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As Einstein's theory tell us it takes infinite amount of energy to get something with a mass to reach the speed limit $c$.

How true is that when observed experimentally either in a laboratory or elsewhere in the universe?

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As you can obviously imagine, no such experiment is possible at the moment, or ever.

Even considering Planck's length as the limit of space/motion, the difference between $c = (10^{43} P_L) $ and $10^{43}-1 \, P_L $ is so tiny that it is impossible to determine whether a particle (an electron, a neutrino...) is travelling at c or at c-1. The detection would be possible if a massive particle travelled at a speed much greater than c.

In a lab, speeding an electron to the latter value is impossible, since it would require trillions of Tera eV, while the highest value possible now (at LHC) is 7 Tera eV.

You probably heard that some time ago they claimed they recorded a neutrino travelling faster than c at GranSasso, but it was acknowledged rejected as a material error

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The answer to your title question is "definitely not." If you found such an object, then special relativity and relativistic quantum field theory would both have to go into the garbage can, you'd be swimming in Nobel Prizes, and physicists all over the world would either love you or hate you, depending on their philosophical inclination.

The closest thing we've found in the real world is neutrinos: they have nonzero rest mass, but they travel so close to the speed of light but no experiment has ever been able to measure them traveling strictly slower than the speed of light. But everyone is very, very confident that with sufficiently accurate measurements, we would indeed find that they travel strictly slower than light.

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  • $\begingroup$ Addendum: it is of course logically impossible to experimentally prove that anything (including light!) travels at exactly the speed of light anyway, because your experiment will always have some uncertainty. At best, you can bound the particle speed's deviation from that of light. $\endgroup$ – tparker Sep 19 '16 at 6:14

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