Quantum entanglement explained by non-local hidden variables when photons are not the propagators of information?

Question

I read in WP that the biggest challenge of non-local hidden variables theory supporters in explaining quantum entanglement is:

Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables.[note 5] They are ready to give up locality, explaining the violation of Bell's inequality by means of a non-local hidden variable theory, in which the particles exchange information about their states. This is the basis of the Bohm interpretation of quantum mechanics, which requires that all particles in the universe be able to instantaneously exchange information with all others. One challenge for non-local hidden variable theories is to explain why this instantaneous communication can exist at the level of the hidden variables, but it cannot be used to send signals?[81]

I wonder if a possible answer to this challenge question could be:

Short Answer: Because we assume possible falsely, that in quantum mechanics long-range information is propagated only by photons.

Long Answer: We assume that information, or signals, are propagated classically—at the macroscopic scale and over long distances—only by photons and the hypothesized gravitons. These are currently the only known long-distance propagators of information. However, what if there exists another unknown long-range particle from the dark sector that propagates information much faster than the speed of light $c$, possibly even instantaneously over intergalactic distances?

This is why we can observe this "spooky instantaneous action at a distance" that cannot be explained via the speed of light signals. But what if we could make superluminal (FTL) signals that are not propagated via light nor gravitational waves?

This hypothetical particle could represent a non-local Hidden Variables-like (HV) mechanism, allowing for superluminal communication without using EM or gravitational waves.

Answer 1

I'm someone who has spent a lot of time with BM. The problem with having another particle mediate faster than light is not that photons move at $c$, but that things that move faster than $c$ are thought to cause paradoxes due to transfer of information to the past (I've heard that questioned recently, but that's what the prevalent opinion is). So, having another particle that moves faster than $c$ would not solve the issue, which is special relativity itself and not the speed of the force mediator, which happens (for photons) to be $c$.

The Bohmian explanation of a Bell-like entanglement experiment doesn't result in FTL signaling. That's because ultimately spin (and other non-position variables) get predicted in Bohmian mechanics through measurements in position space: when you look at the detector setup, there is generally a position being measured in the end, e.g. in a stern-gerlach device. And textbook (fixed-time $t$) quantum mechanical measurements of position provably give the same results in BM as in standard QM. That is why FTL signaling in textbook measurements is possible if and only if it is possible in quantum mechanics, and so there is no FTL signaling in these experiments in BM.

That said, there are many real measurements that are not accounted for in the postulates of textbook QM, because they are not fixed time measurements. That's the point where bets start to be off - for both theories, really. That is a whole rabbit hole/tangent that I will refrain from for now.

Answer 2

Good question, but one that does not have a single satisfactory answer. You can approach this from a couple of angles.

First, what would be the properties of this hypothetical particle/force? It would need to have a very limited interaction with the other forces most of the time, but present itself in entangled situations. After all, that is essentially what it would designed to explain. It's mechanism would be nonlocal, which would match the nonlocality reported in hundreds/thousands of entanglement setups reported in the literature over the past 30+ years. But it can't otherwise be much of a player in the standard model, as that model already successfully explains relationships between the electromagnetic, weak and strong forces. And tests of general relativity confirm its theoretical predictions as well, so no apparent place for it there either.

So we'd conclude: our hypothetical particle potentially solves one question, but appears to create an equally difficult new one. So no net gain.

Second: yes, it's true the mechanism for quantum nonlocality escapes us currently. But a few important things should be noted. Photons (electromagnetic force carriers) are the usual element that appear to manifest entanglement, but are not the exclusive element in that regard. The strong force, via gluons, appears to do the same in recent experiments. And lots of particles (electrons, ions, neutrons, etc.) appear to show entanglement without the necessity of mediation by photons.

Further, virtually any quantum observable (spin, momentum, etc,) can be used to demonstrate entanglement. It is not clear that anything is needed to mediate entanglement. For example: you can entangle systems that have never interacted at all.

Characterizing the nonlocal correlations of particles that never interacted

And... you can even entangle systems that have never even co-existed. That doesn't leave much room for a new hypothetical particle, right? There are even some indications that there are retrocausal elements to entanglement, which explains why a future measurement context is the primary driver of the quantum expectation value for entangled systems.

Entanglement Between Photons that have Never Coexisted

The result is: we need something that answers the confusion of why entanglement exists in its many various forms - without leaving obvious questions and doubts unanswered. So far, no hypothesis - of probably thousands in the literature - has done that to any reasonable degree of satisfaction. Every permutation attempted raises more questions than it answers. And the existing theory, without any new hypothetical mechanisms outside existing QM, predicts exactly what experiments show. So, there's that.

Answer 3

Let's imagine that the particle you postulated exists. Let's call it an adhocion. The adhocion somehow affects the results of entanglement experiments in the following way. (1) The adhocion somehow produces Bell correlations in the particles we observe only in situations where quantum theory predicts that such correlations should be produced. (2) The adhocion also never produces any correlations in the particles we observe that are stronger than Bell correlations.

It doesn't matter whether we have assumed that causal influences only happen as a result of propagation of gravitons or photons. Bell correlations have been experimentally tested and have passed those tests. As a result they pose a problem of why adhocions only produce Bell correlations and not stronger correlations in systems we observe.

Now, you write:

Because we assume possible falsely, that in quantum mechanics long-range information is propagated only by photons.

In quantum field theories that are the most fundamental experimentally tested quantum theories systems affect one another only as a result of changes in quantum fields that propagate at or below the speed of light. For a detailed discussion of causality in quantum field theory see "The Conceptual Framework of Quantum Field Theory" by Anthony Duncan. These theories are the ones used to make predictions about correlations between photons, electrons etc. So if you're postulating the adhocion you're proposing an alternative to quantum theories that are currently used to predict Bell correlations.

Note also that there is an existing quantum explanation of how Bell inequalities arise in quantum theory without collapse:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

https://arxiv.org/abs/2012.11189

The information that gives rise to the correlations is transmitted locally in decoherent systems as locally inaccessible information that doesn't change the expectation values of those systems but is revealed when results of measurements on them are compared.

You haven't suggested any independently testable implications of the existence of adhocions. And since quantum theory already explains Bell correlations it's a bit difficult to see why we need adhocions, or any other hidden variable theory.

Answer 4

One challenge for non-local hidden variable theories is to explain why this instantaneous communication can exist at the level of the hidden variables, but it cannot be used to send signals?

My understanding of what "non-local hidden variables" means is not necessarily that information is mediated from one location to another faster than light - or instantaneously even - but that the controlling variable in question is not at all local to the two (or more) places in question, but local only to a larger field of space consisting of both the places which are wrongly being identified separately.

Those talking of FTL mediation are implicitly returning to the hypothesis that some kind of hidden variable is local to each place, but that they are connected somehow and one responds in sympathy to the alteration of the another.

When one local variable is influenced in one place, the influence must therefore be mediated to the other place in order that the other variable responds.

That conception of the situation, where there are two connected local variables, is not only what non-local hidden variable theories explicitly deny, but is indicated (by other unchallenged physics research) to be an impossible explanation.

I'm struggling to think of analogies about this issue of scale and locality, but consider when I am standing on the floor with my two feet, and someone is stubbornly asking me which one of my ten toes I am standing on. The area where I am standing is not fully covered by any one toe and is much larger than the area covered by one toe, and the answer cannot therefore be localised to any individual toe. The one "locality" of where I am standing must be at least as large as ten toes.

That is what is being alleged with "non-local hidden variables", that the controlling variable in question applies to both places and cannot be localised to any smaller and more local place.

There is also accepted precedent for this in physics, in the sense that there are accepted to be minimum scales such as the Planck length beneath which certain variables cannot be measured even in principle because the variables themselves are encoded in or around a volume of space that is no smaller than that minimum.

Non-local hidden variable theories of QM are effectively arguing that, for the purposes of how certain physical processes work, those minimum scales of locality for the hidden variable are actually as big as the entire experimental setup.

The experimental setup often has an artificially large scale, because it was designed to try and temporarily isolate two connected local variables by enlarging the scale of distance between them, proceeding from the local-variable reasoning which is said to be faulty, rather than to overcome the non-local character of the variable which was already manifesting at much smaller scales and does not need physically large apparatus to demonstrate it.

Again to fall back on the analogy, it's like trying to get around the ten-toe minimum area for where I am standing, by telling me to spread my legs even wider - which only further delocalises the scale of the perimeter within which I am standing, and helps none at all in localising my standing area to a particular toe.

Answer 5

Yes there is a "great mystery" (quote by Feynman) even in the simple double slit experiment (DSE) ... how do the single photons know there are 2 slits and thus interfere? Somehow the photon has exchanged information with the apparatus. The same mystery is also found in thin films in optics ... photons can be reflected or absorbed simply by setting film thickness, somehow the single photons have exchanged information with the film.

A simple answer is that none of these effects are observable unless there is some kind of apparatus, the apparatus has its own EM field that interacts with photon EM field .... this could happen at speed c ... it would explain BM because this interaction is impossible to observe directly ... we can only see the result.