Key points of quantum entanglement as I think
When the general public talks about quantum entanglement, they really do not ask for deep understanding. They would say: When the two particles are far apart, and the information cannot be transmitted faster than light, you measure the (spin) state of one particle and you immediately know the (spin) state of the other particle. They said this is magical: could the information be transmitted from this particle to the other at the speed of faster than light?
But the problem is, if we know that the two particles are in different states (the spins are in opposite directions), and one is detected, of course we will know the other, which does not require any faster than light information transmission. It is as if two people divided a jade seal into two halves, each taking half, and traveled far away. Later when you see any one half, of course you would know that the other person has taken the other half.
The key to the problem lies in the randomness of the spin directions of the two particles. That is to say, although we know that the spin directions of the two particles are opposite, the spin direction of each particle, the particle itself does not even know, because it is not fixed yet, both positive and negative are possible. Only when you measure one, the spin direction of this particle seems to be known by the other, so the other "chooses" to take the opposite spin, this is "spooky action", how does the other know to take different direction? This is equivalent to say that two people each took half of the jade seal, but each person took not a fixed half - not because it is unknown but fixed, rather it can indeed be either this half or that half and may change all the time. The jade halves seem to have spirit and temper. In the hands of one person, it may be this half, or it may be the other half, but it is always the opposite, so that the two people do not know which half they took.
Therefore, the problem of quantum entanglement is not that they are too far apart, and the information propagated by the speed of light cannot reach, but it is still: 1) why a particle may be either this or that; 2) why two are always in different directions. The first question is still the fundamental question of quantum mechanics, namely: why a particle can be this or that, which is called "superposition". The second problem is related to the Pauli exclusion principle.
Since these two problems are fundamental to quantum mechanics and are related to superposition, they must also be related to the uncertainty principle.
(Therefore, it is a question of "realistic" or "anti-realistic".)
In other words, the biggest issue of quantum entanglement is not at the moment when the two particles are separated and measured. The highlight is every moment, especially at the beginning. Let's see what happens when they are together: when these two particles are together, if we think of them as a system with its own pair of covariates, the pair must also satisfy the uncertainty principle. There is one pair of covariates, one of which is the sum of the angular momentum of their spins. According to the Pauli exclusion principle, the two spin directions must be opposite. What is the covariate corresponding to this "sum" covariate? We don't care about it, but it can be the spin of a particle. According to the uncertainty principle, since the "sum" of the angular momentum of the spins of two particles is determined, the spin direction of each particle itself is (extremely) uncertain. Therefore, quantum entanglement is only possible because of the Pauli incompatibility principle and the uncertainty principle. That's also why we can see that Spooky Action.
Therefore, it also made me more convinced of my own hunch for some time, "Pauli's exclusion principle is similar to quantum entanglement in nature." If the two particles are not exchanging information instantaneously, how can they know whether they are compatible or not? Generally, the explanation of Pauli's exclusion principle is based on wave function theory, but such explanations are all "after the fact". That is, they assume that two electrons are already in one orbit, according to the wave function theory their spins must be opposite. But what I care about is the process: suppose there is an electron in a lower orbit and then another electron falls from a higher orbit. The spin of this later electron needs to be different from the previous one. Was it negotiating with the electron in the low orbit on its way down? (I think this must be related to the relativity of time in the theory of relativity, and it must also be related to Roger Penrose's quantum gravity. This will be discussed another time)
If it is in Bohm mechanics, I think there will be no quantum entanglement of the usual sense. There, it was like the jade seal was cut in half, and when you saw half of it, you immediately knew what the other half was. It had nothing to do with the speed of light or not. When we measure the spin of a particle, we indeed don't know its spin direction, but this is because we didn't know it from the beginning. This probability is no different between Bohm's mechanics and the usual quantum mechanics, but the meaning is different. But the problem is that in Bohm mechanics, we are also ignorant of the initial distribution of particles or systems. This seems to move the uncertainty principle from an instant before the measurement to a time before it. The results have no difference. Moreover, Bohm mechanics also caused other things like quantum entanglement.
The debate about Realistic and anti-realistic of quantum mechanics seems to be a dispute between Descartes' dualism and Spinoza's monism. According to Descartes, the soul is independent of matter. How does the soul control the body? He can only say that a gland in the brain controls the body. In Spinoza's monism, material and spirit exist simultaneously and die simultaneously. Monism has basically defeated dualism, but who knows, maybe one day, the development of artificial intelligence will change this conclusion. In any case, the monistic statement is the most concise and conforms to the law of Occam's razor. (Einstein is worthy of being the first apostle of God. He said: The simplest, but not simpler). This "orthodox" quantum mechanics, no matter how unrealistic, is the simplest. Therefore, although Einstein thought of the navigation wave of De Broy-Bohm, he refrained and didin't support this. He is indeed a master.