I Is there a bad intuition or bad explanation in quantum entanglement?

[syed]

TL;DR Summary

Title

I keep reading throughout this forum from many members that the general motivation for finding a deeper explanation within QM, specifically with regards to quantum entanglement, is due to an inability to grasp reality based off of classical intuitions. On the other hand, if QM was truly incomplete, and there was a deeper explanation that we haven't grasped yet that would explain why particles tend to be correlated to each other seemingly instantly despite vast separated distances, then that would mean our current theory simply failed to explain all of reality.

In other words, a failure of an explanation seems to suspiciously look the same as a failure of an intuition. So my question is for the people who propose that there is nothing more to reality when it comes to quantum entanglement, or that reality is fundamentally stochastic: how do you differentiate between quantum entanglement simply not obeying your intuitions vs. physicists just not having a complete theory of quantum entanglement yet?

 

[javisot]

TL;DR Summary: Title

if QM was truly incomplete, and there was a deeper explanation that we haven't grasped yet that would explain why particles tend to be correlated to each other seemingly instantly despite vast separated distances, then that would mean our current theory simply failed to explain all of reality.

The question is whether the textbook and the more complete interpretations are truly complete, in the sense of being able to describe all the results of all possible experiments involving quantum effects. It seems a legitimate question, since we don't know in advance "all the results of all possible experiments involving quantum effects" to truly know if QM is complete in its domain.

Whether QM is complete or incomplete is a separate issue from seeking a classical explanation for entanglement (which contradicts Bell's theorem).

 

[syed]

The question is whether the textbook and the more complete interpretations are truly complete, in the sense of being able to describe all the results of all possible experiments involving quantum effects. It seems a legitimate question, since we don't know in advance "all the results of all possible experiments involving quantum effects" to truly know if QM is complete in its domain.

Whether QM is complete or incomplete is a separate issue from seeking a classical explanation for entanglement (which contradicts Bell's theorem).

Well even regarding the second point, what's the difference between a "non classical" explanation and an incomplete explanation?

 

[pines-demon]

Here is a usual scheme for entanglement

• There are two entangled particles.
• Alice receives one of the particles, Bob receives the other one. Alice and Bob are far away from each other.
• Alice measures the spin z of her particle, it collapses the result of spin z of Bob's particle.

The bad analogy of quantum entanglement that is repeated in most popular physics content:

• There is a pair of shoes (it can also be gloves). The pairs are put randomly in two boxes.
• Alice receives one of the boxes. Bob receives the second box.
• When Alice opens her box, she knows instantaneously the chirality (left/right) of Bob's shoe before Bob opens his Bob. It is like if Alice collapsed Bob's shoe.

Why is it a very bad analogy:

• You are basically explaining the entangled particles with a hidden variable model and there is no issue with that here.
• You kind of want to imply that the particles, contrary to the shoes, were not defined before measurement, but where is that required here? Somebody that challenges quantum mechanics is not going to be convinced with this analogy.
• There is only one observable (spin-z, shoe chirality). Any Bell-like inequality or even the orginal EPR paper have at least another incompatible observable (spin at different angles/position-momentum). This is key.

A better analogy: GHZ experiment as explained by Mermin device.

 

[Peter Morgan]

The idea that QM is incomplete whereas, presumably, CM is complete, has colored the foundations of physics for too long. I suggest that QM is complete in the sense that it has enough resources to model any collection of data from multiple experimental sources: that is, QM is empirically complete.
OK, so what about CM? I suggest taking the no-go theorems as an indication that CM is incomplete, which I suppose leads quickly to asking how CM could be completed to be as-complete-as QM? I presented such a completion well enough for it to be published in Annals of Physics in 2020, where I call that Completed Classical Mechanics 'CM+'.
The starting point for that construction as I had it there was Koopman's Hilbert space formalism for CM, which makes it possible to compare QM with CM in the shared mathematical context of Hilbert spaces. There are two key aspects, which can be characterized as

• QM allows arbitrary unitary transformations whereas CM allows only the much more restricted canonical transformations; fixing this difference is straightforward and allows us to model incompatible experimental contexts in a classically natural way, as contextuality, within CM+. This change can be thought of as introducing the tools of Generalized Probability Theory into CM.
• If we think in a more classical way, one clear question is "What the difference is between quantum fluctuations/noise and thermal fluctuations/noise?" An unequivocal answer to this comes from Quantum Field Theory: quantum noise is Lorentz invariant whereas thermal noise is not invariant under boost transformations. This difference can be used in a classical formalism, but it requires us to work in a Minkowski space formalism, which, together with a desire to match the physics of QFT pushes us into using a classical random field theory formalism.

That out of the way, let us consider the idea of entanglement. I think, crucially, that there is such an idea only if we have an idea of a Hilbert space as a way to model systems and their properties and an idea of a tensor product of multiple Hilbert spaces as a tool for modeling a compound system and its properties. In QFT there is no such idea in the Wightman axioms and it is only by rather hand-waving arguments that we can introduce tensor products (and partial traces, which are natural enough once we have introduced a tensor product). Everything we think we know about entanglement for non-relativistic QM models is tendentious for QFT models, so that my suggestion is that we will be better to come back to entanglement when we better understand the relationship between QFT and CM+.
The ideas in that article in Annals of Physics 2020, in another article in Physica Scripta 2019, and in another in Journal of Physics A 2022 (those are arXiv links, the DOIs for the published versions can be found there) are developed further in various academic talks. As far as I can tell, everybody in physics who comes across these ideas is waiting for someone else to tell them that it's OK or not OK: being published in a reputable old-school physics journal is only a very small step towards ideas becoming widely known (unless an idea makes it into Nature or PhysRevLett or into one a few other very select places). For three of those recent talks, with the most recent, for NSU Dhaka, being the most accessible, I'm told:

• “A Dataset & Signal Analysis Interpretation of Quantum Mechanics” (Announcement, YouTube, PDF) Colloquium, School of Engineering and Physical Science, North South University, Dhaka, May 18th, 2025.
• “A Dataset & Signal Analysis Unification of Classical and Quantum Physics” (Announcement, YouTube, PDF) Special Physics Seminar, Physics Department, Yale University, May 1st, 2025.
• “A Dataset & Signal Analysis Interpretation of Quantum Field Theory” (YouTube, PDF) Philosophy of Physics Seminar, Oxford University, October 24th, 2024.

I emphasize that these do not present a complete story. It will take more than just my blundering about in a complex world to repair a century of misdirection. I don't even claim that I'm getting anything 'right'. This is my best attempt at valley-crossing, which I hope might give someone else the right push for them to do something much better.

 

[javisot]

The idea that QM is incomplete whereas, presumably, CM is complete, has colored the foundations of physics for too long. I suggest that QM is complete in the sense that it has enough resources to model any collection of data from multiple experimental sources: that is, QM is empirically complete.
OK, so what about CM? I suggest taking the no-go theorems as an indication that CM is incomplete, which I suppose leads quickly to asking how CM could be completed to be as-complete-as QM? I presented such a completion well enough for it to be published in Annals of Physics in 2020, where I call that Completed Classical Mechanics 'CM+'.
The starting point for that construction as I had it there was Koopman's Hilbert space formalism for CM, which makes it possible to compare QM with CM in the shared mathematical context of Hilbert spaces. There are two key aspects, which can be characterized as

• QM allows arbitrary unitary transformations whereas CM allows only the much more restricted canonical transformations; fixing this difference is straightforward and allows us to model incompatible experimental contexts in a classically natural way, as contextuality, within CM+. This change can be thought of as introducing the tools of Generalized Probability Theory into CM.
• If we think in a more classical way, one clear question is "What the difference is between quantum fluctuations/noise and thermal fluctuations/noise?" An unequivocal answer to this comes from Quantum Field Theory: quantum noise is Lorentz invariant whereas thermal noise is not invariant under boost transformations. This difference can be used in a classical formalism, but it requires us to work in a Minkowski space formalism, which, together with a desire to match the physics of QFT pushes us into using a classical random field theory formalism.

That out of the way, let us consider the idea of entanglement. I think, crucially, that there is such an idea only if we have an idea of a Hilbert space as a way to model systems and their properties and an idea of a tensor product of multiple Hilbert spaces as a tool for modeling a compound system and its properties. In QFT there is no such idea in the Wightman axioms and it is only by rather hand-waving arguments that we can introduce tensor products (and partial traces, which are natural enough once we have introduced a tensor product). Everything we think we know about entanglement for non-relativistic QM models is tendentious for QFT models, so that my suggestion is that we will be better to come back to entanglement when we better understand the relationship between QFT and CM+.
The ideas in that article in Annals of Physics 2020, in another article in Physica Scripta 2019, and in another in Journal of Physics A 2022 (those are arXiv links, the DOIs for the published versions can be found there) are developed further in various academic talks. As far as I can tell, everybody in physics who comes across these ideas is waiting for someone else to tell them that it's OK or not OK: being published in a reputable old-school physics journal is only a very small step towards ideas becoming widely known (unless an idea makes it into Nature or PhysRevLett or into one a few other very select places). For three of those recent talks, with the most recent, for NSU Dhaka, being the most accessible, I'm told:

• “A Dataset & Signal Analysis Interpretation of Quantum Mechanics” (Announcement, YouTube, PDF) Colloquium, School of Engineering and Physical Science, North South University, Dhaka, May 18th, 2025.
• “A Dataset & Signal Analysis Unification of Classical and Quantum Physics” (Announcement, YouTube, PDF) Special Physics Seminar, Physics Department, Yale University, May 1st, 2025.
• “A Dataset & Signal Analysis Interpretation of Quantum Field Theory” (YouTube, PDF) Philosophy of Physics Seminar, Oxford University, October 24th, 2024.

I emphasize that these do not present a complete story. It will take more than just my blundering about in a complex world to repair a century of misdirection. I don't even claim that I'm getting anything 'right'. This is my best attempt at valley-crossing, which I hope might give someone else the right push for them to do something much better.

Very interesting. One question: Are there differences between CM and CM+, or does CM+ simply represent the idea that CM is complete? Is CM+ a hidden-variable theory, or is it something even deeper?

 

[phinds]

TL;DR Summary: Title

if QM was truly incomplete

Whether QM is complete or incomplete is a separate issue from seeking a classical explanation for entanglement (which contradicts Bell's theorem).

I suggest that QM is complete in the sense that it has enough resources to model any collection of data from multiple experimental sources: that is, QM is empirically complete.

QM is KNOWN to be incomplete, although not regarding entanglement (I make no argument either way on that) but rather because it cannot handle gravity. QM is incomplete because it cannot handle the actions of subatomic particles.

We need a merge of the two into a Quantum Gravity Theory to make both complete. It's possible that that will never happen.

Both are "complete" within their own spheres of influence.

 

[Peter Morgan]

Very interesting. One question: Are there differences between CM and CM+, or does CM+ simply represent the idea that CM is complete? Is CM+ a hidden-variable theory, or is it something even deeper?

CM+ includes contextuality/measurement incompatibility, which allows multiple experiments to be modeled in a single algebraic structure, exactly as one finds in QM. This, I claim, is classically natural.

CM+ can be thought of as a hidden-measurement theory: though it begins as ordinary CM, it's more a version of thermodynamics by the end of my talks. Another way to think about how CM+ is different is that it's more like Signal Analysis than it's like CM: in the first instance there is no idea of a particle in signal analysis as an explanation for features of a noisy signal, which is different from CM, which begins with there are particles.

The idea that particles can be added later, if they can be justified, is closer to how QFT is than to how QM is. IMO, our interpretations ought to be addressing QFT in a natively QFT way instead of saying "for QFT everything is just the same as for QM".

If you watch some of that NSU Dhaka talk, which some people have liked and some have even liked a lot, let me know how you feel about it. You can have a look at the slides before committing to watching.

 

[RUTA]

In other words, a failure of an explanation seems to suspiciously look the same as a failure of an intuition. So my question is for the people who propose that there is nothing more to reality when it comes to quantum entanglement, or that reality is fundamentally stochastic: how do you differentiate between quantum entanglement simply not obeying your intuitions vs. physicists just not having a complete theory of quantum entanglement yet?

Allori has a nice overview of different types of explanation used in quantum foundations here:

https://www.mdpi.com/2624-960X/5/1/7

The two types we contrast in our papers and new book are constructive vs principle. If you want a constructive account of QM, you're looking for an explanation of entanglement via dynamical laws governing the behavior of microphysical objects (aka causal or mechanistic explanation). For example, in the kinetic theory of gases the temperature of a gas is understood constructively via the mean kinetic energy of the gas molecules. According to constructive approaches to QM, such as Bohmian mechanics, standard QM is definitely incomplete.

In contrast, quantum information theorists have developed a principle account of QM whereby its stochasticity is an unavoidable consequence of the observer-independence of Planck's constant h, and entanglement is not a dynamical effect due to some nonlocal or superdeterministic or retro causal mechanism, but a kinematic fact that follows from the relativity principle and Planck's radiation law. Accordingly, QM is as complete as possible.

As Allori writes, "people favoring different theories have profoundly different motivations guiding their search for a satisfactory theory, which leads them to favor specific explanatory structures."

 

[PeterDonis]

entanglement is not a dynamical effect due to some nonlocal or superdeterministic or retro causal mechanism, but a kinematic fact that follows from the relativity principle and Planck's radiation law.

So basically, on the "principle account" view, entanglement in QM is viewed as analogous to, say, relativity of simultaneity, length contraction, and time dilation in SR.

My reservation about this is that entanglement in QM seems to have consequences that are hard to view as "kinematic", such as violations of the Bell inequalities. Those seem analogous to invariants in SR, which are not just "kinematic".

Or, to put it another way, one can make predictions in SR without ever having to make use of any "kinematic" effects like relativity of simultaneity, length contraction, or time dilation: just use something like the tensor formalism that is used in GR. But I don't see any analogous way to make predictions in QM without ever having to make use of entanglement or the properties of entangled states.

 

[RUTA]

So basically, on the "principle account" view, entanglement in QM is viewed as analogous to, say, relativity of simultaneity, length contraction, and time dilation in SR.

Exactly. Entanglement, superposition, complementarity, and randomness all follow necessarily from the relativity principle and the observer-independence of h, just like relativity of simultaneity, length contraction, and time dilation all follow necessarily from the relativity principle and the observer-independence of c.

My reservation about this is that entanglement in QM seems to have consequences that are hard to view as "kinematic", such as violations of the Bell inequalities. Those seem analogous to invariants in SR, which are not just "kinematic".

The fundamental invariant of SR is the spacetime line element and the fundamental invariant of QM is the qubit. Those invariants entail the kinematic consequences listed above.

Or, to put it another way, one can make predictions in SR without ever having to make use of any "kinematic" effects like relativity of simultaneity, length contraction, or time dilation: just use something like the tensor formalism that is used in GR. But I don't see any analogous way to make predictions in QM without ever having to make use of entanglement or the properties of entangled states.

I'm not sure what you mean by this. Please elaborate :-)

 

[Peter Morgan]

I don't see any analogous way to make predictions in QM without ever having to make use of entanglement or the properties of entangled states.

In QFT, as in SR, I take kinematics and dynamics to be merged into a single 3+1-dimensional model of the world (my feeling is that anyone can choose whether to think of that as how the world really is or as a model.) We can still distinguish kinematics and dynamics for that kind of model if we like, but we have to introduce some kind of additional structure for us to be able to do so.
Further, in QFT, entanglement only becomes a concept for us to 'use' if we introduce tensor products and partial traces; doing that is nontrivial, so I prefer to think of the physics as about measurement results in a state that is constructed as a model of part of the world by applying measurement operators to modulate a vacuum state. The vacuum state is an ideal object that is nonlocally defined to be Poincaré invariant and, it turns out, applying measurement operators to modulate that vacuum state typically also has nonlocal (but manifestly Lorentz invariant) consequences.