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When one particle of an entangled pair is measured, it forces the state of the other particle. This effect propagates faster than we can measure, certainly faster than light and possibly instantaneously.

Relativistic observers with radically different viewpoints, perhaps travelling near lightspeed in opposite directions, can observe a time reversal in the order of the two measurement events. Thus observer Alice might see measurement A occurring first and therefore determining the outcome of B, while observer Bob might see measurement B occurring first and therefore determining the outcome of A. This despite the fact that Charlie actually set the experiment up so that the result of measurement A physically triggered the measurement of B.

This creates a paradox for Bob as to whether he should take Charlie's experimental setup or his own temporal observations as the correct causal sequence of events. If he accepts Charlie's experimental design then he must accept that temporal causality is broken in his own observations. But, if he accepts his own observations as correctly-ordered, then he must accept that somehow, measurement B triggered A and not the way round that Charlie assumed when they designed their experiment.

One way out of the paradox is to decide that temporal flow and causal flow are not strictly aligned at the quantum level and that entanglement can break their alignment. Are there other ways out?

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Very good question, which has on-going very active research. Short answer is YES, indeed quantum entanglement makes cause and effect indistinguishable, at least in a usual sense that we get used to in everyday. And this is already proven experimental fact,- Physicists demonstrate new way to violate local causality. So we can talk now only about does causal relationships takes completely a new form in a quantum world or maybe causality concept in ANY from must be dismissed at all at quantum level. I think nobody can be sure about that at this time. Building quantum gravity foundations will shed a light on this subject too. But QG is still on-going research.

EDIT

There are some indications that time is emergent property of entangled systems, quote from this research :

We show how a static, entangled state of two photons can be seen as evolving by an observer that uses one of the two photons as a clock to gauge the time-evolution of the other photon. However, an external observer can show that the global entangled state does not evolve.

So Quantum-Mechanical causality can be defined as entanglement causes time flow.

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  • $\begingroup$ "Thus observer Alice might see measurement A occurring first and therefore determining the outcome of B, while observer Bob might see measurement B occurring first and therefore determining the outcome of A. This despite the fact that Charlie actually set the experiment up so that the result of measurement A physically triggered the measurement of B." Into the the light cone there are not inversion of causality. I do not understand what difference situation more than this are you considering when you introduce a quantum effect in this. $\endgroup$ – Raúl Aparicio Bustillo Apr 3 at 13:06
  • $\begingroup$ Quantum entanglement breaks local causality, so it doesn't makes sense to analyze at all which event (measurement) at Alice or Bob was first (cause) and which - an effect, because these events are indistinguishable. Causality IS violated in this case. $\endgroup$ – Agnius Vasiliauskas Apr 3 at 13:19

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