What makes it so that quantum mechanics doesn’t break locality in entanglement yet hidden variable theories will?

In Bell‘s inequality said that hidden variables theories need to break locality in order to match experiment result. But why on the other hand quantum mechanics are able to preserve locality?

On the internet I found out two explanation on why quantum mechanics doesn't break locality in entanglement:

  1. Since you can't choose what a particle collapsed into, technically you didn't transferred information faster than light

  2. You didn't exchange information faster than light because you are only exchanging information when two observers came together and compare the result, which the process isn't faster than light

So first of all, which is correct? And why can't hidden variables theories use the same explanation?

Also, quantum mechanics noted that if you observers one particle, it'll immediately collapse the other. So does it mean that the signal of "hey I'm observed so go collapse" not consider as part of communicating faster than light? I mean gravitational waves travels only at the speed of light. So if you consider collapse as destroying the structure of the wave in the wave function, it shouldn't be able to immediately collapse the other particle, isn't it?

  • $\begingroup$ What is your question? $\endgroup$ – Norbert Schuch May 6 at 8:47

Statement 2 is correct. No information is transmitted until later, when the results of measurements are brought together. Although Alice has some information relevant to the correlation which will be found, she does not have information about what measurement Bob decided to perform, so she cannot say anything about that until later. Likewise, there is no measurement that Bob can perform which will tell him anything about Alice's measurement, or even whether Alice performed a measurement. One cannot say, for example, that Bob's wave function collapsed because of Alice's measurement. It did not.

The change in Alice's wavefunction for Bob's particle is not a physical change. It is only a change in information, which modifies probabilities and leads to different statistical results than would be the case if there were a physical mechanism connecting the particles. This is what Bell actually said to summarise the results of his theorem

“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously.” — John Stewart Bell, 1964, On the Einstein Podolsky Rosen Paradox

This does not say that a signal propagates instantly, but only that it would have to propagate instantly if there were any classical explanation. Since the statistical results of quantum mechanics are observed, there can be no classical deterministic explanation for the results of quantum mechanics.

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I don't think the Bell's inequalities state that hidden variables theories need to break locality, it simply states that any theory that aim to match the experimental results of quantum mechanics need to respect these inequalities. Hidden variables theories fail at this.

For your second question, it's probably not a good idea to think of entangled particle as communicating. Entanglement is, at it's core, correlation. When we observe entangled particles, their quantum state will be correlated to each other, where as observing two identical particles that aren't entangled will yield entirely random results.

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  • $\begingroup$ Then where does the hidden variables theories failed at? Quantum mechanics said that since it’s random, you can’t use it to transfer information. So does it mean that if we made a hidden variables theory to match experimental result, it’ll need faster than light communication. And since those theory only have pseudo-random, we could use it transfer information, compare to the true random in QM which prevents it? $\endgroup$ – Andrew.Wolphoe May 6 at 4:21
  • $\begingroup$ You don't need to invoke violation of faster than light communication or anything, nor the randomness of quantum mechanics. You don't even need special relativity. I suggest you look into the math of the inequalities, you'll probably understand a lot better. It's basically just that hidden variables theories would violate experimental results of quantum mechanics, which has nothing to do with faster than light communication. $\endgroup$ – Shamaz May 6 at 4:29
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    $\begingroup$ " any theory that aim to match the experimental results of quantum mechanics need to respect these inequalities. Hidden variables theories fail at this." --- On the contrary, quantum mechanics violates Bell inequalities. $\endgroup$ – Norbert Schuch May 6 at 8:46

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