A relativity question got me thinking about this again (I did when I was at college). Basically, the Minkowski spacetime interval formula, which is the basis of Einstein's special theory of relativity postulates, is based on measurements of differences between clocks.
One way thinking about the effect of the Lorentz factor in Einstein's equations is that the very act of measuring, which depends on signal (in some form on EM wave) that limited to travel at 1.0c, disturbs the received data ( if you move a relativistic speeds your measurement signals are either blue or red "shifted" which cause length contraction and time dilation ). But, suppose we can come up with way to creating some sort of quatum entanglement in which a state of a particle can be correlated to its speed, giving us basically an instatenous measurement capabilities. If we then accelerate a particle from such a pair to 0.9999c would we still see the same effects/results as the ones obtained with our "classical" signal measurements?