I mentioned last week that I would not be surprised if neutrinos do travel faster than photons (as suggested by the recent highly-publicised OPERA experiment). But this definitely does not mean that I think Einstein's theory of relativity is wrong or any of the other nonsense that was printed in the papers. If anything, I think Einstein's mistake was calling the maximum speed the "speed of light".
Are Neutrinos Tachyons?
The newspapers have spouted all sorts of nonsense, that if the result is correct it means that neutrinos are tachyons, sending messages back in time would be possible, extra dimensions, etc. Let's look at these first.
It is a common misconception that Einstein said that if you can send a message faster than the maximum speed you can send it backwards in time. I do not believe you can send a message faster than this but if you could the maths does not say that the progress of time becomes negative but in fact it becomes "imaginary" (ie involves the square root of negative numbers). I believe anything that involves imaginary numbers does not exist in the real world.
Another idea is that there are extra spatial dimensions and neutrinos are somehow taking a shortcut. Extra dimensions are often used in theories (eg string theory) but people should remember what Einstein himself said - "keep it as simple as possible, but no simpler". Adding extra dimensions, which we have no proof of, just makes things much more complex.
When people first looked at Einstein's equations they thought that it was possible for particles with special properties to travel faster than the maximum speed and they were called tachyons. However, I don't believe tachyons exist. If you look at the mathematics then again the existence of tachyons relies on use of "imaginary" numbers.
My first thought after reading about the OPERA experiment is if neutrinos are tachyons why don't they travel twice as fast or a million times as fast or 10^300 times as fast. The results of the experiment (if correct) shows they only travel at a tiny fraction more than the speed of photons. This immediately implies to me that photons travel at less than C, rather than neutrinos travel at more than C.
Problems
In any case, I think a lot of our thinking is clouded by nomenclature. People equate the maximum speed "C" with the "speed of light" (really meaning the "speed of electromagnetic radiation in a vacuum"). There are other particles, apart from photons, that are also supposed to travel at the maximum speed, among them neutrinos and Z bosons. To avoid confusion I think we should call the maximum speed simply "C", and distinguish it from the speed of neutrinos, Z bosons, photons in a vacuum, etc, which may possibly be different.
From my understanding there are already problems in this area with current thinking. Neutrinos are believed to travel at C, but recent experiments have shown that neutrinos must have a rest-mass. If something has rest-mass then it takes an infinite amount of energy to accelerate it to C (and like "imaginary" numbers I don't think "infinite" numbers have any basis in reality).
The only conclusion is that neutrinos travel at less than C (even if by a very small amount). If neutrinos travel at less than C I can't see why photons might not also. Nobody has ever found that photons have a rest mass but this may just mean it is too small to yet be measured.
Another reason I think photons have rest-mass is that they are affected by gravity. It will be argued that anything that moves through space must be affected by gravity since gravity bends space. My reply to this would then be that anything that moves through space must have mass. One day we will understand what it really means to have "mass".
Z-Bosons
The latest reason proposed (by Cohen and Glashow) that there is something wrong with the OPERA experiment results is this: If neutrinos were travelling faster than light they would emit particles until they lost energy causing them to slow down. This is similar to the way that electrons emit photons (called Cherenkov radiation) when traveling faster than the speed of light in water.
I will explain my understanding of this, in case you have never heard of Cherenkov radiation. Photons travelling through a medium such as water or glass travel at a significant fraction less than their speed in a vacuum. (The difference in the speed of light in glass and air is why lenses work.) If electrons travel through a medium faster than photons would travel through the same medium (but still less than C, of course) then they emit some of their energy as photons till they slow down. You can think of this as a "sonic boom" but for the speed of light not for the speed of sound.
Electrons only do this because electrons have an electrical charge and photons are electromagnetic particles. Neutrinos will not do this because they have no electrical (or magnetic) charge. However, neutrinos do have a "weak force" charge and the weak force equivalent of a photon is a Z-boson. (I know this is not strictly the full story.)
I think the Cohen & Glashow response does not preclude the OPERA results being valid. It is only relevant if neutrinos travel faster than Z-bosons. But I don't think the neutrinos are travelling faster than Z-bosons only faster than photons. So if the speed of Z-bosons is faster than the speed of light then the neutrinos still do not have to slow down to the speed of light.
I don't believe the speed of Z-bosons has been measured, or at least measured anywhere near as accurately as the speed of light. My belief is that neutrinos travel slightly faster than light but slower than Z-bosons. (Again I remind the reader that nothing travels faster than C.)
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