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Posted 19 August 2007

Is the speed of light constant?

by Frikkie de Bruyn

“ …..over very small distances, on the quantum level, there’s a possibility
that a photon may move at slightly less or slightly more than this [the speed of light] …speed.” Stephen Hawking.

The idea that the speed of light in a vacuum may somehow vary sounds crazy, doesn’t it? Einstein’s Special Theory of Relativity is based on the principle of the constancy of the speed of light! A study of the structure of space and time at the quantum level raises just such a possibility. Fact is that there is a very real possibility that a photon can have an energy dependent speed, and, the surprising part is that it does not violate the principle of relativity.

First, let’s look at a photon, the particle of light. Under normal circumstances a photon moves at a speed of 300 000 kilometres per second in a vacuum. But this is not always the case. In terms of the uncertainty principle of quantum mechanics (and a photon is a quantum object) the position and velocity of a photon can’t be pinned down precisely. All we can say is that the probability of finding a photon is spread out over a region. According to Richard Feynman and others the probability that a photon is travelling at 300 000 kilometres per second may be spread out over some “region” around that speed. It is the same as saying that the speed of a photon fluctuates more or less around what we call the speed of light. Over long distances this fluctuation cancels out and is not noticeable. Over small distances, however, the speed of light may fluctuate.

It is thought that the Big Bang started in a primordial vacuum when the Universe was as small as a quantum and space and time were very compressed. Everything was very dense, not a singularity, but almost there. In such circumstances we become very precise about the position of a photon (or any other particle for that matter) and in terms of the uncertainty principle the probability of the velocity of the photon becomes very imprecise, almost infinite. Near an almost infinite density the possibilities of the speed of light become almost infinite. I am not talking about large variations; in fact they are so small as to be almost undetectable. As we shall see recent experiments with gamma ray bursts in space, when two black holes or two neutron stars merge, may make it possible to detect such variations in the speed of light.
Since the 1980’s attempts to unify Einstein’s General Theory of Relativity with quantum mechanics became partially successful. Loop Quantum Gravity (LQG) and the string theory/M theory are the main contenders. Loop Quantum Gravity, which probes space and time at the Planck scale, found that space is not continuous at the Planck scale, but it is rather made up of discrete elements with a volume roughly the cube of the Planck length (which is 10-33 cm). A surface of one region of space dividing from another has an area only in discrete units, the smallest of which is roughly the Planck length squared. The point is that the volume of space can’t be just anything; it has to fall into some discrete series of numbers, just like the energy levels of atoms. In experiments involving cosmic rays and gamma rays it was found that the discrete structure of space at the quantum level may result in the scattering of the cosmic rays and gamma rays. This would result in such rays being observed at slightly different times, although it was emitted following the same event.

The quantum effect of such scattering is tiny, but at least some of them travelled over long distances, 10 billion light years or so. Over such long distances small effects will amplify to the point where the differences can be observed. In the quantum theory all particles such as protons and neutrons travel as waves. The effects of quantum gravity are also applicable to them. There are already surprises in the observation of cosmic rays, hitting the Earth’ atmosphere with energies more than 10 million times those we have ever produced. Such rays provide scientists with a set of ready-made experiments because they travel through the radiation and matter that fill the Universe. If the results can be confirmed in other experiments, it can be attributed to the effects of quantum gravity.

Scientists calculated how light travels in quantum geometry and the results showed that the speed of light has a small dependence on energy. Photons of higher energy travel slightly slower than low-energy photons. The effects are very small, but it amplifies over time. The result is that two photons produced by a gamma-ray burst 10 billion years ago, one redder and one bluer, should arrive on Earth at slightly different times. Such time delays should be detectable.

If experiments prove the energy dependence of the speed of light, scientists may be forced to modify Einstein’s Special Theory of Relativity. The big question is how drastically would the theory have to be modified? But there is another possibility. This is that the principle of Relativity is preserved, but Einstein’s Special Theory of Relativity
has to be modified, so as to allow photons to have a speed that depends on energy. And this appears to be a very real possibility. The exciting part is, if this proved to be true, it means that the speed of light could change according to conditions. This means that we could have an alternative to the inflation theory of Allan Gutt. If the speed of light was higher in the early Universe, you get an alternative to the inflationary cosmology that explains everything inflation does, without some of the problems.

Frikkie de Bruyn

Note: A good book to read in this regard is Lee Smolin’s "The Three Roads to Quantum Gravity".

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