SpiderET said:
The question was never about superluminal speed, it was about particles with mass reaching speed of light.
I don't think its nitpicking. Relativity is regarded as perfectly confirmed by experiments, but when I go really into detail in some cases I found out that some important predictions have rather weak experimental confirmation or are not excluding other interpretations. If somebody would propose a theory where all particles, with or without mass can reach speed of light, would be there some experiment which would falsify it? It seems that currently there is no such experiment.
To give an example of how we experimentally confirm special relativity; special relativity predicts the time dilation expected of a short lived particle like a muon, as a function of its speed which is in turn a function of its kinetic energy. Muons accelerated with 100 GeV of energy each are going to have a half-life in the reference from of observers at rest in the particle accelerator of X which is much longer than the half-life of a muon not accelerated. The relationship between the energy we use to accelerate a muon and its observed half-life, corresponds closely to the expected value. If the muon were going at exactly the speed of light, however, we would expect the muon to never decay, which is not what we observe, even when we give the muon immense energy boosts. The asymptotic behavior of muon decay rates with respect to energy of acceleration is very powerful evidence that special relativity is true, and if special relativity is true, then massive objects can't actually reach the speed of light.
It turns out to be much easier to measure the energy of acceleration and the decay rates with minimal systemic error, than it is to measure speed itself, because at high energies the marginal increase in velocity from an increase in energy is so small. As energies get higher relative to particle mass, the difference between "c" and the particle's speed in your reference frame becomes arbitrarily small and hence harder to measure, but the time dilation effects become larger and hence much easier to measure. Confirming that a highly boosted particle does not cease to experience time entirely or experience time in reverse is typically much easier to do at extremely relativistic speeds than directly measuring distance measurements.
These calculations are not hard to do. I had problem sets in freshman physics that required that we make them. We had to take on faith the global average measurement of the decay rate of a muon at rest (for which the Particle Data Group provides a bibliography of the experimental results used to reach the result), and we had to take on faith that observed probability that of a particular energy decayed in a particular time period where we were given only the citation to the experiments finding that to be the case. But, with those empirically confirmable measurements in hand, the math checked out and reproduced the observed behavior.
Coming up with a theory that has a formula which exhibits this asymptotic behavior everywhere we can observe it that is exactly the same as special relativity, but which somehow allows a massive particle to reach light speed, is not easy.
In contrast, the speed of light pops out naturally even from the classical Maxwell's equations, the relationship can be deduced logically from other axioms, and we can even measure the speed of light indirectly from general relativity, for example, by using the E=mc^2 relationship to match the expected and observed energy output of a nuclear reaction, or of matter-antimatter annihilation (which also checks out to the limits of experimental accuracy). The fact that the value of "c" in general relativity and special relativity is robust over many different kinds of measurements suggests that the quantity "c" in those equations is an accurate conceptualization of the way that the world really works. Finding an alternative theory in which "c" holds over such a robust range of measurements is much harder than devising a theory that allows massive objects to travel at exactly "c" in just one kind of measurement (like the direct neutrino speed measurement recently conducted by MINOS).
Precise time measurements are also used to test gravitational time dilation. For example, scientists have put one atomic clock at the top floor of the National Institute of Standards building, where the gravitational field is slightly weaker, and another in the basement, where the gravitational field is slightly stronger, and observed precisely and in statistically significant amounts the amount of time dilation due to gravity as would be expected from the differences in the strength of the gravitational field caused by a ca. 50 foot difference in altitude.
Both experiments indirectly prove the formulas relating mass, gravitational field strength, and velocity of special relativity and general relativity respectively in a quantitative manner.
While we can't directly measure the difference between a light relativistic particle and a particle moving at exactly the speed of light with quite as high precision, we can confirm with high precision that the formulas of the theory hold in every circumstance we can measure it, and compare those results with any alternative proposed theory. Special relativity predicts that in the MINOS neutrino case that neutrino speed is less than c by about 1 part per 10^18. The experiment showed that the difference was less than 1 per per 10^6, which is consistent with that result. This may not, by itself, convince you that massive objects can never get all of the way to the speed of light. But, it should convince you that the linear Newtonian mechanics relationship between force and velocity does not hold true, which definitively displaces the most intuitive alternative.
Since general relativity and special relativity match with extreme precision in every circumstance we can measure to within the experimental margin of error, we presume that the theory will continue to hold in more extreme circumstances in the absence of any reason to doubt the result.
Also, because special relativity and general relativity (at least in so far as time dilation due to gravity and E=mc^2) show such precisely and consistent relationships across such a robust range of measurement types, even if we found an experimental case where this did not seem to hold true, we would be inclined to consider other explanations (e.g. that there might be a small number of tiny wormholes for short distances in a given volume, on average, in the topology of seemingly empty space, or that what we were measuring the speed of light in wasn't actually a vacuum) as opposed to trying to tweak special relativity and general relativity per se.
