Curved spacetime and measurement direction

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SUMMARY

The discussion centers on the measurement direction of EPR entangled photons sent to Alice and Bob across vast distances. It concludes that the measurement direction is determined by parallel transport in curved spacetime, which is influenced by the trajectories of the photons from their origin to the observers. This understanding is crucial for interpreting the results of measurements in quantum entanglement under the influence of gravitational fields.

PREREQUISITES
  • Understanding of EPR entanglement and quantum mechanics
  • Knowledge of curved spacetime concepts in general relativity
  • Familiarity with parallel transport in differential geometry
  • Basic principles of photon polarization measurement
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  • Research the implications of curved spacetime on quantum entanglement
  • Study parallel transport in the context of general relativity
  • Explore photon polarization measurement techniques in quantum experiments
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Hill
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TL;DR
How are parallel directions for measurements of entangled particles defined in locations which are far from each other?
To be specific, let's say that two photons in EPR entangled state were sent to Alice and Bob separated by billions of light years. We know that if they measure their photon polarizations in the same direction, they certainly get the same result. My question is, what is the same direction in their case?
I assume that this is determined by the parallel transport in curved spacetime and depends on trajectories of the photons between their origin and Alice and Bob respectively. Is this assumption correct?
 
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