## Monday, December 5, 2022

### What is Entanglement?

Entanglement is supposed tobe the essence of quantum mechanics, but I wonder about it. Wikipedia defines:
Quantum entanglement is the physical phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.[1]

Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise.

It confusingly says it is a "physical phenomenon", and then says it is a property of how quantum states are described. So it is not a physical property. I removed the word "physical".

My bigger issue is "quantum entanglement is at the heart of the disparity between classical and quantum physics". This is conventional wisdom, so it is reasonable for Wikipedia to say this, but it is true?

Classical systems obey entanglement, exactly as it is described here. Suppose you have a system of two balls, and you know their total momentum. Assume that momentum is conserved. Then the balls get separated, and you measure the momentum of one of them. You then know the momentum of the other ball, as it is perfectly correlated and opposite. The momenta must sum to the original total.

You can do the same with angular momentum.

So how is this any different from the quantum entanglement? I do not see any difference.

Anticipating your objections, you might tell me that the quantum momentum and spin are not known until measured, or that Bell's theorem puts limits on certain correlations. Okay, I accept all that, but what does it have to do with the definition of entanglement? Nothing.

Or you might say that entanglement is a nonlocal interaction. Spooky action and all that. But that is a big hoax. Quantum mechanics is a local theory.

A more sophisticated objection says that entanglement is a precious resource that can be used for cryptography, teleportation, and parallel computation. Quantum entangled particles have the necessary magic, and classically entangled ones do not.

This objection is harder to answer, as currently billions of dollars are being spent to try to determine whether any such magic exists. Most say yes, but they have yet to demonstrate anything useful from that magic.

Even if such magic exists, there ought to be a way to define entanglement that makes it clearly a quantum phenomenon, and not a classical one.

Quantum systems are different from classical systems. Bell proved that. The uncertainty principle is different, and so are certain correlations. But I don't see how entanglement is any different.

Lenny Susskind and others have been saying that wormholes and entanglement are the same thing.

Almost a century ago, Albert Einstein realized that the equations of general relativity could produce wormholes. But it would take a number of theoretical leaps and a “crazy” team of experimentalists to build one on Google's quantum computer. Read the full article at Quanta Magazine:
The idea seems to be that if entanglement and wormholes are the same thing, and quantum computers use entanglement to do super-Turing computations, then there should be some wormholes hiding inside a quantum computer. Seems like a joke to me, but I did not read the details.

Update: Peter Woit writes:

The best way to understand the “physicists create wormholes in the lab” nonsense of the past few days is as a publicity stunt ...

I’m hoping that journalists and scientists will learn something from this fiasco and not get taken in again anytime soon. It would be very helpful if both Nature and Quanta did an internal investigation of how this happened and reported the results to the public. Who were the organizers of the stunt and how did they pull it off? ...

his claims in the Quanta video that the result of the Google quantum computer calculation was on a par with the Higgs discovery. Does he really believe this (he’s completely delusional) or not (he’s intentionally dishonest)? ...

Peter Shor says: It seems to me that the string theorists and “it from qubit” community seem to have this unwritten rule that they don’t criticize other members of this community in public.

I used to think that Physics had higher standards than other sciences for truth and professionalism. Apparently not.
I thought you’d be interested to know that the “wormhole created in a quantum computer” story is now being covered in some far-right-wing media. I won’t name them here (they’re very far-right sites, not sure if you’d allow a link here), but they’re essentially saying “isn’t this manifestly stupid? See? Why should we believe scientists when they publish bullshit like this?” and essentially use the story to argue that scientists and science journalists are all a bunch of idiots, hence why should we trust them on vaccines/climate change etc.

This is another consequence of bad publicity stunts like this: it erodes trust in scientists.

Here is one such site. It is so disreputable that Google confiscated its domain name. Possibly the most censored site in the world. It just quotes a NY Times tweet, a Google tweet, a Reuters story, and a couple of more tweets, and adds:
This is very obviously fake and it’s goofy that people think it’s real.
I agree with that. It is goofy that people think that this research is real.

1. You don't mention measurement incompatibility or its algebraic formulation as operator noncommutativity. We can only verify the presence of entanglement, as something distinct from arbitrarily elaborate correlations, if we perform incompatible measurements.

2. I did mention the uncertainty principles, which is based on, as you say, operator noncommutativity and measurement incompatibility. I happen to think that is the essential difference between classical and quantum mechanics. The essays about quantum mysteries should emphasize that. But they usually talk about entanglement, and I think that it is a different topic.

1. You are very confused about Bell. They are very real and reproducible correlations that can only be explained by a "non-local" wave function we can't translate into meaningfully local physics. Your epistemic view of the wave functions is pure anti-science mysticism. I can condition on lambda with Bell's inequality (a pure statement of mathematical truth discovered by Boole), and it suggests a completion of quantum mechanics. Supercorrelation can be produced conditioning on a simple background field, which preserves deterministically local physics without conspiracy. You can simply violate measurement independence, and that's why hydrodynamic models can easily do it. Aside: the fair sampling wasn't really closed by Hensen. et. al. See: https://arxiv.org/abs/1606.00784

2. Sweden just gave a Nobel Prize for Bell test experiments, and the citation does not agree with what you say.

3. You don't even read what I write because you apparently are not knowledgeable enough to comment on these issues. The experiments to date have signaling. That's not a debate. The Nobel committee simply dismisses the probability of these loopholes. The point is that supercorrelation can EXPLAIN the experiments, the same way it explains correlations with simple water waves in a tank. What makes you reject the possibility of a background field? It's a natural explanation, as opposed to your mystification racket about a imaginary wave functions and pseudo-positivism.

Positivism doesn't support your position any more than mine. Your position is so conservative, it's risible sophomore philosophy. Your attitude would have discovered little physics of the modern era because you are essentially rejecting inductive arguments. Popper was an irrationalist crank and David Stove got him right. You don't falsify theories because it gives you no way to generate or prioritize theories. Bohr is Buddha babble.

3. Am in a hurry... and, these points have been discussed for almost a century. I think I've given the correct solution, at least for the NRQM context, via my iqWaves paper.

Anyway, very briefly (and referring to MS QM unless ref to iqWaves is specifically noted):

Quantum entanglement *is* a physical phenomenon. Evidence for it has always been there.

Re. A system of two "classical" balls. The huge difference is that no ball is ever distributed over all space. The W waves of iqWaves are, at all times. In MSQM too, probabilities to measure particles at locations are distributed over all 3D space (and, of course, \Psi is all over the entire config space).

Bell didn't prove entanglement, as you say above. He predicted an inequality concerning entanglement.

Entanglement is an *essential* feature of a system of 2+ QM particles. But QM remains radically different from pre-QM theories even for *single* particle systems. It's not a magic. ... And, if you must (even if only derisively) call it magic because it has non-locality, then I must ask: Why do you repeatedly fail to call the Fourier theory magical? Just because it's "classical"?

Keep this handy slogan in the mind:
"Entanglement = interactions".

Wavefunctions of *non*-interacting particles can be *written* down, and they don't show entanglement. But then, they also don't correspond to reality. *** All real particles are always interacting, and so, are always entangled. *** The entire universe is a giant molecule, in a way, and all parts of it are always entangled.

Note, interactions means "forces". All those one-particle WFs which enter into those tensor product states whose superposition corresponds to the entangled state, are all themselves distributed over the entire 3D space at all times.

So, absence of entanglement would've meant dynamical particles facing each other everywhere, changing everywhere, and still *not* exerting forces on each other. Very abstract and arbitrary idea. Even Newton's mechanics didn't have particles not exchanging forces through the direct contact.

Re. Uncertainty Principle (UP). To "get" QM, none needs to think in terms of UP or related notions like that of the commutator. Why, even Heisenberg himself did *not* use UP back in 1925 --- whether on that island or while writing the Three Man paper. Heisenberg cooked up the UP only later, in 1927. For the history and possible motivation, see: Mara Beller, ``The conceptual and the anecdotal history of quantum mechanics,'', Foundations of Physics, Vol. 26, No. 4., 1996, pp. 545--557. (PDF available on Semantic Scholar.)

So, *remove* UP (and commutator) from all your thought processes concerning the *basic*s of QM, and you will still "get" QM.

All that the UP says is that the QM particles necessarily have a wave-like character. That's all it says. Not that uncertainty bullshit, but the certainty of the waves character. UP is implied by the Fourier theory *and* the Measurement Problem (MP). ... Now, EE folks don't build their signals processing theory starting from UP, do they? ... So, acknowledge and highlight the correct problem --- the MP.

But not your fault either. Unfortunately, not just pop-sci books but even textbooks (even Eisberg and Resnick!) develop arguments using UP, and not the actual arguments, and so, people think that UP is necessary for QM.

For this comment, it's best that I skip over Susskind. I don't understand dS, AdS, and all that... Also, I think others have taken adequate care of that wormhole issue. [As to me Susskind and me: I've even skipped over his Theoretical Minimum books. They give a highly distorted hierarchy of concepts, and so, aren't at all helpful, IMO. In fact, I think, they provide some hindrance to development of correct understanding. An intelligent hindrance.]

Best,
--Ajit