Calculations of QM prediction of -a.b

[Heinera]

Even if you are unable to accept this, I could say: Wonderful, you agree (for different reasons) that Luders projection (indeed, any projection) cannot be applied to space-like EPRB.

On the contrary, I see no problems with applying Lüders projection to space-like EPRB, since the projection does not represent a physical mechanism.

[local]

On the contrary, I see no problems with applying Lüders projection to space-like EPRB, since the projection does not represent a physical mechanism.

Luders projection requires the physical transfer of information (proven in Graft's paper). How can it occur without a physical mechanism? Are you working in woo-woo land?

Just to summarize the assumptions for the derivation:

1. The stations share a single reference frame and hence...

2. The frames are not moving relative to each other.

That should dispel all concerns about the relativity of simultaneity. You apparently now agree about that.

[Heinera]

On the contrary, I see no problems with applying Lüders projection to space-like EPRB, since the projection does not represent a physical mechanism.

Luders projection requires the physical transfer of information (proven in Graft's paper). How can it occur without a physical mechanism? Are you working in woo-woo land?

There is no transfer of information. It is obvious that the projection cannot be a physical mechanism, since it's direction (from A to B, or B to A) depends on the observer's frame of reference. Graft's paper does not prove that this is a physical mechanism.

As I do not find his paper interesting (it is essentially a rehash of the original EPR argument), I end my participation in this thread.

[FrediFizzx]

Well, the -a.b prediction can also be obtained from the outcome pair probabilities,



To finish what Joy posted in the other thread,



We have another way of calculating the QM -a.b prediction. So, what does that mean for Graft's argument?
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[local]

As I do not find his paper interesting (it is essentially a rehash of the original EPR argument), I end my participation in this thread.

LOL. Bye!

[local]

We have another way of calculating the QM -a.b prediction. So, what does that mean for Graft's argument?

Nothing, because that is the joint prediction.

[FrediFizzx]

We have another way of calculating the QM -a.b prediction. So, what does that mean for Graft's argument?

Nothing, because that is the joint prediction.

How is it the joint prediction when it is using the outcome pair probabilities?
.

[local]

We have another way of calculating the QM -a.b prediction. So, what does that mean for Graft's argument?

Nothing, because that is the joint prediction.

How is it the joint prediction when it is using the outcome pair probabilities?
.

Fred, I don't understand what you mean by that. What you posted just quotes the standard QM result and says it is the joint prediction:

"quantum mechanics is well known to predict the following joint probabilities"

If your measurements produce outcome pairs, then it is joint sampling. In separated measurement, a given station's measurement samples the marginal probabilities and produces a single outcome for that side, not a pair of outcomes.

[FrediFizzx]

We have another way of calculating the QM -a.b prediction. So, what does that mean for Graft's argument?

Nothing, because that is the joint prediction.

How is it the joint prediction when it is using the outcome pair probabilities?
.

Fred, I don't understand what you mean by that. What you posted just quotes the standard QM result and says it is the joint prediction:

"quantum mechanics is well known to predict the following joint probabilities"

If your measurements produce outcome pairs, then it is joint sampling. In separated measurement, a given station's measurement samples the marginal probabilities and produces a single outcome for that side, not a pair of outcomes.

Well, that is what I was wondering. Is it actually a "joint' prediction or is it just "the" prediction. At that point you are just crunching numbers so it doesn't seem like the locations of a and b matter. I suppose we need to take a look at how the outcome pair probabilities are derived.
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[gill1109]

You can get the four outcome pair probabilities from the correlation and from the two marginal probabilities.
With “X” standing for tensor product, the correlation is

Expectation of product of spins in a and b directions: <psi| a.sigma X b.sigma |psi>,

state vector: |psi> = ( |+z> X |+z> - |-z> X |-z> ) / sqrt 2.

Expectation of spin of particle 1 in a direction: <psi| a.sigma X identity |psi>,

Expectation of particle 2 in b direction: <psi| Identity X b.sigma |psi>

There are four pair probabilities. They add to 1. The three expectations are linear functions of the pair probabilities. That gives you four equations in four unknowns. It’s easy to solve them...

For instance, correlation = p(++) + p(—) - p(+-) - p(-+)
Expectation of Alice spin = p(++) +p(+-) - p(-+) - p(—)

The reasoning behind this is that”identity” is a self adjoint operator whose eigenvalues both equal +1 ...

[gill1109]

Another route is as follows. Denote by |+a>, |-a> normalised eigenvectors of a.sigma
The probability of ++ is the absolute value, squared, of <psi | (|+a> X |+b> ) , where again I write “X” for tensor product..
You can find expressions for those eigenvectors in many textbooks or figure them out for yourself.

[local]

Fred, joint and separated measurement are physically different, so you need different derivations. There is no single "the" prediction. That is the whole point of Graft's analysis.

Gill is just giving joint derivations for joint measurement. If you form a tensor product of a and b for a single measurement you have illegitimately combined knowledge of a and b for that measurement. In separated EPRB there are two independent measurements, each having access to only its own setting. Gill has not provided a derivation for separated measurement. Apparently he denies the distinction between joint and separated measurement. He also incorrectly states (if I read him correctly) that you can obtain a joint distribution from the marginal distributions. That is wrong. There would be no need for copula theory if that were true, and the marginal expectations for EPRB are 0 in any case. He can believe what he wants, but don't you be fooled.

[FrediFizzx]

Fred, joint and separated measurement are physically different, so you need different derivations. There is no single "the" prediction. That is the whole point of Graft's analysis.

Gill is just giving joint derivations for joint measurement. If you form a tensor product of a and b for a single measurement you have illegitimately combined knowledge of a and b for that measurement. In separated EPRB there are two independent measurements, each having access to only its own setting. Gill has not provided a derivation for separated measurement. Apparently he denies the distinction between joint and separated measurement. He also incorrectly states (if I read him correctly) that you can obtain a joint distribution from the marginal distributions. That is wrong. There would be no need for copula theory if that were true. He can believe what he wants, but don't you be fooled.

What do you mean exactly by "joint measurement"? Does that mean a and b are local to each other?
.

[local]

It just means that there is one sampling (measurement) using a measurement operator that combines a and b. For an intuitive understanding please read Graft's earlier paper:

https://arxiv.org/abs/1309.1153

It's must more accessible to readers not expert in quantum theory and its mathematics. The later paper just cast things in the formal mathematics of quantum theory.

[FrediFizzx]

It just means that there is one sampling (measurement) using a measurement operator that combines a and b. For an intuitive understanding please read Graft's earlier paper:

https://arxiv.org/abs/1309.1153

It's must more accessible to readers not expert in quantum theory and its mathematics. The later paper just cast things in the formal mathematics of quantum theory.

Ok, got it. It doesn't seem like there is ever a single measurement operator that combines a and b. Now, we have what Jay did which is another calculation of the -a.b prediction,



Which is just the product of two distinct measurement operators.
.

[local]

But that is not -a.b. The second term is problematic.

[FrediFizzx]

But that is not -a.b. The second term is problematic.

The second term is not problematic. It is the magnitude of the cross product and unphysical since a and b are separated. IOW, it's zero.
.

[gill1109]

Fred, joint and separated measurement are physically different, so you need different derivations. There is no single "the" prediction. That is the whole point of Graft's analysis.

Gill is just giving joint derivations for joint measurement. If you form a tensor product of a and b for a single measurement you have illegitimately combined knowledge of a and b for that measurement. In separated EPRB there are two independent measurements, each having access to only its own setting. Gill has not provided a derivation for separated measurement. Apparently he denies the distinction between joint and separated measurement. He also incorrectly states (if I read him correctly) that you can obtain a joint distribution from the marginal distributions. That is wrong. There would be no need for copula theory if that were true, and the marginal expectations for EPRB are 0 in any case. He can believe what he wants, but don't you be fooled.

Fred, I just told you the formulas which you got from Jay and rewrote in Mathematica. You asked how to get the separate probabilities of the four possible joint outcomes, and I politely answered your question. How to also get the joint probabilities as well as the correlation, following the same, standard, methodology. The standard approach for joint measurement of two commuting observables on one system, when the system is modelled using the standard tensor product approach, out of two subsystems which can be measured separately.

I am telling you the conventional way to get those probabilities. I am using the same joint state as Jay uses (the singlet state). You may want to argue that the state of the two electrons when they reach the two measurement devices is not the same state they had when they left the source.

I’m not saying the computations are correct. I’m not saying you should believe them. I do not attempt to distinguish between joint and separate measurement. I’m telling you the standard way to get the usual formulas for joint measurement of spin on two spin half systems, together prepared in the singlet state. The formulas which Joy wrote down, the ones which Jay wrote down.

Donald Graft (and many before him) have argued that entanglement is not maintained as the particles separate.

If that were the case, we would not observe violation of Bell inequalities. This is what Caroline Thompson argued, for years. She argued that the Aspect analysis, and the Weihs analysis, were wrong. That they got violation by cheating; by making untestable assumptions about the non-detections. That is why the experimenters gave us the 2015 experiments. But they do not find the singlet correlations. They don’t try to.

[local]

It is the magnitude of the cross product and unphysical since a and b are separated. IOW, it's zero.

Fred, I have no idea what you are talking about. Is there a paper that explains and justifies that, or is it just hand-waving? Also, where do I find Jay's derivation?

Donald Grant (and many before him) have argued that entanglement is not maintained as the particles separate.

You spell his name wrong and you again falsely state that he appeals to decoherence, when he explicitly excludes it, and when I have also clearly refuted that silly acusation earlier in this thread.

[gill1109]

Donald Grant (and many before him) have argued that entanglement is not maintained as the particles separate.

You spell his name wrong and you again falsely state that he appeals to decoherence, when he explicitly excludes it. You are a liar and a charlatan!

Sorry for typo. Thanks for pointing it out.

I did not say he appeals to decoherence. He has written a number of papers, and I refer to the ideas he discussed with me in correspondence years ago, the ideas which many people before him had also championed. He never used the term decoherence.

You call me a disgusting liar, and you call me a charlatan. I think such language is not allowed on this forum. I won’t write down in public the ideas I am getting about your own mentality.