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I was reading this post:

http://motls.blogspot.com/2015/06/locality-nonlocality-and-anti-quantum.html

Specifically here: "There is no nonlocality. There is no action at a distance. There is no doubt about this statement."

I am puzzled how locality is preserved. Suppose we do the standard experiment with two correlated particles. We measure one particles spin along a particularly axis. The other particle has opposite spin along the same axis.

If the particle does not have a spin before it is measured, and if you measure the spin of one, the other has definite opposite spin... how is there not some kind of action at a distance?

EDIT:

Here's a video with Murray Gell-Mann where he says the same thing. But it still doesn't clear up anything for me:

https://www.youtube.com/watch?v=AlIlkn3OxMI

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    $\begingroup$ See no-communication theorem $\endgroup$ – ACuriousMind Feb 21 '16 at 1:13
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    $\begingroup$ @ACuriousMind, I understand communication is not possible using this system. But that's not my question. $\endgroup$ – Ameet Sharma Feb 21 '16 at 1:15
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    $\begingroup$ But that's what locality is - preventing space-like separated events from actually transmitting information. It does not forbid correlation as such. $\endgroup$ – ACuriousMind Feb 21 '16 at 1:17
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    $\begingroup$ There are a red and a blue marble in a bag. We each take one without looking. Then you go to Pluto. I look and see a red marble. I instantly know you have a blue marble. Something to ponder... $\endgroup$ – user10851 Feb 21 '16 at 2:08
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    $\begingroup$ @ChrisWhite, this is fine if the marble has a color when you're not looking. Or it has the property that "if it was looked at, it would be red". If the marble has no such property when you're not looking, then we have the same issue. Action at a distance. $\endgroup$ – Ameet Sharma Feb 21 '16 at 2:12
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In general terms -

Locality is preserved in one of the two ways -

  1. The two entangled particles start with a complex/capable enough wave function that generates the correlation even when independently (without need of any mysterious link) working on two particles. - This is mainstream, most accepted quantum explanation. I guess this is referred to as superposition principle, multiple particle joint amplitude .. If someone has learnt the QM math well enough, then there are high chances that this will be the best solution in his/her opinion.

  2. Many people still seem to think that all possible classical explanations of correlation have not been exhausted, and there can be some explanation that still needs to be discovered.

The correlation means following behavior -

a) anti correlation in every direction, always

b) statistically 50/50 in any one direction for each particle independently

c) statistically Sq(sin(A/2)) correlation at relative angle of A.

d) Please comment if any additions/correction are needed to the above three.

Local variables/plans (i.e. fully pre-determined plans) are not sufficient to exhibit the correlations and this has been mathematically proved by Bell's inequality.

Bell's inequality disproved the ability of "local" "static" "variables" to describe the correlation. It did not disprove same for "local" "functions" like superposition etc.

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  • $\begingroup$ Regarding the first way locality is preserved... do the particles have a spin before measurement is done? If these spins do not exist before measurement, then I don't understand how there can be a correlation in the measurements without some instantaneous action at a distance. $\endgroup$ – Ameet Sharma Feb 21 '16 at 7:04
  • $\begingroup$ That is the mathematical magic, superposition has to perform. Meaning the wave function has multi level deep functionality that makes it so capable. You can get convinced only by learning sufficient QM. I myself do not know the math but I know that is what it is. Due to this "almost magical" mathematical capability of the superposition, some people confuse it with non-locality and think there is an FTL link. $\endgroup$ – kpv Feb 21 '16 at 7:19
  • $\begingroup$ And some people still think there can be another yet to be discovered explanation. One thing that almost everyone agrees is that there is no FTL communication. I personally am not fully convinced with the superposition explanation (partly because, I have not learnt the math), but one has to respect the wisdom of so many credited people. $\endgroup$ – kpv Feb 21 '16 at 7:22
  • $\begingroup$ @AmeetSharma: The first problem with your sentence is the use of the word "particle", the second is the use of plural. There are no particles in quantum mechanics, there are only quanta. There is, truthfully, only one object, at all, and every part of the experiment is really part of that object: the physical vacuum. $\endgroup$ – CuriousOne Feb 21 '16 at 7:24
  • $\begingroup$ @Curious, I don't see how that avoids action at a distance. Even if the universe is just one object, doesn't measuring something at one part of it instantaneously affect what would be measured elsewhere? People keep saying measurements are just correlated, but for correlation some property has to exist prior to measurement. How can non-existent properties be correlated? $\endgroup$ – Ameet Sharma Feb 21 '16 at 7:47
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A quantum system is described by a set of operators called observables. Those observables represent all of the possible outcomes of a particular measurement. When you measure an entangled system, all of the possible outcomes happen. The correlation is only established after the measurement results are 'compared', that is, after information about one result interacts with information about the other, see

http://arxiv.org/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223,

for more detail.

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