Scientists studying radiation from a distant gamma-ray burst have found that the speed of light does not vary with wavelength down to distance scales below that of the Planck length. They say that this disfavours certain theories of quantum gravity that postulate the violation of Lorentz invariance.
Lorentz invariance stipulates that the laws of physics are the same for all observers, regardless of where they are in the universe. Einstein used this principle as a postulate of special relativity, assuming that the speed of light in a vacuum does not depend on who is measuring it, so long as that person is in an inertial frame of reference.
Unifying the cosmic with the quantum
In over 100 years Lorentz invariance has never been found wanting. However, physicists continue to subject it to ever more stringent tests, including modern-day versions of the famous Michelson–Morley interferometry experiment. This dedication to precision stems primarily from physicists’ desire to unite quantum mechanics with general relativity, given that some theories of quantum gravity – including string theory and loop quantum gravity – imply that Lorentz invariance might be broken. In particular, these theories allow for the possibility that the invariance does not hold near the minuscule Planck length – about 10–33 cm – since at this scale quantum effects are expected to strongly affect the nature of space–time.
It is not possible to test physics at the Planck length directly because this length corresponds to an energy of around 1019 gigaelectronvolts – way beyond the reach of particle accelerators (the most powerful of which, CERN’s Large Hadron Collider, will generate collision energies of around 104 gigaelectronvolts). However, this latest research, carried out by a collaboration of physicists under the leadership of Jonathan Granot of the University of Hertfordshire in the UK, has provided an indirect test of Lorentz invariance at the Planck scale.
Granot and colleagues studied the radiation from a gamma-ray burst – associated with a highly energetic explosion in a distant galaxy – that was spotted by NASA’s Fermi Gamma-ray Space Telescope on 10 May this year. They analysed the radiation at different wavelengths to see whether there were any signs that photons with different energies arrived at Fermi’s detectors at different times. Such a spreading of arrival times would indicate that Lorentz invariance had indeed been violated; in other words that the speed of light in a vacuum depends on the energy of that light and is not a universal constant. Any energy dependence would be minuscule but could still result in a measurable difference in photon arrival times due to the billions of light years that separate gamma-ray bursts from us.
The Fermi team used two relatively independent data analyses to conclude that Lorentz invariance had not been violated. One was the detection of a high-energy photon less than a second after the start of the burst, and the second was the existence of characteristic sharp peaks within the evolution of the burst rather than the smearing of its output that would be expected if there were a distribution in photon speeds. The researchers arrived at the same null result when studying the radiation from a gamma-ray burst detected in September last year, but could only reach about one-tenth of the Planck energy. Crucially, the shorter duration and much finer time structure of the more recent gamma-ray burst takes this null result to at least 1.2 times the Planck energy.
Constraining quantum-gravity
According to Granot, these results “strongly disfavour” quantum-gravity theories in which the speed of light varies linearly with photon energy, which might include some variations of string theory or loop quantum gravity. “I would not use the term ‘rule out’,” he says, “as most models do not have exact predictions for the energy scale associated with this violation of Lorentz invariance. However, our observational requirement that such an energy scale would be well above the Planck energy makes such models unnatural.”
Granot says that far more precise measurements would be needed to probe the Planck scale for theories that postulate a quadratic or higher-order dependence of light speed on photon energy. He also points out that his group’s approach probes just one of a number of possible effects of Lorentz invariance violation, and that extremely precise constraints on this violation have been obtained by studying the possible dependence of light speed on photon polarization from X-rays emitted by the Crab nebula. But he adds that his group’s new limit is the most precise for simple energy dependence.
Giovanni Amelino-Camelia of the University of Rome La Sapienza believes that the latest work points to the coming of age of the field of quantum gravity phenomenology, with physicists finally able to submit theories of quantum gravity to some kind of experimental test. “Nature, with its uniquely clever ways, might have figured out how to quantize space–time without affecting relativity. But even a slim chance of being on the verge of a new revolution is truly exciting,” he says.
