The Entangled Brothers Paradox
Two brothers, Rob & John, both have stopwatches that are synchronized to each other and measure time perfectly. Before leaving on a spaceship that travels at a speed of 0.99c (i.e. 99% of light speed), Rob gave John one particle from a quantum entangled pair and then brought the other entangled particle with him on the spaceship.
The two brothers had also agreed upon an experiment whereby Rob would manipulate the state of his particle when his stopwatch indicates that a specified period of time (n) had elapsed since his launch. Per the agreed upon experiment, John would check the state of his particle shortly after that same specified time interval.
Due to the time dilation from traveling at 0.99c and the duration of his spacetime journey, Rob’s stopwatch indicates an interval of n has elapsed at a time when he is now 1 year younger than John rather than 3 years older! Thus, Rob’s stopwatch indicates an interval of n at a relative time long after John’s stopwatch had indicated the same elapsed interval. Therefore, when Rob manipulates the state of his entangled particle, it’s not clear if its influence will be detected when John makes his agreed upon observation.
If John’s observation does reflect Rob’s manipulation, that would mean that the temporal synchronization of entangled particles abides by their individual experience of time rather than some universal objective time reference. This certainly seems reasonable, but it has a profound implication — it would mean that an event in the future is able to retrocausally influence an event in the past.
To clarify a potential point of uncertainty, it may help to imagine that Rob’s spacetime travel has resulted in his return to Earth prior to his stopwatch showing n time elapsed. In this case, Rob & John could be reunited to find that Rob is now 1 year younger instead of 3 years older than his brother John, and that same relative age discrepancy would thus apply to the entangled quantum particles too. The reunited brothers and their particles could then all be spatially colocated in the same laboratory when Rob manipulates his particle. Since John’s stopwatch would have shown an elapsed time of n long prior to this, John would have already long since observed his particle when Rob manipulates his.
Alternatively, if John’s observation does not reflect Rob’s manipulation, that would mean that entangled quantum particles are not subjected to the time dilation dictated by General Relativity. This also seems reasonable, and also has a profound implication — it would mean that unlike spatial dimensions, time does not abide by quantum nonlocality. This would make it possible to establish a universal objective time reference.
