EPR in Bohm formulation

[PeterDonis]

You can follows the argument here at minute 38:00 and later.

First, this is not a valid reference. Second, you should be able to post the math here, just as you did for the QM case.

 

[Nugatory]

No, QM calculation says the probability of getting "opposite spin" in the setup of my post#29 is 1/2, while EPR claims it is at least 5/9.

You are making a mistake in your calculation somewhere, as both are using the ##\cos^2\theta## rule and agree about the probabilities of any measurement at any angle.

Thus the empirical observations that are the starting point are the same: Measurements on the same axis will always show opposite spins, measurements on axes 120 degrees apart will do so 1/4 of the time.

The conflict between EPR and QM does not appear until we take the next step, as I pointed out in post #27.

 

[cianfa72]

EPR claim each particle of an entangled pair has got a definite spin along each of three axes 120 degree apart and on a given axis they are always "opposite".

There are 9 possibile combinations of axes pairs. For a particle of a given entangled pair at least two spins on two axes are the same (both spin-up or spin-down). That means that for a such entangled pair there are 5 combinations in which we get "opposite spin".

Suppose each entangled pair involved in the repeated experiment has got the same spin only over two axes. Randomly picking the two axes we get a probability of 5/9. Furthermore if some of the particle of the entangled pair involved in the experiment has got the same spin over the three axes then the probability is more than 5/9. Hence the EPR probability for this particular setup is at least 5/9.

 

[Nugatory]

You can follows the argument here at minute 38:00 and later.

I just looked. You've misunderstood what he is saying, which is basically a less concise explanation of @DrChinese's "simplest proof of Bell's inequality". The point is that the predicted and observed percentages (which everyone agrees about) cannot be explained by any theory that preassigns the measurement results on any given axis.

Edit: https://drchinese.com/David/Bell_Theorem_Easy_Math.htm is the argument

 

[DrChinese]

EPR claim each particle of an entangled pair has got a definite spin along each of three axes 120 degree apart and on a given axis they are always "opposite".

There are 9 possibile combinations of axes pairs. For a particle of a given entangled pair at least two spins on two axes are the same (both spin-up or spin-down). That means that for a such entangled pair there are 5 combinations in which we get "opposite spin".

Suppose each entangled pair involved in the repeated experiment has got the same spin only over two axes. Randomly picking the two axes we get a probability of 5/9. Furthermore if some of the particle of the entangled pair involved in the experiment has got the same spin over the three axes then the probability is more than 5/9. Hence the EPR probability for this particular setup is at least 5/9.

You must not mix trials in which the selected axes are the same for Alice and Bob with those where those axes are different. The quantum expectation is completely different. Apples and oranges.

 

[Nugatory]

Randomly picking the two axes we get a probability of 5/9.

Randomly picking the two axes gives a probability of 1/2 across the ensemble of pairs, as you correctly calculated in #29. From that ensemble we can select two subensembles - pairs in which we selected the same axis and pairs for which we selected different axes - and within these subensembles we have probabilities 100% and 25% respectively.

To get any sort of conflict between QM and the EPR we have to take the next step. EPR assumes that if (for example) we measure the left-hand particle spin-up on axis A and the right-hand particle spin-up on axis B, then it is valid to say that the left-hand particle is a member of the set A+B- (the set of all particles with the property that a spin measurement on the A axis will be spin-up and a measurement on the B axis will be spin-down). With this assumption, following the logic of that video and DrChinese's argument (and many more) we will eventually find a contradiction: the cardinality of the set A+B- is inexplicably greater than the sum of the cardinalities of the set A+C+ and the set B-C-.

Such violations are observed, and that is why we reject the EPR premise.

 

[cianfa72]

I'm not sure to fully understand the point.
I read https://drchinese.com/David/Bell_Theorem_Easy_Math.htm from @DrChinese and I believe I got it.

Randomly picking the two axes gives a probability of 1/2 across the ensemble of pairs, as you correctly calculated in #29

Ok, so we agree that the QM prediction gives as percentage of "opposite spin" the value 1/2 accross the ensemble of entangled pairs, while according EPR such a percentage is greater equal than 5/9.

Then, do you mean B. Greene is wrong in his video at minute 41:00 and later ?

 

[Nugatory]

Ok, so we agree that the QM prediction gives as percentage of "opposite spin" the value 1/2 accross the ensemble of entangled pairs, while according EPR such a percentage is greater equal than 5/9.

Kinda sorta…. But I wouldn’t use the phrase “according to EPR” because all three of them would have agreed with your #29 calculation that the probability was 1/2 (as everybody did and does).
The historical perspective, with handwaving: Around 1935 EPR presented a plausible argument that quantum mechanics was incomplete in the sense that there had to be some deeper theory underlying it. For the next thirty years no one could propose a candidate theory and the argument appeared untestable, so it remained a plausible but sterile suggestion that we might not be stuck with quantum weirdness forever. Then around 1965 Bell discovered that it could in fact be tested - and after a half-century of experiments….. here we are.

 

[cianfa72]

Kinda sorta…. But I wouldn’t use the phrase “according to EPR” because all three of them would have agreed with your #29 calculation that the probability was 1/2 (as everybody did and does).

You mean that at time Einstein, Podolsky and Rosen wrote their "EPR paper", they would have agreed with standard QM calculation of 1/2.

The point of view changed only around 1965 starting from Bell's seminal paper.

 

[DrChinese]

I read https://drchinese.com/David/Bell_Theorem_Easy_Math.htm from @DrChinese and I believe I got it.

Ok, so we agree that the QM prediction gives as percentage of "opposite spin" the value 1/2 accross the ensemble of entangled pairs, while according EPR such a percentage is greater equal than 5/9.

Then, do you mean B. Greene is wrong in his video at minute 41:00 and later ?

Greene says the 5/9 number (55%) at that point and associates it with the EPR view* that properties must be well-defined prior to measurement. Brian is extrapolating a point, and if we are not careful, we will be referring to differences that merely result from labeling. At the time of EPR, they did not have any specific expectation that the predictions of QM were wrong.

It wasn't until the time of David Bohm (ca. 1950) that specific examples of entangled electron spin even began to be kicked around. So the labeling of the 1/2 prediction as "QM" and the 5/9 prediction as "EPR" simply distinguishes the two, and should not be considered historical.


*Of course they never connected their "elements of reality" to spin, or to any statistical prediction of any kind.

 

[cianfa72]

So the labeling of the 1/2 prediction as "QM" and the 5/9 prediction as "EPR" simply distinguishes the two, and should not be considered historical.

Yes, nobody claims that at time EPR wrote their paper they thought that the predictions of standard QM were wrong. As you pointed out one can call 1/2 "QM" prediction and 5/9 "EPR" prediction for that specific experimental setup (as described in the Green's video and my post#29) just to distinguish the two predictions.