Last October, I had a post that looked at the units known as the Planck length, Planck time, and Planck mass and discussed the question of whether these were just a universal set of standards that replaced the traditional ones of meter, second, and kilogram or foot, second, and pound, or whether they had a more fundamental significance. I pointed to a paper that suggested that the Planck length might represent a fundamental limit to the continuity of space, that at that level space ceased to be continuously divisible and became like a foam.

How would one test this idea? We usually use waves as probes but to be useful the wavelength of the wave has to be roughly comparable to the size of the object being probed in order to detect anything. This is why long sound waves seem to be largely oblivious to obstacles while short light waves are blocked by them. The Planck length is tiny 1.614×10^{-35} meters which at first glance would rule out our ability to measure its effects because our technology does not have anything that could probe on such a small scale. A wavelength of 1.614×10^{-35} meters requires photons to have an energy of about 10^{19} GeV. (If you are not familiar with these units of energy, don’t worry. It is sufficient to know that it is way out the reach of our terrestrial photon sources.)

But physics experimentalists are ingenious people and they have found a way to test this by looking at cosmic rays. These are bursts of high-energy rays that come from deep outer space and investigating their origins is an interesting research topic in its own right. Their energies are much larger than anything we can produce on Earth but we do not know when they will arrive or in what quantities or energies.

The theory is that within the spectrum of energies in an arriving cluster, the higher energy photons (with shorter wavelengths) would be more sensitive to any graininess of space than the lower energy ones (with longer wavelengths). This means that when you examine very brief burst of cosmic rays, higher energy cosmic ray photons would be slowed down by the graininess and would arrive later than lower energy cosmic rays from the same source. A 2005 experiment seemed to find just such a difference with higher energy photons from a galaxy around 500 million light years away arriving four minutes later than their lower energy counterparts, supporting the idea of Planck graininess.

But the effect seen was actually larger than theory predicted. A later study published in the journal *Nature* (vol. 462, pages 331–334, 19 November 2009) did not find such an effect, however. As its abstract states:

A cornerstone of Einstein’s special relativity is Lorentz invariance— the postulate that all observers measure exactly the same speed of light in vacuum, independent of photon-energy. While special relativity assumes that there is no fundamental length-scale associated with such invariance, there is a fundamental scale (the Planck scale,

l_{Planck}<1.62x10^{-33}cm orE_{Planck}=M_{Planck}c^{2}<1.22x10^{19}GeV), at which quantum effects are expected to strongly affect the nature of space–time. There is great interest in the (not yet validated) idea that Lorentz invariance might break near the Planck scale. A key test of such violation of Lorentz invariance is a possible variation of photon speed with energy. Even a tiny variation in photon speed, when accumulated over cosmological light-travel times, may be revealed by observing sharp features in c-ray burst (GRB) lightcurves. Here we report the detection of emission up to ~31GeV from the distant and short GRB090510. We find no evidence for the violation of Lorentz invariance, and place a lower limit of 1.2E_{Planck}on the scale of a linear energy dependence (or an inverse wavelength dependence), subject to reasonable assumptions about the emission (equivalently we have an upper limit ofl_{Planck}/1.2 on the length scale of the effect). Our results disfavour quantum-gravity theories in which the quantum nature of space–time on a very small scale linearly alters the speed of light.

Although the high-energy photon they looked at had an energy of ~31GeV which is far less than the Planck length, it is still high enough that the quantum foam of space theory predicts an observable lag in its arrival time. Not observing it puts a damper on the idea but you can be sure that tests will go on, hoping to observe even yet higher energy photons in cosmic rays.

Rob Grigjanis says

There have been a few distinct improvements on this constraint since then. This paper from 2011 puts the upper limit at about 3e-15 times the above.