Thought experiment: 2 entangled photons, one escape from galaxy to galaxy without hitting an electron and another one got caught between 2 perfect mirrors. Would the redshift (wavelength becomes longer) of the entangled photon affects the one that was caught in the trap? Maybe we can use the ultra cold sodium to trap the photon if mirror one don't work.
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You are just saying entangled photons, but you do not define the entanglement itself. I will assume two type of entanglement to answer your question:
- Entanglement of polarization
The answer is, the red/blueshift of one of the entangled photons does not destroy the entanglement, but it might not affect the other photon's frequency either, because the photons pair is not frequency entangled.
If the polarization of two photons is entangled, redshift or blueshift does not change the entanglement of their polarization.
Entangled photon absorption redshift/blueshift scattering
- Frequency bin entanglement
The frequency of each photon is uncertain, but the sum of the frequencies is well defined. In the case of frequency entanglement, the sum of the frequencies is well defined, and when in your case one of the photon get redshifted by traveling through expanding space, then when measuring any of the two photons will determine the outcome for both photons' frequencies.
Árpád Szendrei
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