To a high degree of repeatability:
1) special relativity
I believe Special Relativity has an object with mass no matter how slight becoming infinitely massive, with a length of zero, and time stopped once it reaches the speed of light. We have experimental evidence of this?
According to the theory of Special Relativity, it would take infinite energy to get to exactly light speed, but particles can be accelerated to almost the speed of light, and their momentum measured directly, and the mass increase derived from the measurement.