Again you're putting words in my mouth I didn't say. The correlation in our scenario is one thing, and Bell's theorem is another. His inequality, which can be derived by Venn's diagram, was trying to prove whether there are hidden parameters or not. You are trying to prove that the wave function is real, and when it collapses, a spooky action at a distance makes sure the law angular momentum is conserved.
I'm not putting words in your mouth. Here is what you said:
zaybu
post #11
zaybu said:
Bell made two assumptions: 1) realism or logic, and 2) locality. If his inequality is violated, which was proved experimentally subsequently by Aspect, it means one of those two is wrong. You have focused solely on the second assumption, but most physicists have realized that it is the first assumption, which I have mentioned at least twice: classical logic fails to describe quantum system.
zaybu
post #411
In this case, you need QM only for the observation that the spins are either up or down. In classical physics, the spin of an object, be it planet earth or a top, can have any value. But at subatomic scale, it is quantized along a given axis. For that, you need QM to explain this result. But for the correlation of Alice's data and Bob's data, plain old fashion classical physics can explain that.
This isn't even wrong, it's just self-contradictory at worst, confusion at best.
zaybu said:
Susskind has a different purpose in mind. His was to show that a quantum system will violate Bell's theorem on theoretical grounds, never mind on experimental grounds. In no way this prove your twisted theory of spooky action.
Susskind's purpose is irrelevant, you were wrong about how to correctly write down the singlet state. Why can't you admit it?
zaybu said:
There's no contradiction, but more of your misunderstanding that is at play. In the first scenario, it hadn't been spelled out clearly if Alice knew that Bob was going to measure an entangled state. So for a while I was asking you from which POV your questions were assuming. That is why I came up with the second scenario so that it would be very clear that she didn't know.
What on Earth are you talking about? I said very clearly from the beginning we are talking about 2 particles in an initial singlet state, IOW an entangled state. If they aren't entangled then obviously there's no need for "spooky action", we all agree there.
zaybu said:
Again, this shows you are still hung up on the "wave collapse" misconception. All we can say is before making the measurement, we don't know in what state it is, that's why we write as a linear combination of ↑↓. After measurement, it will be either this ↑ or that ↓. What it was in the real world beforehand, we don't know. The state vector does not represent a real thing in itself. Just the probabilities.
Here you describe your interpretation, and that's certainly one possible interpretation. Griffiths calls it agnosticism. I don't think it is the most parsimonious interpretation assuming QM is correct and complete. I think the violations of Bell's theorem force you to pick a side, either QM is incomplete or we really, really have to believe what it says at face value (essentially). I would ask you a series of questions to demonstrate this, but past experience suggests you will dodge them.
Therefore, allow me to simply explain my own preferred (orthodox) interpretation, since i.m.o. you haven't done it justice.
The particles exist before we measure them. They therefore exist in some kind of quantum state before we measure them. This state might be difficult for primate brains like ours to imagine. But it does exist, and it can be
represented mathematically by the formalism of QM, i.e. the state vector or wavefunction |Psi>. Furthermore, we can know
exactly what that state is. In the case of 2 entangled fermions with total spin zero, we can know exactly what state the particles are in: they are in the
singlet state. Now, just as a wave may not have a well-defined
position, in the singlet state state each particle does not have well-defined
spin. Only particular states, called
spin eigenstates have well-defined
spin.
I prefer to emphasize the particles in a singlet state
do not have well-defined spins, although it is also of course valid to say
we do not know their spins. Sometimes the latter can be a useful shortcut. But fundamentally, I believe the former is simpler, leads to less confusion, and is less compatible with classical physics. The former is also more compatible with the assumption of an objective reality. The latter could be, in principle, compatible with classical physics. Or it could be interpreted as leading to some kind of indeterminate or subjective reality. This leads to confusion, i.m.o.
Finally, the last piece is measurement. If we take the mathematical formalism of QM seriously at face value, then a measurement (operator) acts on a quantum system (state vector). The state instantaneously "collapses" into one of the eigenstates, and the measurement obtains the corresponding eigenvalue, with probabilities given by the initial state. We are justified in being initially skeptical (as Einstein was) of all this. After all, we know from the beginning that this "measurement" must really be somehow an idealization of an interaction between a quantum system and a macroscopic system. We might expect that there are "partial measurements" where a semi-macroscopic system interacts with a semi-quantum system, and so forth, and maybe in such cases the predictions of QM break down. Or maybe a deeper theory (such as QFT) will show QM is fundamentally wrong. But as far as I know, neither of those things have happened. Aspect's measurements could have disproved the QM picture of "measurement" and "collapse" if he had obtained different results. He could have obtained results consistent with Bell's theorem. Or, he could have shown that the "collapse" is not instantaneous, it actually takes time to travel to Bob's particle. It is the incredible failure to be disproved, in face of many tests, that forces us to really, truly take the formalism of QM seriously, even if that is not the beautiful or intuitive picture we would have liked. (Actually, I find that intuition is fickle; to me, special relativity was counter-intuitive until I fully understood and accepted it as a fact; then it became "intuitive" and no longer "ridiculous").
Let me wrap up with a final comment about spooky action. To me, there is always spooky action going on with any measurement, e.g. the two-slit experiment, it's just that with two particles in an entangled state, we can experimentally rule out other possibilities. In the two-slit experiment the particle
really was in a state without a definite position, before you measured it. When the particle interacted with your detector it collapsed into a
position eigenstate. To me Alice and Bob's experiment is just an extension of the same quantum reasoning to two particles, which are also in a nonlocally "spread out" state, in a certain sense. It's just the spin of two particles which is "spread out" instead of the position of one particle.
