Entanglement and simultaneity According to the special theory of relativity, distant simultaneity depends on the observer's reference frame.
And, according to the quantum theory, in the case of two entangled particles, a measure on one of the particles simultaneously affects the second one. Under which reference frame is this simultaneous?
 A: It doesn't really matter, because the phrase "simultaneously affects the other particle" is misleading.
Let's suppose you have a pair of totally anticorrelated photons. You measure one of them, then you'll know the outcome of the other one. The phrase "the measurement simultaneously affects the other particle" is not physical, because until you actually measure the other particle, you can't even notice anything different. There is no "effect". The only thing we can meaningfully talk about is the two measurements of the two particles. Now, depending on the reference frame, one will come before the other (or they are simultaneous) and whatever we measure, one result will imply the other.
This is why I think that the term "the particle simultaneously affects the other particle" is not very good, because it implies something like an active link - but depending on the reference frame particle A would affect particle B or the other way round. There is no "one particle affecting the other". Only if you are in a specified reference frame, it looks like there is an immediate influence of one particle on another.
A: Measuring one particle does not affect the other at all. Bell's theorem explains that if you try to simulate an entangled quantum system by modelling a quantum system with a classical stochastic variable the result has to be non-local. However, quantum systems are described by Heisenberg picture observables, which are represented by Hermitian operators, not classical stochastic variables. The particles each exist in multiple versions that can interact with one another in interference experiments, which is why they can't be described by classical stochastic variables. Each particle's observables describe quantum information about the relations between the different versions of each particle, but this information can't be revealed by measurements on either particle alone:
http://arxiv.org/abs/quant-ph/9906007
http://arxiv.org/abs/1109.6223
http://arxiv.org/abs/quant-ph/0104033.
In each measurement, both of the outcomes happen and the correlations are established when the results are compared, not when the measurement is done on each particle.
