory and experimental observation. Phenomenological theories are designed to match experimental observation, and are often inspired by ideas from fundamental theory, but generally can’t be derived purely from fundamentals.
For example, some quantum gravity frameworks suggest that space-time is quantized. This could show up as the speed of light depending on the energy of the photons. But if it does, then the speed of light should vary with energy in some generic way that can described by an equation. In particular, it seems reasonable that the speed of light should be modified by a small correction that depends on the ratio of the energy of the light to some other energy scale. Quantum gravity frameworks suggest that the appropriate energy scale is called the Planck energy. And because energy scales and distance scales are related in these frameworks, that energy corresponds to a length called the Planck length, which is about the scale on which space starts to look like it is made up of little chunks rather than a continuum. The Planck length is about 10-35 meters—a proton is about 100 billion billion times larger in diameter.
That equation that relates speed of light to energy can’t yet be deduced strictly from the fundamental quantum gravity ideas but these phenomenological equations should have the right structure and properties. Importantly, the equation can be tested against observation. If scientists could observe light of different energies traveling over long distances, they might be able to notice any differences in speed and see if the equation matches.
If that phenomenological equation does matches observation, it gives theorists a hint that their underlying theories could be on the right track and that the details should predict the kind of universe that equation describes. If not, then theorists had better look elsewhere.
Light from gamma-ray bursts
Physicists realized a decade or so ago that if light of different energies travels at different speeds, then the current generation of gamma-ray space telescopes might be able to observe those effects. What would be needed is to observe light coming from a compact source in a short burst a long way from us. By being compact and from a short burst, physicists could be confident that the light is all starting from the same place at the same time. By being a long way off, the light has enough of a chance to separate out, with the highest energy light being delayed slightly relative to the lower energy light. It might seem strange that it is the highest-energy light that is delayed, but a hand-waving argument for this is that the highest energy photons are more likely to interact with the graininess of space-time and so feel its effects more and are slowed most.
GRB090510 is precisely the kind of burst that physicists were hoping for to make this kind of measurement and test, and the Fermi telescope managed to collect good clean data to analyze.
Of course, nothing in astrophysics is as simple as it might sound, and the situation here is quite messy. For starters, nobody knows precisely what happens in a gamma-ray burst. Without knowing the mechanism of the burst, they can’t pin down precisely where and when the gamma-ray photons come from. That means physicists can’t just compare the arrival times as they depend on energy and calculate a speed. Instead, physicists can place some limits on how much quantum gravity effects could influence the speed working under a set of assumptions about the astrophysics involved. In particular, they can look at their phenomenological equation and see what the measurements say about the energy scale of quantum gravity.
The energy scale of quantum gravity
At what scale should quantum gravity become important? We mentioned earlier that the Planck energy and Planck length might be the reasonable scales. One key reason to choose these scales is that they occur naturally as scales defined by the other various constants of nature such as the speed of light and the strength of gravity. Indeed, one way to look at this is to say that any other choice of energy or length scale would require justification. That is precisely the position particle physicists find themselves in as they try to understand why particles have the masses they have and why various phenomena seem to occur at particular energies. Particle physics doesn’t seem to live in the simplest possible world, so to solve those issues physicists need to invoke ideas like symmetry breaking and other concepts more complicated than what the simplest possible universe would require.
Conceptual arguments and choosing the simplest path forward implies that the appropriate scale to observe effects seems to be this Planck scale, and it is often represented by the Planck mass in the equations. (The Planck energy, length, and mass are all related to each by multiplying or dividing by constants of nature.)
If the dependence of speed on energy has the simplest form possible, then the time delay between high- and low-energy photons depends on the energy difference between them and an appropriate mass scale for quantum gravity. So by measuring the time delay and energy difference, physicists can determine limits on this mass scale and see whether it matches up with the expected Planck mass.
What the measurement says about the mass scale of quantum gravity
When the Fermi team did the calculations, using the most conservative estimates for how astrophysics plays into this, they determined that the mass scale must be at least 1.2 times the Planck mass, and by using reasonable but less conservative assumptions, they derived lower limits on the mass scale of up to 100 times the Planck mass. One way to interpret this is to say that there is no variation of the speed of light coming from any quantum gravity effects at less than 1.2 times the Planck mass. And given that some quantum gravity frameworks predict that effects should be showing up at that point, perhaps those models are simply wrong, and there is no changing speed of light.
There are, however, quite a few caveats. The limit on the mass scale is only true if the quantum gravity effects show up in the simplest possible phenomenology where the time difference is proportional to the energy difference scaled by the quantum gravity mass. Some models suggest that the time difference might be proportional to the square of the energy difference scaled by the quantum gravity mass. That would be a much smaller time difference and not observable in this kind of experiment.
Additionally, other quantum gravity models could still have quantized space-time but wouldn’t show an energy-dependent speed of light in this form. Instead, speed might depend on the polarization of the light (called birefringence, like the optical property of calcite crystals which create two images when you look through them). There are other options floating around as well.
To be fair to the claim, though, ruling out the simplest dependence of speed on energy at the expected Planck scale is a significant constraint on future theories of quantum gravity.
The future of quantum gravity theories
In one sense, this result doesn’t change a whole lot. None of the quantum gravity frameworks were really predicting concrete results so it is not really an explicit test of quantum gravity, nor does it rule out any particular frameworks. It does, however, provide guidance to theorists about what kinds of theories might be viable as they develop their ideas further, and that is pretty important to the field. Any experimental constraints are good constraints, especially as string theory is now in a position of predicting almost anything and this result limits some of the versions of string-like theory. Meanwhile, loop quantum gravity had a class of ideas that have now been ruled out.
What is particularly clear is that the technique of observing gamma-ray bursts is powerful for placing real observational limits on the kinds of predictions that quantum gravity can get away with. The Fermi Gamma-ray Space Telescope likely to see many more bursts that can even more tightly constrain quantum gravity theories and some theorists have suggested that combining the observations of gamma-ray bursts with neutrino observations, it might be possible to develop tighter constraints or even measurements of how much light speed changes with energy if the speed of light does indeed depend on energy.
Read more
Fermi Telescope Caps First Year With Glimpse of Space-Time -- NASA press release, October 28, 2009
Constraining Modified Dispersion Relations with Gamma Ray Bursts -- BackReaction blog, June 26, 2009
Prospects for constraining quantum gravity dispersion with near term observations -- Preprint by Giovanni Amelino-Camelia and Lee Smolin, June 23, 2009
Update: Some other news coverage that has appeared since this was published
An intergalactic race in space and time -- Nature (news section)
Quantum gravity theories wiped out by a gamma ray burst -- ars technica (looks like it got the embargo time wrong so it came out early)
Special relativity passes key test -- Physics World
NASA's Fermi Gamma Ray Space Telescope is an astrophysics and particle physics partnership, developed in collaboration with the U.S. Department of Energy, along with important contributions from academic institutions and partners in France, Germany, Italy, Japan, Sweden and the United States.
