How Does the EPR-Paradox Relate to Entanglement and Nonlocality?

[jfizzix]

jfizzix submitted a new PF Insights post

Steering: How the EPR-Paradox Fits Between Entanglement and Nonlocality

Continue reading the Original PF Insights Post.

 

[Strilanc]

Steering is... a really terrible name for this. From a paper:

The steering task. Bob is skeptical that Alice can remotely affect (steer ) his state. Bob trusts quantum mechanics (represented by the white box), but makes no assumptions about Alice (represented by the black box). The steps in the task, from top (1) to bottom (4) are as follows. 1. Bob receives his qubit. He is unsure whether he has received half of an entangled pair (a) or a pure state sent by Alice (b). 2. After Bob receives his qubit, he announces to Alice his choice of measurement setting from the set {σˆ B k }. 3. Bob records his own measurement results σ B k and receives the result Ak which Alice declares. 4. Bob combines the results to calculate (over many runs) the steering parameter Sn. If this is greater than a certain bound, Alice has demonstrated steering of Bob’s state, and thus Bob can be sure that he received (a) not (b).

I'd have called this "the correlated measurement task". Alice's goal is to match Bob's measurement results.

 

[jfizzix]

Another complication is that when someone in the literature says they're demonstrating EPR-steering, they could mean one of at least three things:
1.) Showing the state could violate a steering inequality
2.) Showing that the correlations between measurements do violate a steering inequality (this is useful for more robust quantum key distribution)
3.) Actually "EPR-steering" something. This would be where Bob does random measurements to reconstruct the state of B, and finds that when he conditions on what Alice tells him, the conditional state he reconstructs is under more of Alice's control than classically possible.

It's generally clear from context, which one of these is being done, though.

 

[Android Neox]

"Action at a distance" requires instantaneous effect over distance, simultaneity. After 110 years of studying and testing special relativity we know the conclusion of non-simultaneity is correct. The concept of instantaneous has no physical meaning for more than one reference frame at a time. It's painfully obvious that action at a distance cannot be a correct interpretation of entanglement.

Imagine a Bell's experiment where the entangled particles fire off in opposite directions, one east and one west. The east-bound particle is measured by an observer moving east at .9c and the other by an observer moving at .9c to the west. From the perspective of an observer in the middle, the observers measure their particles simultaneously. Each of the moving observers see themselves as making the first observation and collapsing the wavefunction. The result of the experiment cannot be explained with the standard explanation. The results will be consistent with both observers making the first observation.

 

[jfizzix]

"Action at a distance" requires instantaneous effect over distance, simultaneity. After 110 years of studying and testing special relativity we know the conclusion of non-simultaneity is correct. The concept of instantaneous has no physical meaning for more than one reference frame at a time. It's painfully obvious that action at a distance cannot be a correct interpretation of entanglement.

Imagine a Bell's experiment where the entangled particles fire off in opposite directions, one east and one west. The east-bound particle is measured by an observer moving east at .9c and the other by an observer moving at .9c to the west. From the perspective of an observer in the middle, the observers measure their particles simultaneously. Each of the moving observers see themselves as making the first observation and collapsing the wavefunction. The result of the experiment cannot be explained with the standard explanation. The results will be consistent with both observers making the first observation.

Consistent, but still not locally explainable.
Quantum mechanics predicts that there is no fundamental limit on the strength of measurement correlations between any pair of observables on a pair of particles.
However, if you assume locality, then there is a fundamental limit to the strength of correlations between a pair of particles (this being that you cannot predict a particle's measurement outcomes with an uncertainty smaller than what the Heisenberg uncertainty principle allows).
Because we can experimentally verify arbitrarily strong correlations and successfully make such predictions, something demonstrably nonlocal must be going on. Whatever comes of it, it's a loose end that remains to be understood.

That being said, the only way for any agent to know that something nonlocal is going on is to have the data from both particles, which would have to be communicated to them at or below the speed of light.

It's a running theme in quantum mechanics that all the weirdest paradoxes and such come from trying to figure out what's going on with quantum systems when they're not being measured.
Cool to think about, though..

 

[Android Neox]

That being said, the only way for any agent to know that something nonlocal is going on is to have the data from both particles, which would have to be communicated to them at or below the speed of light.

Only non-local in a "universe" model, which is obviously inconsistent with QM. Only multiverse interpretations are consistent with QM and possible within known physics, e.g. non-simultaneity.

Action-at-a-distance requires simultaneity and so is obviously not a correct interpretation of entanglement.

 

[Jeronimus]

Only non-local in a "universe" model, which is obviously inconsistent with QM. Only multiverse interpretations are consistent with QM and possible within known physics, e.g. non-simultaneity.

Action-at-a-distance requires simultaneity and so is obviously not a correct interpretation of entanglement.

Wouldn't it be obvious that if there is action at a distance, it would be action at a spacetime-interval(distance) rather than just a space-interval(distance), as as you mentioned already, different observers moving at different velocities relative to each other would consider the two events to be happening at different times.
Only within one specific inertial frame would the events occur "at the same time"

 

[Android Neox]

Wouldn't it be obvious that if there is action at a distance, it would be action at a spacetime-interval(distance) rather than just a space-interval(distance), as as you mentioned already, different observers moving at different velocities relative to each other would consider the two events to be happening at different times.
Only within one specific inertial frame would the events occur "at the same time"

The "action at a distance" interpretation of entanglement is that the act of observing the state of one member of an entangled pair causes, in that instant, the state of its partner to change from a multiplicity of all possible states to one particular state. Simultaneity. Without simultaneity, the argument doesn't work.

But, 110 years of examining and testing of Special Relativity have proven (It's the closest thing to established fact that I can think of.) non-simultaneity. That is, for every frame that sees two physically separated events as simultaneous, there is another equally valid frame for which one preceded the other and another equally valid frame from which the events occurred in reverse order. Non-simultaneity.

I think the only reasonable interpretation is not that observation alters the observed but that observation alters the observer. Do physicists think they are free of the constraints of physical law? If an observer were to observe a mismatch between the entangled particles, (s)he would enter a quantum state for which there would be no Hermitian eigenmatrix. Literally, the observer would enter an "unobservable" (Schrödinger's term, but he probably said it in German) state.

There's no reason to think every event acts backwards through time with the observations altering the observed. Delayed choice experimental results are not reversed time processes. Entanglement doesn't require simultaneity. Just presume the math of QM is correct and remember the rules apply to everything in the universe. Observation alters the observer. Observation of anything inconsistent with the observer's state would put the observer into an impossible state, and so inconsistencies (violations of conservation symmetries) are never observed. But, if every observer is "collapsing the wave function" for themselves, the only way to get an apparently seamless reality is a multiverse in which everything that can happen does happen.

Personally, I prefer causally-consistent models, even if they do require a multiverse.

 

[vanhees71]

There is no action at a distance related to entangledment, but it's described by states of systems that are not localized and thus observations of far-distant parts of the system can be correlated, but this correlation is due to the preparation of the state long before any measurement on the partial systems is done. The new aspect of quantum theory as compared to classical theory is that there can be 100% correlations of observables on partial systems that are utmost uncertain (undetermined), i.e., the quantum correlations described by entangled states, where observables of far-distant parts of the quantum system, are much stronger than allowed by any local-deterministic (hidden-variable) model. There is, however no action-at-a-distance (instantaneous) causal effect by measurement on partial system A on any far-distant measurement on partial system B. This is so by construction of relativistic quantum theory in term of local, microcausal quantum field theories (as is the Standard Model of elementary particles).

 

[Android Neox]

There is no action at a distance related to entangledment, ...
... There is, however no action-at-a-distance (instantaneous) causal effect by measurement on partial system

I agree that there aren't hidden variables, local or otherwise.

Within a universe model, how is the Bell inequality explained? How about the simpler case of an entangled pair of particles? Clearly, at the instant of observation the set of possibilities for future observations changes, for the observer. For example, observing that particle (A) of a pair has spin up would (in the right kind of experiment) guarantee that particle (B) could only be observed to have spin down. For the observer, as soon as the state of (A) is observed, the state of (B) is known. Simultaneity.

Unless all changes to reality are constrained by the speed of light, the theory is going to have serious problems. If it depends upon simultaneity (and I cannot see how to avoid this in a universe model) then it cannot be correct unless special relativity is entirely wrong (which is going to be an even more serious problem).

 

[bhobba]

Within a universe model, how is the Bell inequality explained?

By QM.

How about the simpler case of an entangled pair of particles? Clearly, at the instant of observation the set of possibilities for future observations changes, for the observer. For example, observing that particle (A) of a pair has spin up would (in the right kind of experiment) guarantee that particle (B) could only be observed to have spin down. For the observer, as soon as the state of (A) is observed, the state of (B) is known. Simultaneity.'

Put a red bit of paper in an envelope, a green bit of paper in another and send one to the other side of the universe. Open one and you know the contents of the other with all that is said above holding. Yet its not some deep deep mystery - but for some reason some want to make out EPR is. Its exactly the same - just a correlation. The key difference is QM is silent about the value of quantities until observed. The paper is red or green at all times. This crucial difference allows a correlation between objects with statistical properties different to the paper slips. That's all EPR is - just a correlation with novel statistical properties. Its not some great deep mystery - QM explains those statistical properties easily so we know exactly what's going on. The issue is simply this - since QM is silent on the value of quantities before observation what if we insist they do have values. QM doesn't say one way or the other. It turns out if you insist then you need FTL communication - but only if you insist. That is very very interesting, and would have rightly earned Bell a Nobel prize had he lived - but if FTL worries you simply don't insist.

Unless all changes to reality are constrained by the speed of light, the theory is going to have serious problems. If it depends upon simultaneity (and I cannot see how to avoid this in a universe model) then it cannot be correct unless special relativity is entirely wrong (which is going to be an even more serious problem).

There is no issue with FTL or even instantaneous communication and relativity providing it can't be used to send information. The interesting thing about standard QM is its based on classical mechanics, and as Landau explains in his beautiful but terse textbook, right at its foundations it is non-local (it obeys the Galilean transformations - and so does ordinary QM):
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

In fact you can see the dynamics QM developed from that assumption alone in Chapter 3 of Ballentine - but that is just bye the bye.

One needs to go to QFT to rectify that and the concept of locality there is rather more subtle:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

One needs to exclude correlated systems, and bell states are correlated. This leaves the whole question of locality and EPR in a rather interesting position. One could argue, and I do, the question of locality doesn't even apply. But that is a matter of interpretation and opinion.

Thanks
Bill

 

[vanhees71]

I agree that there aren't hidden variables, local or otherwise.

Within a universe model, how is the Bell inequality explained? How about the simpler case of an entangled pair of particles? Clearly, at the instant of observation the set of possibilities for future observations changes, for the observer. For example, observing that particle (A) of a pair has spin up would (in the right kind of experiment) guarantee that particle (B) could only be observed to have spin down. For the observer, as soon as the state of (A) is observed, the state of (B) is known. Simultaneity.

Unless all changes to reality are constrained by the speed of light, the theory is going to have serious problems. If it depends upon simultaneity (and I cannot see how to avoid this in a universe model) then it cannot be correct unless special relativity is entirely wrong (which is going to be an even more serious problem).

I don't know, what you mean by "universe model", but for the two particles or photons it's clear. Say we have the usual singlet state for the polarizations of two photons $|\Psi \rangle=(|HV \rangle-|VH \rangle)/\sqrt{2}$. If now A measures that her photon is horizontally polarized, and then she knows immediately that B must find a vertically polarized photon, but B doesn't know it instantaneously, but A must send him a message of her knowledge, for which she can only use signals which spread at most with the speed of light. If B doesn't get this information from A he'll just find a vertically polarized photon, but he cannot predict this. For him, the stream of photons in an ensemble of such prepared photons is still just a stream of unpolarized photons. Only exchanging the information on their measurements A and B can observe the 100% polarization correlations (when they measure the polarization in orthogonal directions; for arbitrary angles between the polarizers at A and B you get other statistics for the pairs of polarizations, including such that violate the Bell inequality based on local deterministic hidden-variable models). Thus, there's no faster-than-light communication possible using entangled states.

 

[Lynch101]

"Action at a distance" requires instantaneous effect over distance, simultaneity. After 110 years of studying and testing special relativity we know the conclusion of non-simultaneity is correct. The concept of instantaneous has no physical meaning for more than one reference frame at a time. It's painfully obvious that action at a distance cannot be a correct interpretation of entanglement.

Imagine a Bell's experiment where the entangled particles fire off in opposite directions, one east and one west. The east-bound particle is measured by an observer moving east at .9c and the other by an observer moving at .9c to the west. From the perspective of an observer in the middle, the observers measure their particles simultaneously. Each of the moving observers see themselves as making the first observation and collapsing the wavefunction. The result of the experiment cannot be explained with the standard explanation. The results will be consistent with both observers making the first observation.

Apologies if this is considered resurrecting a zombie thread, but I was searching for information on this and I wasn't sure my question warranted a thread of its own.

The example you give above, pertaining to the simultaneous measurements of the particles, has both observers making a measurement simultaneously (in a given reference frame).

What if only one of the observers measures the particle, will we still have two simultaneous events (in the given frame) i.e. the measurement in one frame with the collapse there, and the collapse of the other particle to a definite momentum/position?