Is There an Intrinsic Weight to Entanglement in Quantum Systems?

[Borek]

Hi guys, a dumb chemist here.

There is a paper http://arxiv.org/abs/1412.4007 by David Edward Bruschi. It stirred some interest between my Polish colleagues and friends, but none of us is skilled enough to understand the details, so we prefer to see it discussed by others.

 

[phinds]

Hi guys, a dumb chemist here.

There is a paper http://arxiv.org/abs/1412.4007 by David Edward Bruschi. It stirred some interest between my Polish colleagues and friends, but none of us is skilled enough to understand the details, so we prefer to see it discussed by others.

Just thinking out loud here, but it seems impossible to me for the following reason: If entanglement has a gravitational effect then making a measurement of one of an entangled pair would remove the entanglement and thus change the gravitational effect of the other of the pair and you could at least theoretically measure that and now you are transmitting information FTL. Am I missing something? It seems very unlikely that those authors have overlooked something that obvious, so I guess I MUST be missing something.

 

[strangerep]

Just thinking out loud here, but it seems impossible to me for the following reason: If entanglement has a gravitational effect then making a measurement of one of an entangled pair would remove the entanglement and thus change the gravitational effect of the other of the pair and you could at least theoretically measure that and now you are transmitting information FTL.

Presumably your measurement of 1 particle would change $T_{\mu\nu}$ in a small neighborhood of that particle, but not at the other. I would have thought that the resultant changes in the spacetime curvature would then propagate only at light speed.

For the benefit of other readers...

The basic idea in the paper is to use a semiclassical version of GR, and quantum fields on Minkowski spacetime to represent the 2 particles with variables degrees of entanglement. They show that, in a low order approximation, the expectation value of $T_{\mu\nu}$ associated with the pair of particles varies with the degree of entanglement, and they estimate the resultant effect on the gravitational field via the semiclassical Einstein equations.

The authors express their hope (near the end) that this investigation may "help in better understanding the overlap of relativity and gravity theories, and ultimately in the quest of a theory of quantum gravity". I'm skeptical of this because they're only working in lowest-order approximation, neglecting the subtleties of inequivalent representations that arise when working with QFT in curved spacetime.

I also wonder what related results might be obtainable by treating this simply as a standard QFT scattering problem -- with a gravitational interaction potential of Newtonian (or maybe post-Newtonian) form.

 

[strangerep]

For those who haven't already noticed...

Bee Hossenfelder has written a rather uncomplementary blog post about this paper -- apparently in response to an anonymous(?) arXiv blog post praising the paper.

It's good that Bee made the effort to do this -- I learned a few extra things from her blog post.

 

[atyy]

According to Bee, the paper is actually ok.

"Don’t get me wrong, the paper isn’t actually bad. This would have been a very interesting paper 30 years ago. But we’re not living in the 1980s. Unfortunately the author doesn’t seem to be familiar with the literature. And the person who has written the post hyping this paper doesn’t seem to know what they were talking about either." http://backreaction.blogspot.com/2015/01/no-long-sought-after-link-between.html

 

[strangerep]

According to Bee, the paper is actually ok. [...]

Rubbish. You only quoted a bit at the end.

At the beginning, she says:

The Physics arXiv blog has praised a paper called “On the weight of entanglement” and claimed that the author, David Edward Bruschi, found a new link between quantum mechanics and general relativity. Unfortunately, the paper is mostly wrong, and that what isn’t wrong isn’t new.

Last time I checked, "mostly wrong" $\ne$ "actually ok".

Others should read her entire blog post for themselves.

 

[noahcharris]

Just thinking out loud here, but it seems impossible to me for the following reason: If entanglement has a gravitational effect then making a measurement of one of an entangled pair would remove the entanglement and thus change the gravitational effect of the other of the pair and you could at least theoretically measure that and now you are transmitting information FTL.

Maybe a gravitational effect conferred by entanglement wouldn't have to disappear upon measurement?

 

[Demystifier]

Just thinking out loud here, but it seems impossible to me for the following reason: If entanglement has a gravitational effect then making a measurement of one of an entangled pair would remove the entanglement and thus change the gravitational effect of the other of the pair and you could at least theoretically measure that and now you are transmitting information FTL. Am I missing something? It seems very unlikely that those authors have overlooked something that obvious, so I guess I MUST be missing something.

Yes, I think you are missing something. If you could transmit FTL information in that way, then by a similar mechanism you could transmit FTL information by measurement even if entanglement had no gravitational effect. But of course you cannot do that because, in general, measurement cannot be used for FTL transmission of information. Why not? Because the effect of measurement has a random outcome, and random "information" is not information.

 

[phinds]

Yes, I think you are missing something. If you could transmit FTL information in that way, then by a similar mechanism you could transmit FTL information by measurement even if entanglement had no gravitational effect. But of course you cannot do that because, in general, measurement cannot be used for FTL transmission of information. Why not? Because the effect of measurement has a random outcome, and random "information" is not information.

Perhaps I'm misunderstanding you, but it seems that all you have done is tell me what I clearly stated that I already know, which is that FTL transmission of information is not possible. I am in fact using exactly that argument to say that I find the gravitational/entanglement concept unlikely.

 

[Demystifier]

Perhaps I'm misunderstanding you, but it seems that all you have done is tell me what I clearly stated that I already know, which is that FTL transmission of information is not possible. I am in fact using exactly that argument to say that I find the gravitational/entanglement concept unlikely.

Perhaps I was not sufficiently clear, so let me rephrase what I said. Even if there is gravitational entanglement, you cannot use it to transmit FTL information. This is because measurement creates random "information", while random "information" is not really information. Consequently, gravitational entanglement does not lead to FTL information transfer, so FTL information transfer cannot be used as an argument against gravitational entanglement. In other words, gravitational entanglement is compatible with the principle that there should be no FTL information transfer.

 

[Physics Monkey]

It may be that the measurement argument is not devastating if one takes into account the apparatus/environment. In other words, suppose one has some entanglement between two distantly separated objects (call them 1 and 2) in an otherwise empty space (and let us turn off gravity for the moment). Then the following crude account suffices to describe to measurement: an apparatus A is introduced (now space has three things in it) which entangles itself with one of the two objects. The apparatus is supposed to be big enough so that this entanglement process is essentially irreversible. Perhaps the apparatus also copies records of its measurement into outgoing photons or something. After the "measurement" the quantum state of the whole system is $$ (|00\rangle_{12} + |11\rangle_{12} ) |a_{\text{init}}\rangle_A \underbrace{\longrightarrow}_{\text{measure}} |00\rangle_{12} |a_0\rangle_A + |11\rangle_{12} |a_1\rangle_A. $$ The crucial point about this state is that while 1 and 2 are no longer entangled, 1 is still entangled with 2A as a composite system. So if A sits near 2 and measures 2, then the non-local entanglement between stuff near 1 and stuff near 2 has not changed. Now turning on gravity, if there were some semi-classical gravitational response associated directly with entanglement it seems to me that there need not be any conflict with causality in this particular case.

That being said, I think the crucial point (which the paper itself mentions) is that entanglement does not directly have an effect on the gravitational field. Gravity is still sourced universally by the stress tensor. And while it is true that entanglement within an object (composed of pieces) can change the average energy of the object, it is still just the average energy which matters classically (independent of the presence or absence of entanglement). So without commenting on any of the other issues Bee raises, the basic point of the paper rings a bit hollow to me. It is the average energy that matters, but one has the observation that the average energy sometimes depends on entanglement (and sometimes not). This later observation is certainly well known. Now I haven't thought carefully about this next bit, but it seems to me that the fact that gravity doesn't distinguish between energy associated with "non-entanglement" and energy associated "entanglement" (assuming one can even make such a distinction) has probably already been tested via equivalence principle tests since presumably a sizable fraction of the mass of nuclei, being due to interactions, is associated with entanglement.

Or maybe I missed something!

 

[atyy]

Now I haven't thought carefully about this next bit, but it seems to me that the fact that gravity doesn't distinguish between energy associated with "non-entanglement" and energy associated "entanglement" (assuming one can even make such a distinction) has probably already been tested via equivalence principle tests since presumably a sizable fraction of the mass of nuclei, being due to interactions, is associated with entanglement.

Maybe all the things that have been tested have about the same entanglement of some restricted form - isn't that the philosophy of the tensor product ansaetze?

 

[Physics Monkey]

Maybe all the things that have been tested have about the same entanglement of some restricted form - isn't that the philosophy of the tensor product ansaetze?

Maybe so. I haven't thought through it very carefully. My rough intuition is that as one increases, say, the number of constituents in a nuclei, the entanglement also goes up (and is of a pretty generic type). One might not expect a tensor product ansatz to work well since the protons and neutrons are all grouped together in a cluster without a lot of spatial structure.

 

[Jimster41]

Seems like there is clearly one "piece of information" that is exchanged FTL (or shared non-locally) - the unique location and "identity" as a space-time phenomenon of the other member of the entangled set. The idea that this map exists in the pair but is perfectly masked or invisible, "non-interacting" with space-time itself seems paradoxical to me - as if there is absolutely no observable difference between say a regular quantum and one entangled. I can buy that there might not be. But doesn't that imply something kind of weird about all quanta. We can only know if something was entangled or not by examining the post hoc correlation between it's state and (which others)? Does that mean every quantum thing correlated was - entangled?

So I guess It doesn't feel totally impossible that they could identify some tricky way of telling whether or not a quanta was "split" or "entangled" at all. Surely they must be "different" in space-time than other quanta somehow.

Lord only knows though, on this subject esp, I am probably missing ten things.

May be I'm just getting Bell EPR better... And that Indistinguishability between entangled and non-entangled quanta is exactly what those proofs dictate, and yes quantum mechanical correlation via entanglement is all reality is, period. But if the spacetime connection between the spacetime separated pairs is definitively not mapped through spacetime, through what is it mapped? if it is mapped through spacetime, through what "inaccessible" degree of freedom does it operate? If they are able to differentiate between more or less entangled pairs in spacetime, seems like an FTL communication device would have to be possible - an alphabetically indexed array made up of entangled and non-entangled quanta into which bob could type "hello world"?