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Bell's therorem seems to disprove localism because measuring, let's say spin of an entangled electron, seem to communicate the measurement to it's another pair instantaneously.

But isn't another thing possible?

Maybe the electrons are not communicating anything and instead the two instruments which are measuring the electrons "know" at what angle the other instrument is measuring the other electron and that is a part of the measuring process of instrument and thus the Bell's equality is violated but local realism is still valid. Here the two instruments and the people who are performing the experiments are in some kind of weird sync where they cannot measure arbitrarily in any direction but instead the measurement angles are predetermined before hand and the instruments already know the angles with of each other which are used to measure, hence the spin directions can be correlated. This would mean that Universe is deterministic but also locally real.

Is this at least theoretically possible? If it is possible wouldn't it be more saner theory to adopt rather than throwing local realism away? Why? Why not?

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    This is one of the possible loopholes. If I read you correctly, you are talking about "statistical independence" or "superdeterminism" loophole. To put it simply, you'd have to explain why there is a "weird sync" that pre-determines the measurements to be what they are. – Maximal Ideal Jul 10 '23 at 19:10
  • @MaximalIdeal Yeah even if the sync is left unexplained wouldn't it be still a better alternative than "spooky action at a distance"?? – Hari Kumar Jul 10 '23 at 19:17
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    Does this answer your question? Why is superdeterminism generally regarded as a joke? (It's not a great question, but there are some decent answers.) – benrg Jul 10 '23 at 19:38
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    Superdeterminism (the word for what you're describing) isn't falsifiable, so it's not really in the realm of science. – DanielSank Jul 10 '23 at 20:01
  • Bell's theorem(s) shows quantum theory violates certain inequalities and any theory belonging to a certain class of hidden variable theories considered by Bell has to be non-local to reproduce that. Bell's or similar theorems do not disprove world is local or some such thing, because they're just theorems based on assumptions. To prove something about the world, one has to do experiments. There are experiments manifesting violation of Bell's inequalities, and thus the orthodox view is any good hidden variable theory that can capture that has to be non-local. – Ján Lalinský Jul 10 '23 at 22:44
  • However, there is also unorthodox current in theoretical physics which points out Bell assumed something called "statistical independence", which is not a strictly necessary assumption. This is also known as the "free will" assumption - that the experimenter is free to choose what he measures, and this choice is not correlated with the measured system state. – Ján Lalinský Jul 10 '23 at 22:48
  • @DanielSank why is it not falsifiable? Can you share a link to such analysis? – Ján Lalinský Jul 10 '23 at 22:56
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    @JánLalinský it's self evident. How can you possibly falsify the statement "this experiment was pre-determined to yield the results that it yielded"? – DanielSank Jul 10 '23 at 23:58
  • https://physics.stackexchange.com/a/106761/28512 – alanf Jul 11 '23 at 06:38
  • A local explanation of the Bell correlations that uses quantum physics instead of making up new stuff that is unnecessary https://physics.stackexchange.com/questions/746135/how-does-bells-theorem-disprove-realism/746167#746167 – alanf Jul 11 '23 at 07:15
  • @alanf that anawer is very confusing. What exactly do you mean by quantum theory?? Can you link any article which explains it?? How is it local if the communication is instantaneous?? – Hari Kumar Jul 11 '23 at 08:54
  • @HariKumar The communication isn't instantaneous. The correlations are established when the results are compared not before as explained in the links in the answer. – alanf Jul 11 '23 at 09:04
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    You cannot use superdeterminism to save local realism - superdeterminism is much stronger: once you accept that any observation is what it is for the only "reason" that is has been determined to be so, there is no need for any other organizational principle, not even for logic actually. There is just no room left for science anymore, nothing to study, nothing to comprehend. Superdeterminism is to physics what solipsism is to philosophy: a sterile, unfalsifiable, paranoiac way to make sense of things. – Stéphane Rollandin Jul 11 '23 at 10:14
  • @StéphaneRollandin Hmm I'm not sure whether I'm arguing for superdeterminism. I'm rather arguing for entanglement between measuring apparatus(including humans) where the communication is slower than the speed of light hence preserving local realism. – Hari Kumar Jul 11 '23 at 11:30
  • @DanielSank okay but that is more of a philosophical/worldview statement. Superdeterminism in the context of QT is a more specific idea: that hidden variables need not always be independent of the detector settings. It is a mathematical property, not some grandiose statement about the world. Cf. https://www.frontiersin.org/articles/10.3389/fphy.2020.00139/full – Ján Lalinský Jul 11 '23 at 14:41
  • @JánLalinský If it's unfalsifiable then it's philosophy and not science, by definition. – DanielSank Jul 11 '23 at 15:07
  • @DanielSank So what, the important thing is it leads to exploration of different, hopefully falsifiable mathematical models. – Ján Lalinský Jul 11 '23 at 22:35

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Maybe the electrons are not communicating anything and instead the two instruments which are measuring the electrons "know" at what angle the other instrument is measuring the other electron

The problem with that is that you don't have to make the decision about which way to measure it until the moment of measurement, and in that case how can the two instruments 'know'? You are simply replacing FTL-communicating electrons with FTL-communicating measurement instruments.

They also did an experiment where the choice of which direction to measure was decided by the light from two distant quasars on opposite sides of the universe, for which there is no sub-lightspeed way for them to have communicated. It still worked.

'Superdeterminism' is a logically possible alternative, but effectively abdicates any need for explanation, which negates the whole purpose of physics.

But isn't another thing possible?

Oh, yes. If you throw away the assumption that the macroscopic world obeys different rules and that the wavefunction collapses, and instead take seriously the idea that the rules of quantum mechanics known to work at the microscopic level are in fact universal, you find you get a theory that explains our observation of a 'classical' world, as well as all those entangled long-distance quantum correlations, while being entirely local, deterministic, and realist. That's the Everett Interpretation.

Yeah even if the sync is left unexplained wouldn't it be still a better alternative than "spooky action at a distance"??

You would think so, wouldn't you?