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Instantaneous action at a distance may occur due to an experiment being performed within a train. A particle may decay in the middle of the train, and when decaying it may split into 2 entangled particles that fly apart in opposite directions. Let's say that these particles are photons. When measuring properties of one particle when it reaches one end of the train, it is said that this will instantaneously affect the other particle at the opposite end of the train.

However, if this experiment was performed again as the train passed by a train station, observers at the train station do not see the two photons reach the two opposite ends of the train at the same time, thus to them there is no instantaneous action at a distance taking place at all.

Thus how is it that what appears to the obsevers on board the train to be instantaneous action at a distance is physically confined to this one frame of reference only ?

Edit: I will add to the details here, that the photons are said to be in superposition of states until being first measured at one end of the train or the other. Which end measures first may depend on the accuracy of the experiment that was set up. But either way both photons are said to be in superposition of states until that moment that they reach the train ends, +/- measurement error.

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There is no action at a distance in quantum mechanics. This is a misunderstanding that is common even among physicists. Since there is no action at a distance there is also no need for a preferred frame.

In classical physics, a system can be described by a set of numbers whose values can all be measured using a single instance of that system. There is a mathematical result called Bell's theorem saying that no local theory can reproduce the predictions of quantum mechanics using classical physics. Quantum mechanics is not classical physics and so it is not surprising that they give rise to different predictions.

In quantum mechanics, a system is characterised by the values of observables where those values are represented by mathematical objects called Hermitian matrices. To describe how information is transferred between quantum systems you have to describe the ways in which the observables of one system depend on those of another. In general, an observable does not represent just a single valued measurable quantity changing over time. Rather, it represents a more complex structure that involves multiple different versions of that quantity interfering with one another. And if there are going to be multiple versions of each system, then any given system has to carry information about how a particular version of that system will interact with a particular version of another system. In general, you can't get that sort of information by measuring just one system and for that reason it is called locally inaccessible information. An explanation of how locally inaccessible information gives rise to EPR correlations, teleportation etc by entirely local interactions is given here:

http://arxiv.org/abs/quant-ph/9906007.

See also

http://arxiv.org/abs/1109.6223.

For popular treatments see "The Fabric of Reality" and "The Beginning of Infinity" by David Deutsch.

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