Calculations of QM prediction of -a.b

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Calculations of QM prediction of -a.b

Postby FrediFizzx » Wed Nov 11, 2020 8:31 am

jreed wrote:
FrediFizzx wrote:Here is a fairly simple QM joint calculation of -a.b a little bit different from what Jay wrote,

Image
.

I don't see any equation 1.11 in the paper referenced earlier. Which paper did that equation come from?

Sorry, you can disregard the equation reference. It came from an early paper Jay wrote and I'm too lazy to find it. The important thing about it is that it seems to only work if every thing is local to each other. How would you add the distance between a and b to it?
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Calculations of QM prediction of -a.b

Postby FrediFizzx » Wed Nov 11, 2020 6:28 pm

Of course, one could argue that since this is just a probability calculation of just numbers no physical location is needed. The same would hold true for the other product calculations. However, from a particle physics perspective, where all interactions are strictly local, it looks like everything is local to each other. We do have two separated local interactions though.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Calculations of QM prediction of -a.b

Postby gill1109 » Wed Nov 11, 2020 7:13 pm

FrediFizzx wrote:
jreed wrote:
FrediFizzx wrote:Here is a fairly simple QM joint calculation of -a.b a little bit different from what Jay wrote,

Image
.

I don't see any equation 1.11 in the paper referenced earlier. Which paper did that equation come from?

Sorry, you can disregard the equation reference. It came from an early paper Jay wrote and I'm too lazy to find it. The important thing about it is that it seems to only work if every thing is local to each other. How would you add the distance between a and b to it?
.

Writing “X” for tensor product, Jay’s formula is the standard:

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.

The observables are “at” the locations where a and b are.
The state is the state of the two particles on emission from the source. A superposition of up, up with down, down.

The state vector is the non-local hidden variable.

I think Donald Grant imagines it decaying rapidly to an ordinary separable mixed state as it leaves the source. The quantum predictions would then be completely random, uncorrelated outcomes.

Actually the Delft statistics are best “explained” by a roughly 80-20 mixture of the singlet state with the completely random state. It’s better than a 2/3 - 1/3 mixture. At 2/3 - 1/3 the state would have been separable (can be written as a mixture of product states, no Bell violation).

You can say, the formula expresses what we would expect to see if we did the two spin measurements “at the source”. The measurements might as well have been instantaneous and simultaneous with emission.

Donald Graft imagines an instantaneous measurement at the source of both particles in the z direction. With 50-50 probability one finds up, down or down, up. After that, we have measurement of up or down particles in the a and b directions.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Calculations of QM prediction of -a.b

Postby FrediFizzx » Wed Nov 11, 2020 7:35 pm

gill1109 wrote:The state vector is the non-local hidden variable.

More freakin' nonsense. I did tell you to STOP posting nonsense. This is your last warning.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Calculations of QM prediction of -a.b

Postby Austin Fearnley » Thu Nov 12, 2020 1:00 am

Gill wrote:Actually the Delft statistics are best “explained” by a roughly 80-20 mixture of the singlet state with the completely random state. It’s better than a 2/3 - 1/3 mixture. At 2/3 - 1/3 the state would have been separable (can be written as a mixture of product states, no Bell violation).


That is interesting,

I dug out my June 2020 VB program to simulate Malus's Law results particle-at-a-time.
Malus's Law depends on polarisation and not entanglement. So Malus's Law works on a statistical basis and approaches the trig formula result best for large N.
I have run it (only once) on 100000 particles and obtained:
N= 100000; intensity passing filter = 0.85368; equivalent Bell correlation = 0.70735; equivalent S statistic from CHSH =2.82944

I have today run it (once) for comparison with 2015 real experiment on
N= 250; intensity passing filter = 0.82; equivalent Bell correlation = 0.64; equivalent S statistic from CHSH =2.56

I have also run it (once) on
N= 25; intensity passing filter = 0.92; equivalent Bell correlation = 0.84; equivalent S statistic from CHSH =3.36

I cannot exactly remember the 2015 outcome but I think it was about S = 2.4. If so, that is not too different from my 2.56 result.
I have made a few more runs for N =250 pairs:
S = 2.82, 2.88, 2.62, 2.72, 2.66, 2.43, 2.91

I think these are the sorts of results my retro method would give for Bell experiments with only 250 pairs.
Austin Fearnley
 

Re: Calculations of QM prediction of -a.b

Postby local » Thu Nov 12, 2020 1:58 am

And he continues to misrepresent Graft and speak for him. What he says about Graft's views is totally fabricated and nonsensical. One has to wonder why he needs to spout this duplicitous nonsense. He's not doing his cause any good.

Graft does not say that the state decoheres; rather, he explicitly excludes that. Decoherence is of course possible but it is not appealed to as it is not required for his analysis and would only complicate matters. The essential element is the inapplicability of Luders projection. And Graft certainly does not "imagine" that a joint measurement occurs at the source. His analysis is based on two measurements occurring at the detection stations at different times, i.e., separated measurement. Gill should give Graft's work the same careful consideration that he asks us to give his own work.
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Re: Calculations of QM prediction of -a.b

Postby gill1109 » Thu Nov 12, 2020 4:27 am

local wrote:And he continues to misrepresent Graft and speak for him. What he says about Graft's views is totally fabricated and nonsensical. One has to wonder why he needs to spout this duplicitous nonsense. He's not doing his cause any good.

Graft does not say that the state decoheres; rather, he explicitly excludes that. Decoherence is of course possible but it is not appealed to as it is not required for his analysis and would only complicate matters. The essential element is the inapplicability of Luders projection. And Graft certainly does not "imagine" that a joint measurement occurs at the source. His analysis is based on two measurements occurring at the detection stations at different times, i.e., separated measurement. Gill should give Graft's work the same careful consideration that he asks us to give his own work.

I have corresponded with Donald. I didn't read the final versions of his published works in detail because earlier versions and earlier conversation told me all I thought I needed to know. What I do know is that his theory cannot reproduce the experimental results of the 2015 "loophole-free" experiments, if we assume the reliability of the random number generators used for the setting selection. Why? Because Donald's point of view is local-realist. For him, it is axiomatic that that is how physics is. (He's not the only one. Caroline Thompson also had this view)

I happen to think that Bell's theorem can be posed as a true mathematical theorem. [We can discuss elsewhere what precisely is the mathematical theorem that people refer to; and we should discuss whether or not it would have any physical relevace]. Anyway, I hope one is allowed to say so on this forum, and I hope one is allowed to discuss the possible mathematics behind all this.

Those experiments were not perfect, and I have a lot of problems with how they did their setting choice. I think it was very unwise to rely on quantum optics devices and hence use prior quantum physics assumptions.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Calculations of QM prediction of -a.b

Postby local » Thu Nov 12, 2020 4:34 am

Graft's paper is a theoretical one, containing mathematical derivations. The experiments are another matter. Mathematics stands on its own. You want us to consider your mathematics, but you won't return the favor. Stop with the misdirection.

As stated many times, neither I nor Graft deny the validity of Bell's inequality. Stop with the misdirection.

I too communicate with Graft. He tells me that you never discussed the paper we are talking about.

You are correct. Both Graft and myself are proud local realists.

Finally, what you said does not mitigate your misrepresentation of Graft's work.
Last edited by local on Thu Nov 12, 2020 4:47 am, edited 1 time in total.
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Re: Calculations of QM prediction of -a.b

Postby gill1109 » Thu Nov 12, 2020 4:46 am

local wrote:Graft's paper is a theoretical one, containing mathematical derivations. The experiments are another matter. Mathematics stands on its own. You want us to consider your mathematics, but you won't return the favor. Stop with the misdirection.

As stated many times, neither I nor Graft deny the validity of Bell's inequality. Stop with the misdirection.

You are correct. Both Graft and myself are proud local realists.

Finally, what you said does not mitigate your misrepresentation of Graft's work.

Sorry about that! I acted "in good faith" but of course I can be wrong.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Calculations of QM prediction of -a.b

Postby local » Thu Nov 12, 2020 4:48 am

Thank you.

Graft asserts that for separated measurement, the first station to measure samples the singlet marginally and projects the state for the other station. The issue is the nature of that projection. If it is Luders projection then -a.b is obtained. But Luders projection is unphysical for space-like separation.

Graft is careful to cite prior work on the significance of projection for EPRB by Khrennikov.
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Re: Calculations of QM prediction of -a.b

Postby Heinera » Thu Nov 12, 2020 5:18 am

local wrote:Graft asserts that for separated measurement, the first station to measure samples the singlet marginally and projects the state for the other station.

What exactly do you mean by "first station to measure"? For space-like separated events there is no first measurement; which one is first depends on the frame of reference.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Calculations of QM prediction of -a.b

Postby local » Thu Nov 12, 2020 5:52 am

Yes, you are correct. Graft addresses that in his paper:

"To separate the quantum joint solution we need to account for two samplings each restricted to knowledge of the local measurement angle. We can do this by considering two sequential measurements, specifically, a measurement at side A using the measurement angle a, followed by a measurement at side B using b. In the degenerate case of the measurements occurring at exactly the same time, the measurement order is chosen arbitrarily. Refer to Section 5 for further discussion of the relativistic aspects."

and in Section 5:

"In our context, there are always three operational domains relating the measurement times at the two sides (taking the measurement time to be the time of its completion if it is extended in time). In the first domain, measurement A precedes measurement B in the shared frame. In the second domain, measurement B precedes measurement A in the shared frame. In these two domains denote the first measurement by t0 and the second by t1. In the third domain, the measurements are simultaneous, to a certain experimental precision. In this domain, for the purposes of calculation, arbitrarily designate one side’s measurement time as t0 and the other’s as t1. It is interesting that quantum mechanics has nothing to say about which side projects the other in the case of simultaneous measurements, and I accordingly do not speculate on how the symmetry is broken physically."

Possibly the third domain is vanishingly small. So it doesn't matter which frame we choose, as one measurement will always precede the other. Note that two marginal measurements occurring simultaneously is not equivalent to joint measurement. Finally, you can say that the side that projects the other must have been the first one to measure (turning things around a bit). And again, QM has nothing to say about which side does the projection when the measurements are simultaneous in the chosen frame.

Regarding moving frames:

"Here I consider only the case where the two sides share an inertial frame and make their measurements in that inertial frame. It would be possible to consider relatively moving frames for the two measurement stations, however, nobody claims that quantum entanglement requires relatively moving frames, so allowing for it is an unnecessary complication. It may be interesting to go further and analyze the effects of relativistic motion, but it is not directly germane to the argument here."

Shan Gao has written extensively on the matter of wavefunction collapse (projection) versus Lorentz invariance. You may like to see what he has to say about it. There is a chapter about it in the online book that Richard kindly linked, and some treatment in the paper that I linked.

Any improvements you can suggest for this analysis would be welcomed.
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Re: Calculations of QM prediction of -a.b

Postby Heinera » Thu Nov 12, 2020 1:14 pm

local wrote:and in Section 5:

"In our context, there are always three operational domains relating the measurement times at the two sides (taking the measurement time to be the time of its completion if it is extended in time). In the first domain, measurement A precedes measurement B in the shared frame. In the second domain, measurement B precedes measurement A in the shared frame. In these two domains denote the first measurement by t0 and the second by t1. In the third domain, the measurements are simultaneous, to a certain experimental precision. In this domain, for the purposes of calculation, arbitrarily designate one side’s measurement time as t0 and the other’s as t1. It is interesting that quantum mechanics has nothing to say about which side projects the other in the case of simultaneous measurements, and I accordingly do not speculate on how the symmetry is broken physically."


Ok, but this seems a very odd way to deal with special relativity (i.e., dividing the theory into three separate domains, the difference of which can have no physical significance, since they depend on a particular frame of reference).

Why doesn't Graft try to make his argument covariant?
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Calculations of QM prediction of -a.b

Postby local » Thu Nov 12, 2020 3:36 pm

You'll have to ask him. To me, it is intuitive to suppose that one of the measurements occurs first, and that is all that is needed.
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Re: Calculations of QM prediction of -a.b

Postby Guest » Thu Nov 12, 2020 4:37 pm

local wrote:You'll have to ask him. To me, it is intuitive to suppose that one of the measurements occurs first, and that is all that is needed.


But the truth of the statement "one of the measurements occurs first" depends on which reference frame we're talking about.
Guest
 

Re: Calculations of QM prediction of -a.b

Postby local » Thu Nov 12, 2020 6:36 pm

We just discussed that in detail. It doesn't matter which one goes first, so what is your point? Did you read what I posted about it above?
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Re: Calculations of QM prediction of -a.b

Postby gill1109 » Fri Nov 13, 2020 1:02 am

local wrote:I too communicate with Graft. He tells me that you never discussed the paper we are talking about.

He sent me some work and we discussed it. We discussed a lot of things. If he didn’t tell me about a new paper then maybe I never saw it - and obviously, I did not talk to him about it. But maybe he sent me something and I did not look at the email straight away and later forgot about it? Many things are possible.

I should take a new look at his latest work, obviously. Thanks.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Calculations of QM prediction of -a.b

Postby gill1109 » Fri Nov 13, 2020 1:13 am

local wrote:Thank you.

Graft asserts that for separated measurement, the first station to measure samples the singlet marginally and projects the state for the other station. The issue is the nature of that projection. If it is Luders projection then -a.b is obtained. But Luders projection is unphysical for space-like separation.

Graft is careful to cite prior work on the significance of projection for EPRB by Khrennikov.

I am not aware of any experiment with space-like separation in which -a.b is obtained, without adding further, untestable (though possibly physically attractive) assumptions. Aspect, Weihs etc etc all “reconstruct” -a.b by adding assumptions like “fair sampling”, “no enhancement”, ... The 2015 experiments do *not* recover -a.b. They don’t even claim to have generated the singlet state. The Delft and Munich states are, maybe, singlet plus a lot of noise. The Munich and Vienna states are close to pure states but deliberately far from maximally entangled pure states. That’s because the Munich and Vienna experiments have a big detector inefficiency.

Just suggesting - it could be interesting to study QM derivations of the actually observed 2015 experimental statistics.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Calculations of QM prediction of -a.b

Postby Heinera » Fri Nov 13, 2020 9:23 am

local wrote:You'll have to ask him. To me, it is intuitive to suppose that one of the measurements occurs first, and that is all that is needed.

Ok, but to me this is a death knell for Grafts argument. If the direction of the projection (from A to B or B to A) depends on the frame of reference, it clearly shows that the Lüders projection cannot be a physical mechanism, but simply a mathematical book keeping device. And then there is no reason why special relativity's limit on the speed of physical transmission should apply to Lüders projection. After all, there is no way to use the projection to transfer a signal from A to B or vice versa.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Calculations of QM prediction of -a.b

Postby local » Fri Nov 13, 2020 10:47 am

I don't like rhetoric such as "death knell" but let it go.

Graft wrote in the paper:

"Here I consider only the case where the two sides share an inertial frame and make their measurements in that inertial frame."

So in the chosen frame one measurement precedes the other.

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. But then you are left bereft of any quantum prediction for separated measurement. You cannot just throw your hands up and apply the joint prediction, because it requires a joint measurement that does not occur in separated EPRB. Graft made a reasonable attempt to obtain a solution for separated measurement and it is remarkable that the standard Luders projection leads to -a.b. Remarkable enough to be published in a peer-reviewed journal.

Yes, of course Luders projection is a "bookkeeping device". No physicist has ever identified a physical mechanism for space-like projection. Passion-at-a-distance is fantasy. QM itself is just a bookkeeping device.

Graft was the first to draw attention back in 2013 to the real physical distinction between joint and separated measurement:

https://arxiv.org/abs/1309.1153

The later paper was intended to forward this argument in a purely quantum form, and to again demonstrate the terrible error many quantum physicists have made of applying the joint prediction to separated measurement.

Your ideas for deriving an acceptable quantum prediction for separated measurement that produces -a.b and respects relativity would be most welcome, and highly publishable.
local
 
Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

Next

Return to Sci.Physics.Foundations

Who is online

Users browsing this forum: No registered users and 74 guests

cron
CodeCogs - An Open Source Scientific Library