But what is it?

Everything is Entangled in Quantum Mechanics: Are the Orthodox Measures Physically Meaningful?According to a lot of modern scholars, entanglement is a resource that can be exploited to give secure communication and super-Turing computability.Christian de Ronde, Raimundo Fernandez Moujan, Cesar Massri

Even though quantum entanglement is today's most essential concept within the new technological era of quantum information processing, we do not only lack a consistent definition of this kernel notion, we are also far from understanding its physical meaning [35]. These failures have lead to many problems when attempting to provide a consistent measure or quantification of entanglement. I

The paper discuss various definitions in the literature and concludes:

We have shown how entanglement, as the unitary multiscreen effect of a single power, is an irreducible aspect of the operational content of the theory of quanta. The theory talks about powers of action each one them producing a multiscreen (non-local) effect that can be observed in the lab. Consequently, there is nothing non-entangled in QM. There is no meaningful distinction between something that is entangled and something that is not entangled within the theory of quanta. The attempt of quantifying or measuring the level of entanglement becomes meaningless.I think that entanglement is not something real. It is an artifact of how QM works, but there is no way to objectively say whether a particle is entangled or not. So we should not talk about entanglement as if it is some mysterious resource.

Maybe I will be proved wrong by some quantum computer that uses entanglement to break RSA or some other calculation that cannot be done otherwise. Then I will have to admit that entanglement is real and useful. But nothing like that has ever been done.

Sean M. Carroll tries to explain entanglement in a recent podcast:

I 0:20 think you know entanglement arises 0:22 directly from that statement we made 0:23 long ago that when you have a Quantum 0:25 system you do not have separate wave 0:27 functions for each part of it you only 0:29 have one wave function for the whole 0:30 thing and the job of the wave function 0:33 is to make predictions for observational 0:35 outcomes so if that's all true then it 0:38 could be the case that if you predict 0:41 the outcome for one thing and another 0:43 thing particle a and particle B there 0:46 might be correlations or connections 0:48 between those measurement outcomes so I 0:50 don't know what I'm going to see when I 0:52 ask what is the spin of particle a and I 0:54 don't know what I'm going to seeIf this is the definition of entanglement, then there is nothing quantum mechanical about it. Classical physics shows the same phenomenon.when I 0:56 ask what is the spin of particle B but I 0:58 know they're going to be opposite so 1:00 then that's entanglementand it tells me 1:02 were I to measure particle a I have no 1:04 idea what I'm going to observe but as 1:06 soon as I do I know what the outcome is 1:08 for particle B and this bugs people 1:11 because how does particle B know what 1:13 its outcome is supposed to be it could 1:15 be light years away

If split a classical system with angular momentum zero, separate the halves, and measure the angular momentum of one half, then the other half will have the opposite angular momentum. Just like how Carroll described QM.

When asked for more explanation, he says that he prefers the Everett many-worlds interpretation. However he admits that no one knows whether the effect of a measurement propagates at the speed of light or less in the universal wave function, or propagates instantaneously.

What? I thought that the whole point of Everett was to clarify what happens quantum mechanically when a measurement takes place. But if he cannot tell how the result propagates, then I do not see how it can tell me anything.

See also this podcast, where he starts by saying the Everestt theory is the most straightforwad interpretation of the Schroedinger equation, but it requires splittings into parallel worlds and we do not know what a world is. We also do not know if the wave function is real. Later, at 45:30 he says, "I mean the real answer there is I don't think about all those other worlds, that much again the worlds are a prediction of the theory they're not what the theory is fundamentally about."

Carroll goes on to explain the Bell tests:

also in the 1960s John Bell proved his 6:17 theorems he proved theorems about the 6:20 different predictions between a local 6:22 Theory and a non-local theory like 6:24 quantum mechanics and that made it an 6:27 experimentally accessible question so 6:29 people did the experiment and they just 6:31 won the Nobel Prize a couple years ago 6:33 so physicists are very interested now 6:35 because there's an experiment you can do 6:37 of course the experimental result was 6:38 exactly what schrodinger would have 6:40 predicted back in the 1920s it didn't 6:42 change our idea of quantum mechanics but 6:44 as long as you can do an experiment 6:45 they're happy having said that because 6:48 physicists have ignored the foundations 6:49 of quantum mechanics for so long even 6:52 theAgain, this is startlingly foolish. He correctly says that the prize-winning experiments just confirmed what quantum mechanics would have predicted in the 1920s, and did not change our idea of quantum mechanics.Nobel Prize press release botched it6:55 they gave the wrong explanation for what 6:57 was going on because they didn't really 6:59 understand what they just give the Nobel 7:00 Prize

So how did the Nobel press release botch it? It certainly did not say that the experiment changed our view of QM. That would have been big news. See my earlier post for more details.

Carroll's real gripe is that he wants to fund more research in the foundations of QM, and the Nobel committee refused to acknowledge that the experiments left unsettled issued. In particular, he wants to push many-worlds theory, but it gets no Nobel endorsement. The Nobel committee correctly said that the experiments confirmed what everyone thought for many decades.