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Imagine a photon decaying into an electron-positron pair. Which have entanglement such that one is "up" and one is "down".

There are a few mini black holes near by so that one of the electrons circles round the black holes for a bit before coming back near it's entangled partner.

Due to it's transport through curved space, will the pairs still be in orthogonal states? Could the "up-ness" have been rotated to a "left-ness"? (Because parallel transport of a vector through a loop in curved space does not bring a vector back to the original).

i.e. if the original particle is measured to be "up", might the second particle not now automatically be "down"?

  • As far as I know (which is not very far), QM/QFT in curved spacetime is still unitary. Therefore, my guess is that this question reduces to "If you have entangled spins and perform a unitary rotation on one, are they still entangled?" – Rococo Dec 09 '18 at 19:00
  • afaik there is no definitive quantization of gravity. String theories do have quantization of gravity and could be used as models, except I have not seen discussions of how entanglement appears in string theory. searched andfound this https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.066025 – anna v Dec 09 '18 at 19:34
  • Entanglement seems to have nothing to do with this question. Let $U$ represent any unitary transformation that takes "up" to "left". You're asking whether passing half of an entangled pair past a black hole can implement a transformation of the form $U\otimes 1$. THis is clearly equivalent to asking if the same passage by an unentangled particle can implement a transformation of the form $U$. So is that your question? – WillO Dec 09 '18 at 20:31
  • Entanglement + black hole = firewall paradox – safesphere Dec 10 '18 at 06:06
  • Well you have to have two particles to compare their spins –  Dec 10 '18 at 11:46

1 Answers1

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Imagine a photon decaying into an electron-positron pair. Which have entanglement such that one is "up" and one is "down".

What you described as up and down is the relation of the directions of the intrinsic magnetic dipole moment and the intrinsic spin. If the moving electron gets deflected under the influence of an external magnetic field in one direction when the positron - moving in the same direction - gets deflected to the opposite direction.

Under influence of the surrounding, be this a magnetic, a gravitational or an electric field, the direction of the particles magnetic field could be rotated in any direction.

There are a few mini black holes near by so that one of the electrons circles round the black holes for a bit before coming back near it's entangled partner.

In the special case of the (non)influence of the curved space the particle indeed could came back to the same position in space and with rotated by 180° direction of his magnetic dipole moment. It is the same as a comet, which rotates and the axis of rotation lays in the plane of movement, follows the geodesic path around the sun. So no Black hole or more than one massive body is needed.

Due to it's transport through curved space, will the pairs still be in orthogonal states? Could the "up-ness" have been rotated to a "left-ness"? (Because parallel transport of a vector through a loop in curved space does not bring a vector back to the original).

The entanglement of the “created” together particles will be destroyed by the influence of external fields easily. For the experimentalist it’s more an advantage to protect entangled particles from such influences.

i.e. if the original particle is measured to be "up", might the second particle not now automatically be "down"?

Absolutely no. As described above, the up and down is another expression for the different orientations of spin to magnetic dipole moment in a particle and its antiparticle AND the parallel/anti-parallel orientation of these axis in space at the moment of the particle creation. Being under the influence of external fields the entanglement will be destroyed.

But as long as one is able to calculate the external influence, the orientation of the second particle could be predicted by the measurement of the first particle. Your example of a moving particle along a geodesic path is such a case, but the influence of all of the electric and magnetic field will change the orientation unpredictable.

Last thing. The measurement of oriented particles has the same difficulties as measuring the orientation of photons. So the knowledge of entanglement of two particles is a statistical knowledge only.

HolgerFiedler
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