It is well accepted that quantum theory has well adapted itself to the requirements of special relativity. Quantum field theories are perfect examples of this peaceful coexistence. However I sometimes tend to feel little uneasy about some aspects. Consider an EPR pair of particles light years apart. Suppose there are 2 observers moving relative to each other with constant relative velocity. Let us consider, there are spin detection mechanism at both end for each particle. Now suppose one of the observer is at rest w.r.t. the detector for the first particle. As soon as the detection made, the wave function of the 2 particle entangled system will collapse instantaneously and the second particle must realize a definite opposite spin value. Now due to relativity of simultaneity, the second observer may claim that the collapse of the wave function for the two particle system is not simultaneous. He may even claim that the second particle is measured first. In that case a special frame of reference will be privileged, the frame at which the wave function collapsed instantaneously. This will cause a significant strain on the core principle of special relativity.
I am sure the above reasoning is flawed. My question is where?
Best Answer
The reasoning is flawed for multiple reasons. One of them is that there is no physical wave-function collapse so in particular there can't be any problem with relativity. More precisely, entanglement is only about correlations between particles. That is, if you carry out experiments and later (after both observers who measured individual particle meet) they will notice that there was a correlation.
And this has to do with another flaw: locality. You are simply not allowed to say anything about stuff you don't measure. And that is only the stuff in your past light-cone. You just can't say anything about the other particle which is space-like separated from you (for all you know, it might no longer exist, having been absorbed by a BH).
Sure, this is because there is no notion of causality between space-like separated events. This alone should be enough to convince you that wave-function collapse is completely unphysical. It is just a convenient tool of Copenhagen interpretation (which simply ignores the measurement problem) that has its limitations.