A question about quantum entanglement

[starchaser137]

How would 2 quantum-entangled particles interact with each other if one of them was placed in a gravitational field strong enough to distort time for that particle with a considerable deviation? Would there be any lag? If so, doesn't that contradict quantum entanglement?

[swansont]

There is generally no interaction between entangled particles. It’s not obvious to me that gravitational time dilation would have any effect on the entanglement. 

[Markus Hanke]

I think this is an interesting question, and the answer is certainly not obvious. I would expect that, if you were to place one part of an entangled system into a different gravitational potential, then this should have a measurable effect on the entanglement relationship, simple because the two parts of the system no longer evolve in time in the same way, meaning something would need to change in the overall wave function describing that pair. At the same time though I don’t see how this could possibly affect the fundamental non-separability of that wave function, so some notion of entanglement should persist. I have no idea what this would really mean in physical terms, though.

I did a Google search, but this was the only thing I could find on the subject. The experiment hasn’t been performed yet, but clearly the author also expects there to be an observable effect of some kind (he talks about “entanglement degradation”).

18 hours ago, starchaser137 said:

If so, doesn't that contradict quantum entanglement?

No, because a) entanglement is usually discussed on the premise of the entire system being in the same inertial frame, and b) even if gravity does have an effect, there would still be entanglement, though aspects of it might be subtle different.

[geordief]

3 hours ago, Markus Hanke said:

I think this is an interesting question, and the answer is certainly not obvious. I would expect that, if you were to place one part of an entangled system into a different gravitational potential, then this should have a measurable effect on the entanglement relationship, simple because the two parts of the system no longer evolve in time in the same way, meaning something would need to change in the overall wave function describing that pair. At the same time though I don’t see how this could possibly affect the fundamental non-separability of that wave function, so some notion of entanglement should persist. I have no idea what this would really mean in physical terms, though.

I did a Google search, but this was the only thing I could find on the subject. The experiment hasn’t been performed yet, but clearly the author also expects there to be an observable effect of some kind (he talks about “entanglement degradation”).

No, because a) entanglement is usually discussed on the premise of the entire system being in the same inertial frame, and b) even if gravity does have an effect, there would still be entanglement, though aspects of it might be subtle different.

Is this at all related to the relationship  between two objects one of which goes behind the event horizon of a BH  and the other that does not? (I thought I saw that scenario mentioned quite recently somewhere on the forums)

 

[studiot]

It is worth reviewing some aspects of entanglement here.

First quantum entanglement is not fully understood in that all the ramifications and implications have not been worked out (perhaps een not most of them) in the way that has been done in classical mechanics.

Secondly there are two views of entanglement, viewed from two ends of the telescope if you like.

One view is that you start with discrete or separate 'particles' : These have separate wave functions which do not interact with each other so can be individually interacted with by agencies outside the sysem. Upon entanglement, there are no longer two separate independent wavefunctions, but a single wavefunction that describes the whole system of entangled particles. Outside agencies can no longer interact with the original wavefunctions as they could before entanglement.

The other view is that you start with a wavefunction for the entangled system and cause the single wavefunction degenerate into two separate individual wavefunctions by some means.

Now the OP asks if gravity might be such a degenerating outside agency.
Are related question would be are any such effect significant ?
I don't know of any real or thought experiments about this but,
I suggest that we consider the attached diagram (From Hyperphysics)

 

Look at the column marked 'strength'.
This shows the relative strength of the forces acting inside the atom where it can readily be seen just how weak gravity is compared to the other forces, which is why standard models ignore gravity in their calculation.
Oh yes it should be pointed out that all our 'calculations' are really just models
And with models, what you leave out (ignore) is just as important as what you put in, so you hope you haven't missed out anything significant.

Finally we come to the twin unspecified questions of what particles we would choose to separate and how this would be achieved.

[Markus Hanke]

19 hours ago, studiot said:

The other view is that you start with a wavefunction for the entangled system and cause the single wavefunction degenerate into two separate individual wavefunctions by some means.

I’m struggling to follow you on this one - if you do this, then the system is no longer entangled. It is precisely the non-separability of the wave function that is the essence of what ‘entanglement’ means.

19 hours ago, studiot said:

Are related question would be are any such effect significant ?

I think this is a matter of degrees, i.e. it depends on what ‘significant’ means for a specific scenario.
In principle, I would argue the following: let’s say you prepare two identical entanglement pairs, both of which consisting of two entangled particles each. Keep one of these entangled pairs in a locally inertial frame, simply for reference purposes. For the other pair, place the system such that there is a gravitational gradient present between the two particles that make up the entanglement pair, i.e. there is relative acceleration between their geodesic world lines as they age into the future.

Both of these pairs will now have wave functions that are of the same form and are both non-separable; however, the evolution of these wave functions must differ, because in the presence of gravity the propagator is a purely local operator, so the two parts of the non-separable wave function subject to gravity will evolve differently, as compared to the reference pair that is not subject to gravity. So clearly, gravity must have some effect on the entanglement relationship.

But of course I agree with you in that for most real-world scenarios such effects should be entirely negligible - unless you are in a spacetime with extreme tidal gravity, such as near the event horizon of a microscopic black hole.

[studiot]

18 minutes ago, Markus Hanke said:

I’m struggling to follow you on this one - if you do this, then the system is no longer entangled. It is precisely the non-separability of the wave function that is the essence of what ‘entanglement’ means.

I think this is a matter of degrees, i.e. it depends on what ‘significant’ means for a specific scenario.
In principle, I would argue the following: let’s say you prepare two identical entanglement pairs, both of which consisting of two entangled particles each. Keep one of these entangled pairs in a locally inertial frame, simply for reference purposes. For the other pair, place the system such that there is a gravitational gradient present between the two particles that make up the entanglement pair, i.e. there is relative acceleration between their geodesic world lines as they age into the future.

Both of these pairs will now have wave functions that are of the same form and are both non-separable; however, the evolution of these wave functions must differ, because in the presence of gravity the propagator is a purely local operator, so the two parts of the non-separable wave function subject to gravity will evolve differently, as compared to the reference pair that is not subject to gravity. So clearly, gravity must have some effect on the entanglement relationship.

But of course I agree with you in that for most real-world scenarios such effects should be entirely negligible - unless you are in a spacetime with extreme tidal gravity, such as near the event horizon of a microscopic black hole.

Thank you for your thoughts.

I see my typinglexia has got in the way again. Sorry.

Quote

I’m struggling to follow you on this one - if you do this, then the system is no longer entangled. It is precisely the non-separability of the wave function that is the essence of what ‘entanglement’ means.

This is exactly the point I was trying to bring out , obviously I didn't succeed.

The definition of entangled is that there is only one wavefunction for system.

Conversely for an unentangled system there must be at least two waveforms.

So there are important distinctions to be made.

'Separate' can refer to three things. The physical separation of the particles. The decomposition of the wavefunction into two (or more) wavefunctions and the mathematical process of the separation of variables of a differential equation. Writers (myself included) do not always make clear which one they mean.

19 hours ago, studiot said:

Finally we come to the twin unspecified questions of what particles we would choose to separate and how this would be achieved.

This was a very important point particularly if we are asking what happens to two particles when they are entangled and then physically separated so that one is then in a high gravity environment.

With respect you are not clear about your answers to this.

 

My excuse is that I am always in a rush at this time of the motning.

🙂

[Markus Hanke]

21 hours ago, studiot said:

With respect you are not clear about your answers to this.

To be honest, I did not consider any specific scenario (but the author of the paper I linked earlier did), I was thinking only about general principles with this. So I don’t have any specifics to offer. 

What I will say though is that, in order to bring one of the particles to rest at a different gravitational potential wrt to the other one, some form of acceleration needs to be applied, which is (assuming constant a) already locally equivalent to a uniform gravitational field. So even before the final state is achieved, the question of what effect gravity has here already arises.

21 hours ago, studiot said:

This is exactly the point I was trying to bring out , obviously I didn't succeed.

So do you mean to say that subjecting an (already) entangled system to the influence of gravity will break the entanglement?

Of course entanglement means non-separability of the wave function, so perhaps my earlier comment was misleading - I did not mean that the two parts of the system evolve separately (in that they have separate propagators), only that the 2-particle system as a whole must evolve in a different way than the one that isn’t subject to gravity. Simply on account of them not sharing the same notion of time. I think I didn’t express this very well.

I am not clear though what this would really mean mathematically, since the spatiotemporal embedding of such a system would span a region of spacetime that is now no longer necessarily Minkowskian. This should have an impact on the wave function itself (does the tensor product reference the metric?), as well as on its propagator (how to formulate this, if time is a local notion?).