So far as I can remember, there are these two equations in Einstein’s special theory of relativity:
l1 = l(1-v2/c2)1/2……. (1)
t1 = t((1-v2/c2)1/2……. (2)
From the above two equations, two conclusions can be drawn that are as follows:
1) Time and distance are not absolute, they are relative;
2) At light speed, both travel time and travel distance become zero.
Now reality may be such that
1) Time and distance are only relative, but in no circumstances they become zero (A);
2) Time and distance are not only relative but at one particular case, they also become zero (B).
If reality is A, then the above two equations are not required at all to represent that reality; it can be equally represented by the following two equations:
l1 = l(1-v2/xc2)1/2……. (3)
t1 = t((1-v2/xc2)1/2……. (4)
In (3) and (4) above, x will have a value greater than one but less than infinity. But it cannot have a value equal to one or infinity. If the value of x is one, then we will go back to Einstein’s equations, whereas if its value equals infinity, then we will have Newton’s equations instead. From (3) and (4) above, it can clearly be seen that time and distance will be relative as before, but they will never be zero even at the speed of light due to the presence of the factor 1/x in the equations.
Now, I know very well that it is not possible to experimentally demonstrate what is actually happening at the speed of light and so, it is reasonable to doubt whether time and distance really shrink to zero at light-speed. However, there is an alternate way to verify it.
Suppose scientists have repeated the Michelson-Morley experiment or any newer version of it, and suppose that they have arrived at equations (3) and (4) instead of equations (1) and (2). Then, based on these two equations (3) and (4), they can say that the shrinkage of time and distance to zero at light-speed is only a myth.
But, nature knows better than any one of us what is actually happening at the speed of light and so, whenever an actual experiment is performed with light and an interferometer, it is always returning us equations (1) and (2) only and not equations (3) and (4) even for a single time. This is nature’s indirect way to inform us that we are not doing any mistake when we are saying that time and distance become zero for light.
Scientists usually do not question this and so, we can find such statements in their writings on SR:
1) ‘For the light itself, the whole universe is only zero millimeters long.’ – Sascha Vongehr, in The Fundamental Nature of Light, Science 2.0 (February 3rd, 2011);
2) ‘At the speed of light there’s no time to cover any distance, but there’s also no distance to cover.’ – Ask a Mathematician/Ask a Physicist
There is a reason as to why scientists do not question this. The reason is that they know very well that they are in the domain of physics, and not in the domain of metaphysics. In the domain of physics, if they want to challenge something, then they cannot do so by using logic and reason only. Rather, they will have to experimentally demonstrate that that particular thing is wrong; they will have to experimentally demonstrate that equations (1) and (2) must be replaced by equations (3) and (4). So far, no one has been able to do this. So far, no one has been able to falsify SR.
There is one more reason why we can say that time and distance indeed shrink to zero at light-speed. Main-stream physicists are now saying that spacetime is not fundamental, but emergent. Spacetime is emergent means the source from which spacetime has emerged cannot be within any spacetime, for the simple reason that there cannot be any spacetime prior to its emergence. So, by stating that spacetime is emergent, physicists have already acknowledged the existence of something spaceless and timeless in nature from which our known spacetime has emerged. I know that physicists are describing this source as non-spatiotemporal, but I also know this that ‘non-spatiotemporal’ is only a new scientific term that replaces our old term ‘spaceless and timeless.’ If there is something spaceless and timeless in nature, then it is quite obvious that science would show how anything can be spaceless and timeless, because it is the job of science to provide an explanation for every phenomenon, event and effect in nature. In SR, we get those requisite explanations for spacelessness and timelessness. So, although we cannot directly verify whether time and distance really shrink to zero at light-speed, yet we can say that emergent spacetime is an indirect validation of it.