Proving Entanglement: Measuring Spin of Photons for Bell's Inequality

[gamow99]

I'm slighting confused about the experiments which try to prove that Bell's Inequality is violated. Here's what would satisfy me that Bell's Inequality has been violated: we measure the spin of a photon and its entangled pair at time 1, then at time 2 we change the spin on photon 1 and measure simultaneously the spin of photon 2 at time 2. If it's always the case that if you change the spin of one then the other photon's spin changes simultaneously then that would be good evidence that entanglement is real. Have experimenters been able to do this?

 

[Strilanc]

You have misunderstood what entanglement is. Read this.

 

[Nugatory]

If it's always the case that if you change the spin of one then the other photon's spin changes simultaneously then that would be good evidence that entanglement is real. Have experimenters been able to do this?

That's not what entanglement says should happen. Entanglement says that when I measure the spin of particle A for the first time particle B will behave as if its spin has been changed to whatever value is consistent with the measurement of A. The key phrase there is "for the first time" - after that first measurement the particles are no longer entangled so subsequent measurements of either have no effect on the other.

Bell's inequality applies to the results when we make one measurement on each member of a large number of entangled pairs. Thus, repeated measurements on the members of the same pair are not necessary to find violations - that's not what the theorem is about.

 

[gamow99]

Entanglement says that when I measure the spin of particle A for the first time particle B will behave as if its spin has been changed to whatever value is consistent with the measurement of A.

How do you know that Einstein's thesis put forward in the EPR paper was not right in that the particles always had the spin they had, we just don't know about it until we measure their spin?

 

[Nugatory]

How do you know that Einstein's thesis put forward in the EPR paper was not right in that the particles always had the spin they had, we just don't know about it until we measure their spin?

That's what Bell's inequality does. There is a subtle but experimentally detectable difference between the statistical correlations you find across a large number of pairs if the EPR model is correct and if the quantum mechanical model is correct: the former cannot violate the inequality and the latter can.

An excellent website maintained by one of our members has more detail: http://www.drchinese.com/Bells_Theorem.htm

 

[gamow99]

That's what Bell's inequality does. There is a subtle but experimentally detectable difference between the statistical correlations you find across a large number of pairs if the EPR model is correct and if the quantum mechanical model is correct: the former cannot violate the inequality and the latter can.

That doesn't make any sense. If I measure particle A and find out that it is spin up at time 1 and then I measure particle B and find out that it is spin down at time 1, then it doesn't follow that the spin of particle A affects the spin of particle B instantaneously, nor does it follow that the spin of particles A and B were in a superposition at time 0. It only follows that I learned something at time 1 which was already a fact at time 0.

 

[Nugatory]

If I measure particle A and find out that it is spin up at time 1 and then I measure particle B and find out that it is spin down at time 1, then it doesn't follow that the spin of particle A affects the spin of particle B instantaneously, nor does it follow that the spin of particles A and B were in a superposition at time 0. It only follows that I learned something at time 1 which was already a fact at time 0.

You are right about that. However, you will find that the same line of thought won't work if we measure along different directions at the two sides. In an ideal Bell thought experiment, at both sides the experimenter chooses at random whether to orient his spin-measuring device at 0, 120, or 240 degrees for each pair. Thus, when they get together afterwards and compare their results, they'll have some pairs on which they measured on the same axis and always got opposite results; other pairs they measured on axes 120 degrees apart and sometimes got opposite results and sometimes not.

It just so happens that quantum mechanics and the EPR-style fixed-but-unknown spin models both predict the same result when the measurement axis is the same on both sides.

 

[DrChinese]

That doesn't make any sense. If I measure particle A and find out that it is spin up at time 1 and then I measure particle B and find out that it is spin down at time 1, then it doesn't follow that the spin of particle A affects the spin of particle B instantaneously, nor does it follow that the spin of particles A and B were in a superposition at time 0. It only follows that I learned something at time 1 which was already a fact at time 0.

Nugatory has steered you correctly. You might benefit from reviewing a web page I created to discuss this exact hypothesis - that the entangled spin of both photons was predetermined at time 0. Bell discovered a fact which was overlooked for 30 years after EPR: that there are no datasets for which the results match the quantum mechanical predictions at other angles. 120 degrees is the easiest angle set to follow (as Nugatory mentioned), and is used in this page.

http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

Without understanding Bell's Theorem, you will go 'round in circles.

 

[afcsimoes]

To whom may concern:
Notice about a new paper on the subject (Dated: November 11, 2015):
"A strong loophole-free test of local realism" at http://arxiv.org/pdf/1511.03189v1.pdf