OK Corral: Local versus non-local QM

[JesseM]

Jesse, I looked at them, and they are helpful. Thanks.

But what I am still hoping for is a derivation that starts where Bell starts <s.a*s'.b'> and ends where Bell ends -a.b'.

But the derivation I linked to plus the additional comments I made does show that, just using some different notation. s.a*s'.b' in Bell's notation just means the product of the two measurement results (one using angle a and the other using angle b), where each measurement yields either spin-up (+1) or spin-down (-1), so on a given trial the product will be +1 if both are measured to have the same spin on their respective measurement axes, and -1 if they are measured to have opposite spin on their respective measurement axes. What the linked page shows is that on a given trial, the probability that s.a*s'.b' is +1 will be sin^2((a-b)/2), and the probability that s.a*s'.b' is -1 will be cos^2((a-b)/2). And by the definition of "expectation value", <s.a*s'.b'> must be:

(+1)*Probability(s.a*s'.b' = +1 on each trial) + (-1)*Probability(s.a*s'.b' = -1 on each trial)

As I showed in my comments, when you work this out using the above probabilities, you conclude that <s.a*s'.b'> will be equal to -cos(a - b).

 

[vanesch]

For those who are interested, I did explicitly the calculation of Bell's expression.

The expansion over the singlet state is a bit clumsy:

the singlet state is 1/sqrt(2) ( |+> |-> - |->|+>)
|+> is the (1,0) element, and |-> is the (0,1) element in the hilbert space.

So we expand the expectation value:

< singlet | O1 O2 | singlet >as:

( < + | < - | - < - | < + |) O1 O2 ( |+> |-> - |->|+>)

= < + | O1 | +> < - |O1 |-> + < - | O1 | - > < + | O2 | + > - < + |O1 |-> < - | O2 | + > - < -| O1 | + > < + | O2 | - >EDIT: where I forgot the front factor of 1/2, because of the double presence of the square root.
(but in the notebook, it is ok).

See attachment.

 

[DrChinese]

1. Hmm, but when you say "QM=correct predictions", you're talking about some subset of its predictions rather than all possible predictions made by QM, right? After all, one of QM's predictions is that the inequality will be violated in certain experiments! Are you just talking about the prediction that whenever both experimenters measure their particles at the same angle, they always get opposite results? If my guess about what you meant in the "correct predictions" step is right, then no dispute...but if it isn't, could you clarify?

2. But that's my point, you can show a proof is flawed simply by presenting a counterexample in some circumstances. In general, if a proof makes a statement like "for all cases where X is true, Y is true", then producing a single case of the form "X is true, but Y is false" shows the proof must have a flaw somewhere, without identifying which step in the proof must be flawed.

In this case, if Bell proves something like "IF the entangled-particles experiment always produces opposite spins when the experimenters choose the same angle AND local realism=assumed, THEN Inequality must be true". If wm could come up with a purely classical way of duplicating all the results of the entangled-particles experiment, including both the fact that the experimenters always get opposite results when they pick the same angle, and also the fact that the inequality is FALSE when they pick certain different angles, and it was clear by construction that wm's experiment respected local realism, then this would be sufficient to show that Bell's general statement was false, so that there must be some flaw in a proof.

3. The expectation value is simply on the spin each experimenter will find when their detector is at a given angle, which on a given trial is either spin-up (+1) or spin-down (-1). You can also look at the expectation value for the product of their two results, either the same (+1) or different (-1). Either way, you can certainly come up with a classical experiment where, on each trial, each experimenter will get either the result +1 or -1, decided based on their choice of angle combined with some classical signal or object sent from a central source, and possibly with a random element as well. If you could further set things up so that the experimenters always get opposite results when they choose the same angle, and all the conditions necessary for Bell's theorem are obeyed (like the condition that the source has no foreknowledge of what angle each experimenter will choose on a given trial), do you disagree that Bell's proof should apply in exactly the same way to this experiment, and lead you to conclude that the same inequality should be obeyed as long as the experiment does not violate local realism?

1. Sure, we are talking about the situation where QM makes a prediction. In this case, the prediction is not that the Inequality is violated, it is the "cos theta" relationship. That the Inequality is violated is applicable only when local realism is also present. There is no A, B and C in QM of course, only A and B.

2. As I pointed out, such an attempt will not work using the path described. The logic statement I showed was equivalent to Bell's Theorem is:

IF Inequality=fails AND Local Realism=demonstrated, THEN QM=Limited Validity

So all wm would be doing with his classical experiment is proving it is a classical experiment where QM doesn't apply or is wrong. I don't see it as disproving Bell's Theorem. I guess when wm or someone actually conceptualizes and executes such an experiment, we'll have more to discuss. Right now, I would place it up there with theories of perpetual motion machines.

 

[vanesch]

For those who are interested, I did explicitly the calculation of Bell's expression.

BTW, it occurred to me that the way Bell writes his stuff, and the mistake wm made, is a nice illustration of how quantum theory can get around doing "local" things in a way that a classical view cannot.

wm made the calculation of the correlation, thinking he was doing a kind of classical calculation, where the "sign" of (s.a) determined the outcome at Alice, and the sign of (s.b) determined the outcome at Bob. The outcomes were supposed to be +1 or -1. So the true correlation would in fact be:

< sign(a.s) . sign(b.s) >, and not < (a.s) (b.s) >

However, by some mathematical coincidence, if s is a uniformly distributed unit vector in R^3, these two expressions come out the same.

As JesseM and I demonstrated, however, they do not equate -(a.b), but rather -(a.b)/2 or -(a.b)/3, depending on whether one considers them in 2 or in 3 dimensions.

Nevertheless, the thing is that the ACTUAL RESULT OF MEASUREMENT, if it is truly "sign(a.s)" (hence, a numerical value of +1 or -1 for each trial) is then indeed "locally produced" (because only depending upon a and s)).

As we see, however, the correlation then comes out to be -(a.b)/2, which doesn't violate the Bell inequalities - as expected.

Now, quantum theory does, apparently, the same thing. So why can't we say that in its "inner workings", instead of transporting a unit vector s, this funny 3-some of Pauli matrices is transported ?

The reason is that in the expression < (sigma.a) (sigma.b) >, we write down a *quantum-mechanical* expectation value of an OPERATOR. We do not write the STATISTICAL expectation value of A PRODUCT OF TWO RESULTS.

In other words, the outcome at Bob was NOT (sigma.b) ! It was ONE OF ITS EIGENVALUES (which happens to be +1 or -1). As such, we cannot really say that "we transport the outcome at Bob, which is (sigma.b), to Alice, where her outcome is (sigma.a), and multiply the two together".

If that were true, indeed, this would have been a local mechanism. But the result at Alice is NOT (sigma.a), and the result at Bob is NOT (sigma.b). The results are of the kind +/- 1...

Or are they ?

Well, we COULD say, if we wanted to, that the outcome at Alice is not +1 or -1, but (sigma.a). And we COULD say that the outcome at Bob is (sigma.b). But that's a funny situation! It would mean that Alice didn't, after all, get a genuine numerical result such as -1 or +1, but rather a mathematical operator over hilbert space. If that were true, then wm's reasoning would be correct in a way. We take the result at Alice (again: it is not -1 or +1, but an operator over hilbert space!), which is determined purely by what happens at Alice, and similarly at Bob's, and at the point of their meeting, they multiply their outcomes (which, again, are not -1 or +1, but are now operators over hilbert space) and hurray, we get the right correlations.

But what could that possibly mean, that Alice didn't get -1 or +1 at a trial, but each time an operator ? Well, it means that Alice got BOTH results. It means that Alice and Bob now have a quantum-mechanical description, and that they are in a superposition of having -1 and +1 (the operator contains both eigenvalues). This is exactly the MWI view on things, and it illustrates how in MWI, there is indeed no problem with locality. But the price to pay is rather high: you cannot say anymore that Alice got a measurement result which was each time -1 or +1 !

Now, independently of interpretation, the reason why the quantum formalism can make predictions which defy classical theories is that in the formalism of quantum theory, there is a difference between the mathematical representation of a measurement (which is a hermitean operator), and actual individual results of a measurement (which are eigenvalues of that hermitean operator). In a classical theory, the representation of a measurement is necessarily its outcome.

 

[wm]

For those who are interested, I did explicitly the calculation of Bell's expression.

The expansion over the singlet state is a bit clumsy:

the singlet state is 1/sqrt(2) ( |+> |-> - |->|+>)
|+> is the (1,0) element, and |-> is the (0,1) element in the hilbert space.

So we expand the expectation value:

< singlet | O1 O2 | singlet >


as:

( < + | < - | - < - | < + |) O1 O2 ( |+> |-> - |->|+>)

= < + | O1 | +> < - |O1 |-> + < - | O1 | - > < + | O2 | + > - < + |O1 |-> < - | O2 | + > - < -| O1 | + > < + | O2 | - >


EDIT: where I forgot the front factor of 1/2, because of the double presence of the square root.
(but in the notebook, it is ok).

See attachment.

Hi vanesch

I see only 5 viewers so far of your welcome appended note. I wonder if others too are having trouble accessing it?

Can you tell me its format please; or where we might get the right software to read it?

I cannot open it.

Thanks, wm

 

[vanesch]

Hi vanesch

I see only 5 viewers so far of your welcome appended note. I wonder if others too are having trouble accessing it?

Can you tell me its format please; or where we might get the right software to read it?

I cannot open it.

Thanks, wm

Ah, sorry. It is a mathematica notebook. You can freely download a reader for them on the wolfram website http://www.wolfram.com

I guess this is the path: http://www.wolfram.com/products/mathreader/

 

[wm]

Many thanks!

Ah, sorry. It is a mathematica notebook. You can freely download a reader for them on the wolfram website http://www.wolfram.com

I guess this is the path: http://www.wolfram.com/products/mathreader/

:!) :!) Thanks; got it; great. :!) :!)

But there are some odd looking symbols: like

o/oo. = i?

And it starts:

pauli1 = ::0, 1<, :1,0<<. = Pauli matrix in mathematica notation?

(I can work them out if you are too busy -- but what about all the new readers that will soon come to it -- see below.)

Sorry also I question but I need to be certain that there is no implication of non-locality whatsoever in the derivation. (That's why I've been requesting such a derivation here for so long.)

Because:

1. I believe that QM, correctly understood, can derive most of its results locally; and I'm pretty sure you've done that.

2. I'd like to put such LOCAL maths into my own high-school framework and understanding.

[ Being a good girl ''I don't do non-local''. ]

3. Most important of all: I'd like to comment on locality in QM by saying:

The EPR-Bohm correlation can be derived wholly locally using the prescription in Bell (1964, equation (3)); refer vanesch (Physics Forums) https://www.physicsforums.com/showpost.php?p=1255185&postcount=122

Would you agree with this statement?

4. AND SO, finally: Do you need to spend a little time to polish up your notebook page? BECAUSE I think you will find it becoming very popular. It is a very nice result. Especially from my point of view as a localist: IN FACT, I suggest it would be beaucoup worth the trouble to post it in LaTeX. (Or maybe I could learn my LaTeX on it; with some help from JesseM :!) to whom I owe much.)

Thanks, wm

 

[vanesch]

Thanks; got it; great. :!)

But there are some odd looking symbols: like

o/oo

And it starts:

pauli1 = ::0, 1<,1 :1,0<< ?

That's very strange. I re-downloaded the notebook and it looks ok for me. (ok, I don't use the MathReader, but mathematica 4.1, but at least, the file is not corrupt)

I ask about them because I need to be sure that there is no implication of non-locality whatsoever in the derivation. (That's why I've been requesting such a derivation here for so long.)

Because:

1. I believe that QM, correctly understood, can derive most of its results locally; and I'm pretty sure you've done that.

2. I'd like to put such LOCAL maths into my own high-school framework and understanding. (''I don't do non-local''. )

3. Most important of all: I'd like to comment on locality in QM by saying:

The EPR-Bohm correlation can be derived wholly locally using the prescription in Bell (1964, equation (3)); refer vanesch (Physics Forums) https://www.physicsforums.com/showpost.php?p=1255185&postcount=122

Would you agree with this statement?

4. AND SO, finally: Do you need to spend a little time to polish up your notebook page? BECAUSE I think you will find it becoming very popular.

Thanks, wm

Unfortunately, the derivation in QM is local, or non-local, at one's interpretation. As I said, in order to be able to consider it "local", one needs to make the hypothesis that there is no genuine unique measurement result at Alice and Bob, for each particle pair. Only then is one allowed to say that the result is an operator (and not simply a real value). And in that case, one can apply the kind of reasoning you wanted to apply with the unit vector s.

The STANDARD way of looking upon things in quantum mechanics, is non-local, or undefined. Using the projection, which affects, when Alice measures, also the state at Bob, is obviously non-local as a "calculation".

Now, depending on whether one assigns any "reality" to the wavefunction, this either means 1) (wavefunction is real) that the projection is an "action-at-a-distance" or 2) (wavefunction is not real) that this is an abstract calculational procedure which has nothing to do with any local or non-local mechanism.

 

[JesseM]

Unfortunately, the derivation in QM is local, or non-local, at one's interpretation. As I said, in order to be able to consider it "local", one needs to make the hypothesis that there is no genuine unique measurement result at Alice and Bob, for each particle pair. Only then is one allowed to say that the result is an operator (and not simply a real value). And in that case, one can apply the kind of reasoning you wanted to apply with the unit vector s.

It's probably worth expanding on this to make sure wm understands the sense in which QM can be "local" according to mainstream physics. I'm sure vanesch would agree that Bell's theorem rules out conventional local realism in which each measurement yields a unique result; but there is a loophole in which you can regain locality if you accept something like the many-worlds interpretation in which there is no "collapse of the wavefunction" on measurement, instead each spin measurement simply results in a superposition of states which includes both a state where the experimenter saw a result of spin-up and a state where the experimenter saw a result of spin-down. And the key to preserving locality is that the universe doesn't have to decide how to link the versions of experimenter #1 over here with the versions of experimenter #2 over there until there has been time for a signal moving at the speed of light to pass between them.

On a previous thread I gave a simple picture which attempts to show conceptually how you can preserve locality as long as you imagine each experimenter splitting into multiple "copies" with each measurement (although this picture should be taken with a grain of salt since there are problems with using a simple frequentist notion of counting 'copies' to derive subjective probabilities of seeing different results in the many-worlds interpretation). Recall that one of the Bell inequalities says that if Alice and Bob always get opposite spins + and - when they measure along the same axis, then when they measure along different axes, conventional single-universe local realism implies the probability of getting opposite results should be greater than or equal to 1/3. But here's my conceptual picture showing how if you accept they each split into multiple copies with each measurement, you can explain how they'll get opposite results on different axes on less than 1/3 of trials:

say Bob and Alice are each receiving one of an entangled pair of photons, and their decisions about which spin axis to measure are totally deterministic, so the only "splitting" necessary is in the different possible results of their measurements. Label the three spin axes a, b, and c. If they always find opposite spins when they both measure their photons along the same axis, a local hidden-variables theory would say that if they choose different axes, the probability they get opposite spins must be at least 1/3 (assuming there's no correlation between their choice of which axes to measure and the states of the photons before they make the measurement). The actual probability of opposite spins along different axes depends on the difference in their detector angles, but all that's important is that it's less than 1/3, so for the sake of the argument let's say that when Alice chooses axis c and Bob chooses axis a, they only get opposite results 1/4 of the time, a violation of Bell's inequality.

So now suppose that when Bob makes a measurement on axis a in one location and Alice makes a measurement on axis c in another, each splits into 8 parallel versions, with 4 measuring spin + and 4 measuring spin -. Label the 8 Bobs like this:

Bob 1: a+
Bob 2: a+
Bob 3: a+
Bob 4: a+
Bob 5: a-
Bob 6: a-
Bob 7: a-
Bob 8: a-

Similarly, label the 8 Alices like this:

Alice 1: c+
Alice 2: c+
Alice 3: c+
Alice 4: c+
Alice 5: c-
Alice 6: c-
Alice 7: c-
Alice 8: c-

Note that the decision of how they split is based only on the assumption that each has a 50% chance of getting + and a 50% chance of getting - on whatever axis they choose, no knowledge about what the other one was doing was needed. And again, only when a signal traveling at the speed of light or slower passes from one to the other does the universe need to decide which Alice shares the same world with which Bob...when that happens, they can be matched up like this:

Alice 1 (c+) <--> Bob 1 (a+)
Alice 2 (c+) <--> Bob 2 (a+)
Alice 3 (c+) <--> Bob 3 (a+)
Alice 4 (c+) <--> Bob 5 (a-)
Alice 5 (c-) <--> Bob 4 (a+)
Alice 6 (c-) <--> Bob 6 (a-)
Alice 7 (c-) <--> Bob 7 (a-)
Alice 8 (c-) <--> Bob 8 (a-)

This insures that each one has a 3/4 chance of finding out the other got the same spin, and a 1/4 chance that the other got the opposite spin. If Bob and Alice were two A.I.'s running on classical computers in realtime, you could simulate Bob on one computer and Alice on another, make copies of each according to purely local rules whenever each measured a quantum particle, and then use this type of matching rule to decide which of the signals from the various copies of Alice will be passed on to which copy of Bob, and you wouldn't have to make that decision until the information from the computer simulating Alice was actually transmitted to the computer simulating Bob. So using purely local rules you could insure that, after many trials like this, a randomly-selected copy of A.I. Bob or A.I. Alice would record the same type of statistics that's seen in the Aspect experiment, including the violation of Bell's inequality.

Note that you wouldn't have to simulate any hidden variables in this case--you only have to decide what the spin was along the axes each one measured, you never have to decide what the spin along the other 2 unmeasured axes of each photon was.

And wm, please note that I included this loophole way back in post #133 of the other thread where I stated all the conditions which must be assumed in order to prove that quantum results are incompatible with local realism:

do you agree or disagree that if we have two experimenters with a spacelike separation who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like), then if they always get opposite answers when they make the same measurement on any given trial, and we try to explain this in terms of some event in both their past light cone which predetermined the answer they'd get to each possible measurement with no violations of locality allowed (and also with the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial, so their measurements are not having a backwards-in-time effect on the original predetermining event, as well as the assumption that the experimenters are not splitting into multiple copies as in the many-worlds interpretation), then the following inequalities must hold:

1. Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures B and gets +) plus Probability(Experimenter #1 measures B and gets +, Experimenter #2 measures C and gets +) must be greater than or equal to Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures C and gets +)

2. On the trials where they make different measurements, the probability of getting opposite answers must be greater than or equal to 1/3

 

[Doc Al]

but there is a loophole in which you can regain locality if you accept something like the many-worlds interpretation in which there is no "collapse of the wavefunction" on measurement, instead each spin measurement simply results in a superposition of states which includes both a state where the experimenter saw a result of spin-up and a state where the experimenter saw a result of spin-down.

But there are folks--and I count myself among them--who think that the "many worlds" interpretation does such violence to the usual notion of reality--with its multiple copies of experimenters and experimental results--that preserving locality with such a model is at best a Pyrrhic victory. Given such a metaphysics, locality is the least of one's worries. With all due respect to vanesch (a gentlemen and scholar--unlike Deutsch, who belongs in the loony bin )--I just don't see how it solves anything.

 

[wm]

Good stuff. And worth clarifying.

BTW, it occurred to me that the way Bell writes his stuff, and the mistake wm made, is a nice illustration of how quantum theory can get around doing "local" things in a way that a classical view cannot.

(With some minor editing and emphasis throughout.)

Comment: This post is very helpful to me. Thanks.

For the moment (for reasons to later appear): Can we have a superposition?

|Y> = V|wm wrong> + W|wm right>.

wm made the calculation of the correlation, thinking he was doing a kind of classical calculation, where the "sign" of (s.a) determined the outcome at Alice, and the sign of (s.b) determined the outcome at Bob.

Comment: wm made a classical calculation, at the level of high-school maths and logic. Maybe she went astray with her short-cut involving s and s', each a unit-vector relating to angular-momentum, and thus each a unit-axial-vector = (strictly) a bi-vector. wm believes they may transform differently.

The outcomes were supposed to be +1 or -1. So the true correlation would in fact be:

< sign(a.s) . sign(b.s) >, and not < (a.s) (b.s) >

However, by some mathematical coincidence, if s is a uniformly distributed unit vector in R^3, these two expressions come out the same.

I think this maybe not a coincidence (to be developed).

As JesseM and I demonstrated, however, they do not equate -(a.b), but rather -(a.b)/2 or -(a.b)/3, depending on whether one considers them in 2 or in 3 dimensions.

Yes; treating (standard) unit-vectors, these are both well-known relations for (standard) unit-vectors. See http://mathworld.wolfram.com/Vector.html (eg; eqn (9)).

If my comments were not clear, apologies to those who thought I was ignoring these results. My focus then was on another, equally interesting, result with bi-vectors.

SO: The question still open (for me) relates to the transformation of axial-vectors (bi-vectors; relating to angular-momentum). Maybe someone knows this answer already?

I suspect that I just need to apply Pauli matrices to classical angular momentum? Maybe some has done this already too? Would this not be possible (or not be correct) for any reason?

Nevertheless, the thing is that the ACTUAL RESULT OF MEASUREMENT, if it is truly "sign(a.s)" (hence, a numerical value of +1 or -1 for each trial) is then indeed "locally produced" (because only depending upon a and s)).

As we see, however, the correlation then comes out to be -(a.b)/2, which doesn't violate the Bell inequalities - as expected.

Yes; exactly as expected because this is the correct and well-known classical transformation for standard unit-vectors.

Now, quantum theory does, apparently, the same thing. So why can't we say that in its "inner workings", instead of transporting a unit vector s, this funny 3-some of Pauli matrices is transported ?

The reason is that in the expression < (sigma.a) (sigma.b) >, we write down a *quantum-mechanical* expectation value of an OPERATOR. We do not write the STATISTICAL expectation value of A PRODUCT OF TWO RESULTS.

In other words, the outcome at Bob was NOT (sigma.b) ! It was ONE OF ITS EIGENVALUES (which happens to be +1 or -1). As such, we cannot really say that "we transport the outcome at Bob, which is (sigma.b), to Alice, where her outcome is (sigma.a), and multiply the two together".

If that were true, indeed, this would have been a local mechanism. But the result at Alice is NOT (sigma.a), and the result at Bob is NOT (sigma.b). The results are of the kind +/- 1...

I believe it is a wholly local mechanism, relating to the conservation of angular momentum (to be developed).

Or are they ?

Yes; they certainly are. For sure! With the detectors so programmed, no one of my acquaintance has seen anything but elements from the set {+1, -1, +1', -1'}; the prime denoting Bob's results

Well, we COULD say, if we wanted to, that the outcome at Alice is not +1 or -1, but (sigma.a). And we COULD say that the outcome at Bob is (sigma.b). But that's a funny situation! It would mean that Alice didn't, after all, get a genuine numerical result such as -1 or +1, but rather a mathematical operator over hilbert space. If that were true, then wm's reasoning would be correct in a way. We take the result at Alice (again: it is not -1 or +1, but an operator over hilbert space!), which is determined purely by what happens at Alice, and similarly at Bob's, and at the point of their meeting, they multiply their outcomes (which, again, are not -1 or +1, but are now operators over hilbert space) and hurray, we get the right correlations.

vanesch, we COULD say lots of things here; BUT why would we want to say other than the truth?

1. That Alice did indeed get {+1, -1}; and while we were with her we saw these results with our own eyes and with our own friends.

2. That when we went over to Bob's lab we saw {+1', -1'}, etc.

3. And whenever we drop in at either lab (unannounced) we see the same consistent detector outputs; even when Alice and Bob were absent! Why not come with us? (For I miss your point here.)

4. Then you can join us in the correlation-checking, which we do (and can only do in this wondrously local quantum world) after we have hold of each set of related results:

Settings anti-parallel on this occasion:

Alice's paper-tape: +1, +1, -1, +1, -1, -1, ...

Bob's paper-tape: +1', +1', -1', +1', -1', -1', ...

But then; you already know the correlation from your (maybe non-local in your eyes) calculation. So all you really need is to see the tapes (and leave the correlation analysis to us). Why is not like this, please?

But what could that possibly mean, that Alice didn't get -1 or +1 at a trial, but each time an operator ? Well, it means that Alice got BOTH results. It means that Alice and Bob now have a quantum-mechanical description, and that they are in a superposition of having -1 and +1 (the operator contains both eigenvalues). This is exactly the MWI view on things, and it illustrates how in MWI, there is indeed no problem with locality. But the price to pay is rather high: you cannot say anymore that Alice got a measurement result which was each time -1 or +1 !

Seriously; save your money or give it to me.

Every Alice known to me has reported (to me, by phone or in person) the measurement results +1 and -1 only; each being a distinct printout on a permanent-record paper-tape.

Now, independently of interpretation, the reason why the quantum formalism can make predictions which defy classical theories is that in the formalism of quantum theory, there is a difference between the mathematical representation of a measurement (which is a hermitean operator), and actual individual results of a measurement (which are eigenvalues of that hermitean operator). In a classical theory, the representation of a measurement is necessarily its outcome.

I believe rather that QM is advanced probability theory and that we are quantum machines in a wholly quantum world.

That's very strange. I re-downloaded the notebook and it looks ok for me. (ok, I don't use the MathReader, but mathematica 4.1, but at least, the file is not corrupt)

OK; I'll see what I can do.

Unfortunately, the derivation in QM is local, or non-local, at one's interpretation. As I said, in order to be able to consider it "local", one needs to make the hypothesis that there is no genuine unique measurement result at Alice and Bob, for each particle pair. Only then is one allowed to say that the result is an operator (and not simply a real value). And in that case, one can apply the kind of reasoning you wanted to apply with the unit vector s.

Well I don't mind people holding non-local intepretations. BUT I'm sure glad we're living in a common-sense local and realistic quantum world.

The STANDARD way of looking upon things in quantum mechanics, is non-local, or undefined. Using the projection, which affects, when Alice measures, also the state at Bob, is obviously non-local as a "calculation".

That's fine with me: probability theory is ideally equipped to deal with non-local calculations; WHICH, incidentally, are only ever confirmed via local communications.

Now, depending on whether one assigns any "reality" to the wavefunction, this either means 1) (wavefunction is real) that the projection is an "action-at-a-distance" or 2) (wavefunction is not real) that this is an abstract calculational procedure which has nothing to do with any local or non-local mechanism.

Thank you; I'll take 2) every time. I'm not inclined to see as real abstract-elements of abstract spaces. Moreover, there is that maths theorem from 1915 that shows that any probability distribution CAN ALWAYS be represented by the absolute square of a Fourier polynomial ( = wave-function?).

With thanks again for your expansionary comments.

Regards, wm

 

[wm]

World-view?

But there are folks--and I count myself among them--who think that the "many worlds" interpretation does such violence to the usual notion of reality--with its multiple copies of experimenters and experimental results--that preserving locality with such a model is at best a Pyrrhic victory. Given such a metaphysics, locality is the least of one's worries. With all due respect to vanesch (a gentlemen and scholar--unlike Deutsch, who belongs in the loony bin )--I just don't see how it solves anything.

Doc, you seem ''sympathetic'' to the way I see the world. And the way I see MWI. (I hope so.)

Would you mind expanding on your world-view please? And pointing me to some of your papers?

I am not a physicist, but I see no reason to abandon my common-sense realism (which allows for measurement perturbation) and Einstein locality. (My post before this sets out some of my ideas.)

I do not accept what I call Bellian realism; a concept which Peres said (I believe) had nothing to do with QM. I feel that way and am truly surprised so few others see the world that way.

Thanks, wm

 

[wm]

It's probably worth expanding on this to make sure wm understands the sense in which QM can be "local" according to mainstream physics. I'm sure vanesch would agree that Bell's theorem rules out conventional local realism in which each measurement yields a unique result; but there is a loophole in which you can regain locality if you accept something like the many-worlds interpretation in which there is no "collapse of the wavefunction" on measurement, instead each spin measurement simply results in a superposition of states which includes both a state where the experimenter saw a result of spin-up and a state where the experimenter saw a result of spin-down. And the key to preserving locality is that the universe doesn't have to decide how to link the versions of experimenter #1 over here with the versions of experimenter #2 over there until there has been time for a signal moving at the speed of light to pass between them.

On a previous thread I gave a simple picture which attempts to show conceptually how you can preserve locality as long as you imagine each experimenter splitting into multiple "copies" with each measurement (although this picture should be taken with a grain of salt since there are problems with using a simple frequentist notion of counting 'copies' to derive subjective probabilities of seeing different results in the many-worlds interpretation). Recall that one of the Bell inequalities says that if Alice and Bob always get opposite spins + and - when they measure along the same axis, then when they measure along different axes, conventional single-universe local realism implies the probability of getting opposite results should be greater than or equal to 1/3. But here's my conceptual picture showing how if you accept they each split into multiple copies with each measurement, you can explain how they'll get opposite results on different axes on less than 1/3 of trials: And wm, please note that I included this loophole way back in post #133 of the other thread where I stated all the conditions which must be assumed in order to prove that quantum results are incompatible with local realism:

Jesse, it's not your fault, but I am not that good with words; I struggle.

But now that we have some maths before us; can we discuss things more in the context of specific experiments and related specific maths?

I think that it would be good to have vanesch's addendum converted out of mathematica (which I do not have) into a LaTeX post.

Is there a program that would do that? (It is only very short.)

This was something I have chased for awhile and since it is central QM, discussion of it will equally be central QM and common non-physicist mistakes.

I will still study your words, which I welcome every time. But mess-ups and time-delays are likely.

PS: To be clear, I do NOT think that QM is incompatible with common-sense local realism. NOT IN ANY WAY do I think that. Have I said that?

wm

 

[JesseM]

PS: To be clear, I do NOT think that QM is incompatible with common-sense local realism. NOT IN ANY WAY do I think that. Have I said that?

I never said that YOU think that. What I said is that mainstream physicists would all agree QM is incompatible with common-sense local realism, based on Bell's theorem (which need NOT include any assumption that measurements don't disturb the particle, if that's what you mean by 'Bellian realism') and that I am sure vanesch would agree, since when he talks about QM being 'local' he is only referring to a non-commonsense interpretation where measurements do not yield a single unique outcome. Do you think his derivation suggests the -cos(a-b) expectation value is compatible with common-sense local realism? If you do, then you have misunderstood something.

Also, do you still claim that you have a classical method of reproducing the -cos(a-b) expectation value based on sending two classical vectors s and -s to different experimenters, or have we managed to convince you that your math was incorrect in that case, and that the expectation value would be either -(1/2)*cos(a-b) or -(1/3)*cos(a-b) depending on whether s was a 2-vector or a 3-vector?

 

[Doc Al]

Doc, you seem ''sympathetic'' to the way I see the world. And the way I see MWI. (I hope so.)

Don't jump to conclusions. While I am sympathetic to your desire for a local interpretation of QM, I just don't see it as a serious possibility given Bell's theorem and current experimental results.

Would you mind expanding on your world-view please? And pointing me to some of your papers?

I certainly have no papers on this topic. One person I admire is Bell himself.

I am not a physicist, but I see no reason to abandon my common-sense realism (which allows for measurement perturbation) and Einstein locality. (My post before this sets out some of my ideas.)

I suspect that's because you don't appreciate the import of Bell's theorem.

I do not accept what I call Bellian realism; a concept which Peres said (I believe) had nothing to do with QM. I feel that way and am truly surprised so few others see the world that way.

Not sure what you mean by "Bellian realism". As I understand it, and I'm hardly an expert, is that Bell's theorem (combined with the experimental facts of QM and the reasoning of Einstein himself in EPR) leads to the conclusion that no theory satisfying Bell locality can accurately describe the world as we know it.

 

[wm]

Replying to a back-reference to another thread.

Although I tailored the short proofs I gave above to a particular thought-experiment, it's quite trivial to change a few words so they cover any situation where two people can measure one of three properties and they find that whenever they measure the same property they get opposite results. If you don't see how, I can do this explicitly if you'd like. I am interested in the physics of the situation, not in playing a sort of "gotcha" game where if we can show that Bell's original proof did not cover all possible local hidden variable explanations then the whole proof is declared null and void, even if it would be trivial to modify the proof to cover the new explanations we just thought up as well. I'll try reading his paper to see what modifications, if any, would be needed to cover the case where measurement is not merely revealing preexisting spins, but in the meantime let me ask you this: do you agree or disagree that if we have two experimenters with a spacelike separation who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like), then if they always get opposite answers when they make the same measurement on any given trial, and we try to explain this in terms of some event in both their past light cone which predetermined the answer they'd get to each possible measurement with no violations of locality allowed (and also with the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial, so their measurements are not having a backwards-in-time effect on the original predetermining event, as well as the assumption that the experimenters are not splitting into multiple copies as in the many-worlds interpretation), then the following inequalities must hold:

1. Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures B and gets +) plus Probability(Experimenter #1 measures B and gets +, Experimenter #2 measures C and gets +) must be greater than or equal to Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures C and gets +)

2. On the trials where they make different measurements, the probability of getting opposite answers must be greater than or equal to 1/3

Jesse,

1. Do you see here how long you have sentences?

2. Does not my classical model (of old) refute this Bellian-Inequality easily? Are you not giving conditions which my model meets?

3. Are you not saying (as I will let you):

a. That Alice may make a countable-inifinity of detector-settings, each delivering outcome of {+1, -1}.

b. That Bob may make a countable-infinity of detector-settings, each delivering outcomes of {+1', -1'}.

4. Anyway: Down-hill skiers, dirty-socks, books and the like will satisfy your inequality. More subtle, less wholly concrete objects will sink it for some detector combinations. Yes?

5. Is my conclusion not what vanesch has shown?

wm

 

[JesseM]

But there are folks--and I count myself among them--who think that the "many worlds" interpretation does such violence to the usual notion of reality--with its multiple copies of experimenters and experimental results--that preserving locality with such a model is at best a Pyrrhic victory. Given such a metaphysics, locality is the least of one's worries. With all due respect to vanesch (a gentlemen and scholar--unlike Deutsch, who belongs in the loony bin )--I just don't see how it solves anything.

Yes, I do think philosophical questions are unavoidable when discussing the many-worlds interpretation. But when discussing a possible universe where observers are constantly splitting upon measurement (which is certainly logically possible, we could simulate such a universe on a computer), I think it makes sense to relate this to the subjective probabilities experienced by each observer using the "self-sampling assumption" which the philosopher Nick Bostrom argues is implicit in all forms of anthropic reasoning. Basically, this assumption says that it makes sense in many circumstances to reason as if you were randomly sampled from the set of all observers, and to use this assumption to update your estimate of the probabilities of different events using Bayes' rule. On his website anthropic-principle.com he discusses this principle in detail, and includes many thought-experiments to show why it is plausible, such as these ones from the paper Self-Location and Observation Selection Theory:

Dungeon

The world consists of a dungeon that has one hundred cells. In each cell there is one prisoner. Ninety of the cells are painted blue on the outside and the other ten are painted red. Each prisoner is asked to guess whether he is in a blue or a red cell. (And everybody knows all this.) You find yourself in one of these cells. What color should you think it is? – Answer: Blue, with 90% probability.

In the doomsday argument FAQ he quotes a similar thought-experiment by John Leslie:

firm plan was formed to rear humans in two batches: the first batch to be of three humans of one sex, the second of five thousand of the other sex. The plan called for rearing the first batch in one century. Many centuries later, the five thousand humans of the other sex would be reared. Imagine that you learn you’re one of the humans in question. You don’t know which centuries the plan specified, but you are aware of being female. You very reasonably conclude that the large batch was to be female, almost certainly. If adopted by every human in the experiment, the policy of betting that the large batch was of the same sex as oneself would yield only three failures and five thousand successes. ... [Y]ou mustn’t say: ‘My genes are female, so I have to observe myself to be female, no matter whether the female batch was to be small or large. Hence I can have no special reason for believing it was to be large.’

If we accept this sort of reasoning as valid, then it can be applied to a situation where I am constantly being copied, since if I reason as though I am randomly sampled from the set of all copies of me, I can draw probabilistic conclusions about what I am likely to see over the result of many measurements.

 

[DrChinese]

PS: To be clear, I do NOT think that QM is incompatible with common-sense local realism. NOT IN ANY WAY do I think that. Have I said that?

You continue to ignore Bell's Theorem conveniently as if it does not exist. There is no substantive difference between your "common-sense" definition of realism (per your page) and Bell's. Even if there were, no one would care because Bell's maps to the debate of concern to Einstein, Bohr, and everyone who follows EPR's argument.

You should quit confusing people with your statements, and acknowledge as follows:

1. You believe in locality.
2. You believe in your version of realism, which is slightly different than Bell's but you are not sure how so mathematically.
3. You do not accept Bell's Theorem as valid.
4. You accept 3. as a matter of faith because you believe 1. and 2., and you think other folks should too.
5. You have no actual plan for developing your pet theory, but hope that those of us here at Physicsforums will help you.

I would like to point out that this discussion belongs in Theory Development, and not quantum physics.

 

[wm]

Don't jump to conclusions. While I am sympathetic to your desire for a local interpretation of QM, I just don't see it as a serious possibility given Bell's theorem and current experimental results.


I certainly have no papers on this topic. One person I admire is Bell himself.


I suspect that's because you don't appreciate the import of Bell's theorem.


Not sure what you mean by "Bellian realism". As I understand it, and I'm hardly an expert, is that Bell's theorem (combined with the experimental facts of QM and the reasoning of Einstein himself in EPR) leads to the conclusion that no theory satisfying Bell locality can accurately describe the world as we know it.

Thanks darn it! But while I'm here: For me I would change the last two sentences to put in my language:

"Bellian realism" is the constrained realism that we may associate with Bell (1964; for example); where A+, originally a measurement outcome, is subtly changed to a property of the particle itself; what I call the d'Espagnat move (from Sci. Am). As I understand it, and I'm hardly an expert, Bell's theorem (combined with the experimental facts of QM and the reasoning of Einstein* on locality) leads to the conclusion that no theory satisfying Bellian realism describes the world as we know it.

PS: * Einstein did not see the final draft; disagreement was later such that Einstein never again spoke to the author (Podolsky). That is why I believe many pot-shots at Einstein over EPR can be a bit misleading.

wm

 

[JesseM]

Jesse,

1. Do you see here how long you have sentences?

Well, if the long sentences are hard to follow, just ask for clarification, it's usually pretty easy to break them up into a list of distinct statements or assumptions...in the quote above, I could rewrite the assumptions like this:

do you agree or disagree that IF we have:

1. two experimenters with a spacelike separation
2. who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like)
3. then if they always get opposite answers when they make the same measurement on any given trial
4. and we try to explain this in terms of some event in both their past light cone which predetermined the answer they'd get to each possible measurement
5. with no violations of locality allowed
6. and also with the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial, so their measurements are not having a backwards-in-time effect on the original predetermining event
7. as well as the assumption that the experimenters are not splitting into multiple copies as in the many-worlds interpretation)

THEN the following inequalities must hold:

1. Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures B and gets +) plus Probability(Experimenter #1 measures B and gets +, Experimenter #2 measures C and gets +) must be greater than or equal to Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures C and gets +)

2. On the trials where they make different measurements, the probability of getting opposite answers must be greater than or equal to 1/3

2. Does not my classical model (of old) refute this Bellian-Inequality easily? Are you not giving conditions which my model meets?

I would say your old model, where the source knows what detector setting Alice will use before it sends out a signal, is violating condition 6 above, "the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial". In your "yoked" experiment, the angle that Alice measures the polarization is not independent of the polarization of the light sent out (and knowing both Alice's measurement angle and the polarization of the light does predetermine the result).

Of course my condition 6 also talked about a "backwards-in-time influence", which isn't true in your yoked scenario, since you assume there is enough time between Alice choosing her measurement angle and Alice actually making a measurement for a signal to have gotten back to the source and told it what the angle would be before it sent out the polarized light. I guess in condition 1 I was implicitly assuming that each experimenter's choice of detector setting was immediately before they actually made a measurement, so that there is also a spacelike separation between these two pairs of events:

1. (Alice randomly choosing her measurement angle) AND (Bob measuring the signal/object sent to him from the source)
2. (Bob randomly choosing his measurement angle) AND (Alice measuring the signal/object sent to her from the source)

So, if you add this condition explicitly to my list, then it would be impossible for the source's choice of what signals/objects to be sent out to be correlated with Alice and Bob's choice of detector settings, unless somehow the information was traveling backwards in time (or unless there was a weird cosmic conspiracy in the initial conditions of the universe which caused the source's output to be correlated with Alice and Bob's choices on each trial even though no signal could travel between them).

3. Are you not saying (as I will let you):

a. That Alice may make a countable-inifinity of detector-settings, each delivering outcome of {+1, -1}.

b. That Bob may make a countable-infinity of detector-settings, each delivering outcomes of {+1', -1'}.

Yes.

4. Anyway: Down-hill skiers, dirty-socks, books and the like will satisfy your inequality. More subtle, less wholly concrete objects will sink it for some detector combinations. Yes?

Nope, as long as you obey my conditions 1-7 above (including the clarification of what I meant by condition #1...also, note that #4 is not so much a condition as a logical conclusion necessitated by the other 6), then it is impossible for the inequalities to be violated by any experiment whatsoever. Therefore, since the inequalities are empirically violated in QM, it must be that QM violates one of the assumptions 5-7...either QM allows nonlocality, or QM allows backwards-in-time signalling, or QM allows experimenters to split into multiple copies (I suppose QM could also just violate the rules of logic, but I was assuming traditional logic must be obeyed).

5. Is my conclusion not what vanesch has shown?

Not at all--where did you get that idea? Vanesch just shows that when you use the conventional quantum rules to make predictions, you get the prediction that the expectation value is -cos(a-b). But the conventional quantum rules themselves do not say anything about locality or nonlocality, that's a matter for interpretation.

 

[JesseM]

"Bellian realism" is the constrained realism that we may associate with Bell (1964; for example); where A+, originally a measurement outcome, is subtly changed to a property of the particle itself

Again, you are free to assume that A+ is not a property of the particle itself, but that the particle just has some properties P which, when the particle is disturbed by a measurement of type A, leads deterministically to the result +. I tried to explain the logic behind the need for determinism in particle properties and measurement setting in post #56, if you don't see the logic it might help if you answered my questions there. Note that the assumption here is not that the whole universe is deterministic--indeed, the particular properties P of the particle sent out on each trial may be randomly created by the source, and the experimenter's choice of measurement setting may be random too--just that, if we know the complete properties of the particle and the measurement setting on a given trial, that is enough to uniquely determine the result on that trial.

 

[wm]

Ah ha!

You continue to ignore Bell's Theorem conveniently as if it does not exist. There is no substantive difference between your "common-sense" definition of realism (per your page) and Bell's. Even if there were, no one would care because Bell's maps to the debate of concern to Einstein, Bohr, and everyone who follows EPR's argument.

Bell's theorem (1964) is ever in my thoughts; so why do you say this?

You should quit confusing people with your statements, and acknowledge as follows:

1. You believe in locality.
2. You believe in your version of realism, which is slightly different than Bell's but you are not sure how so mathematically.
3. You do not accept Bell's Theorem as valid.
4. You accept 3. as a matter of faith because you believe 1. and 2., and you think other folks should too.
5. You have no actual plan for developing your pet theory, but hope that those of us here at Physicsforums will help you.

I would like to point out that this discussion belongs in Theory Development, and not quantum physics.

1. Yes.

2. Yes, re my realism. Then, No; I am sure now that I have seen vanesch's addendum (which I repeatedly requested of you) that mathematically I will be similar in deriving the EPR-Bohm correlation.

3. Just to be careful here: If you would define it, I would expect to give you a definite answer. Please define.

4. See 3 above. When it comes to maths, I'm not a faith-based person. So you are dead wrong again and again. (Why not follow JesseM and ask questions rather than promote lies and error (as you here do)?

5. (a) No! This is quite false and you must know that it is false!

Evidence: How would you know that it is false?

(a) I wrote to you off-PF and you replied that you were going to look at a matter and get back to me. You have not.

(b) So I am tending to read your question as an attempt to bias helpful communications from others with me. I take it you too can see where we're heading mathematically, thanks to vanesch. Put it another way: I see no theory of mine under threat.

SO why don't you ask an upfront question instead of non-locally reading my mind! Or should I rather say: Your non-locality fails again! (Many expletives deleted. But are you a PhD? By any chance, DrtC?)

5. (b) The PF communications have helped me greatly, especially JesseM, vanesch, hurkyl, DocAl +++

If I were familiar with LaTeX I would be more expansive.

PS-1. As to ''theory development'': This confirms my view that you can see where vanesch's maths (not yet mine) takes us.

PS-2. I hope the authorities will see that you are wrong (once again).

PS-3. Please provide evidence: What is the new theory that I am developing, please. (Please do not misunderstand or misrepresent the hidden-variables revealed on my website -- I should have picked you up on this before.)

PS-4. Finally: How many refereed papers do you want shoved down your fabricacious mouth?

wm

 

[JesseM]

PS-1. As to ''theory development'': This confirms my view that you can see where vanesch's maths (not yet mine) takes us.

If you think vanesch's math somehow shows QM is compatible with common-sense local realism, then you have totally misunderstood it (it would help if you explained why you think there is anything 'local' about his math).

And if you are not at least open to the possibility that Bell's theorem is valid and that common-sense local realism is definitively ruled out by quantum results such as the -cos(a-b) expectation value, then I agree this should go in theory development. If you are hoping to find a hole in Bell's theorem, but admit the fault may be in your understanding and are trying to improve your understanding through these discussions, then I think it's OK to continue the discussion here. So which is it?

 

[wm]

Well, if the long sentences are hard to follow, just ask for clarification, it's usually pretty easy to break them up into a list of distinct statements or assumptions...in the quote above, I could rewrite the assumptions like this:

do you agree or disagree that IF we have:

1. two experimenters with a spacelike separation
2. who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like)
3. then if they always get opposite answers when they make the same measurement on any given trial
4. and we try to explain this in terms of some event in both their past light cone which predetermined the answer they'd get to each possible measurement
5. with no violations of locality allowed
6. and also with the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial, so their measurements are not having a backwards-in-time effect on the original predetermining event
7. as well as the assumption that the experimenters are not splitting into multiple copies as in the many-worlds interpretation)

THEN the following inequalities must hold:

1. Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures B and gets +) plus Probability(Experimenter #1 measures B and gets +, Experimenter #2 measures C and gets +) must be greater than or equal to Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures C and gets +)

2. On the trials where they make different measurements, the probability of getting opposite answers must be greater than or equal to 1/3

I would say your old model, where the source knows what detector setting Alice will use before it sends out a signal, is violating condition 6 above, "the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial". In your "yoked" experiment, the angle that Alice measures the polarization is not independent of the polarization of the light sent out (and knowing both Alice's measurement angle and the polarization of the light does predetermine the result).

Of course my condition 6 also talked about a "backwards-in-time influence", which isn't true in your yoked scenario, since you assume there is enough time between Alice choosing her measurement angle and Alice actually making a measurement for a signal to have gotten back to the source and told it what the angle would be before it sent out the polarized light. I guess in condition 1 I was implicitly assuming that each experimenter's choice of detector setting was immediately before they actually made a measurement, so that there is also a spacelike separation between these two pairs of events:

1. (Alice randomly choosing her measurement angle) AND (Bob measuring the signal/object sent to him from the source)
2. (Bob randomly choosing his measurement angle) AND (Alice measuring the signal/object sent to her from the source)

So, if you add this condition explicitly to my list, then it would be impossible for the source's choice of what signals/objects to be sent out to be correlated with Alice and Bob's choice of detector settings, unless somehow the information was traveling backwards in time (or unless there was a weird cosmic conspiracy in the initial conditions of the universe which caused the source's output to be correlated with Alice and Bob's choices on each trial even though no signal could travel between them).
Yes. Nope, as long as you obey my conditions 1-7 above (including the clarification of what I meant by condition 1), then it is impossible for the inequalities to be violated by any experiment whatsoever. Therefore, since the inequalities are empirically violated in QM, it must be that QM violates one of the assumptions 5-7...either QM allows nonlocality, or QM allows backwards-in-time signalling, or QM allows experimenters to split into multiple copies (I suppose QM could also just violate the rules of logic, but I was assuming traditional logic must be obeyed). Not at all--where did you get that idea? Vanesch just shows that when you use the conventional quantum rules to make predictions, you get the prediction that the expectation value is -cos(a-b). But the conventional quantum rules themselves do not say anything about locality or nonlocality, that's a matter for interpretation.

Jesse, Do the following short-answers answer most of your questions:

1. vanesch has enabled me to clearly see that your last sentence is one that I can now wholeheartedly endorse!

2. You have been equally helpful in that important (for me, crucial) process; for which I thank you too.

3. Given the number of believers in non-locality, I had been searching for the origin of such a strange belief (which is totally alien to my present world-view).

4. I see now that I can happily persist with my concrete thinking-style; and bring more powerful arguments as to why non-locality is ...

5. I'm sorry if my slow-learning style upsets you. If I'm allowed to stay here (refer DrC prior post) then I think my arguments against non-locality will be be improved; coming from a more enlightened student.

Cheers, wm

 

[JesseM]

1. vanesch has enabled me to clearly see that your last sentence is one that I can now wholeheartedly endorse!

But I'm sure vanesch would also agree that "the conventional quantum rules themselves" + Bell's theorem do imply that common-sense local realism is ruled out, and that the only local options involve noncommonse interpretations like the many-worlds interpretation or perhaps the transactional interpretation (in which future events can effect past events that lie in their past light cone). Obviously you do not endorse this conclusion, so if you're open to the possibility that this might be due to an error in your understanding, it would help if we discussed the reasoning behind Bell's theorem more carefully.

4. I see now that I can happily persist with my concrete thinking-style; and bring more powerful arguments as to why non-locality is ...

No you can't, not unless you wish to persist in your confused understanding of Bell's theorem.

Again, to get around this confusion, please address the following:

1. Do you agree that none of the classical experiments you've presented so far (the "yoked" polarizer experiment and the experiment sending two classical vectors) both satisfy my conditions above (including the clarifications I added) and show a violation of any Bell inequality?

2. Do you agree that in a classical universe obeying locality, if experimenters always get the same (or opposite) result when using the same setting, and there is no possibility the source can know their choice of settings in advance (see my clarification of condition 1), then the only way to explain this correlation is to assume the complete properties of the object/signal sent out by the source + the choice of detector setting -> a deterministic result for that measurement? If you don't agree, please address my questions 1-3 in post #56, or provide an alternate classical explanation for the correlation.

 

[wm]

Thanks for asking questions!

If you think vanesch's math somehow shows QM is compatible with common-sense local realism, then you have totally misunderstood it (it would help if you explained why you think there is anything 'local' about his math).

And if you are not at least open to the possibility that Bell's theorem is valid and that common-sense local realism is definitively ruled out by quantum results such as the -cos(a-b) expectation value, then I agree this should go in theory development. If you are hoping to find a hole in Bell's theorem, but admit the fault may be in your understanding and are trying to improve your understanding through these discussions, then I think it's OK to continue the discussion here. So which is it?

Jesse; more misunderstandings; is my writing that bad?

1. I had understood that there were POWERFUL arguments for NON-LOCALITY.

2. vanesch shows me (us all, surely) that there are not.

3. My world-view is common-sense local realism (CLR).

4. I would call that my interpretation of the QM and its formalisms.

5. Does my CLR interpretation cause any problems here on PF?

6. For it seems to be a fairly-mild mid-range belief compared to others and extremes that I find here on PF.

7. vanesch enables me to discuss my view in the light of QM maths; with no need to dispute the maths.

8. vanesch enables me to bring better arguments to my view in the light of QM maths.

8. I think it more like that I am more here to find any holes in my world-view. (PS: While I am doing that, Am I permitted to poke holes in other views; especially using maths as my main argument now.)

9. I think I am very happy: and mostly due to about 6 lines of vanesch maths: 6 lines that you know I've been asking for for quite a while.

10. Is this above acceptable, please?

wm

 

[JesseM]

Jesse; more misunderstandings; is my writing that bad?

What exactly have I "misunderstood"?

1. I had understood that there were POWERFUL arguments for NON-LOCALITY.

2. vanesch shows me (us all, surely) that there are not.

WHY DO YOU THINK THIS? Vanesch just gave a recipe for calculating things in QM, the recipe itself is not based on local or nonlocal signals between events, it doesn't explain anything about why you see the correlations you do between measurements on entangled particles. However, if you take the results given to you by the recipe, and then you take Bell's theorem, it is clear that logically the results DO absolutely rule out common-sense local realism.

You seem to be confusing these two statements:

-Vanesch's calculations do not in themselves say anything either way about nonlocality vs. locality

-Vanesch's calculations are equally compatible with nonlocality and (common-sense) locality

But they are NOT equivalent--the first is true while the second is totally false! Logically the results are completely incompatible with common-sense local realism, it's just that this is not immediately obvious from looking at the calculations, you have to provide some additional logical arguments which go by the name of "Bell's theorem".

3. My world-view is common-sense local realism (CLR).

4. I would call that my interpretation of the QM and its formalisms.

But it is an invalid interpretation, definitively ruled out by quantum predictions. Bell's theorem shows this.

5. Does my CLR interpretation cause any problems here on PF?

Yes, no mainstream physicist would accept it as a valid "interpretation", because it does not make logical sense. You would see this if you actually made an effort to understand Bell's theorem, which is why I have been trying to walk you through it. If you're not trying to understand it, then this is equivalent to advancing the "interpretation" that perpetual motion is possible without listening to people's attempts to explain why it is ruled out by the laws of thermodynamics.

9. I think I am very happy: and mostly due to about 6 lines of vanesch maths: 6 lines that you know I've been asking for for quite a while.

10. Is this above acceptable, please?

No, because you have given no explanation for why you think vanesch's math somehow supports your idea. It doesn't, all vanesch's math gives is a recipe for calculating the probabilities, and then Bell's theorem proves that these probabilities are absolutely incompatible with common-sense local realism.

 

[wm]

Maybe too many questions now?

But I'm sure vanesch would also agree that "the conventional quantum rules themselves" + Bell's theorem do imply that common-sense local realism is ruled out, and that the only local options involve noncommonse interpretations like the many-worlds interpretation or perhaps the transactional interpretation (in which future events can effect past events that lie in their past light cone). Obviously you do not endorse this conclusion, so if you're open to the possibility that this might be due to an error in your understanding, it would help if we discussed the reasoning behind Bell's theorem more carefully. No you can't, not unless you wish to persist in your confused understanding of Bell's theorem.

Again, to get around this confusion, please address the following:

1. Do you agree that none of the classical experiments you've presented so far (the "yoked" polarizer experiment and the experiment sending two classical vectors) both satisfy my conditions above (including the clarifications I added) and show a violation of any Bell inequality?

2. Do you agree that in a classical universe obeying locality, if experimenters always get the same (or opposite) result when using the same setting, and there is no possibility the source can know their choice of settings in advance (see my clarification of condition 1), then the only way to explain this correlation is to assume the complete properties of the object/signal sent out by the source + the choice of detector setting -> a deterministic result for that measurement? If you don't agree, please address my questions 1-3 in post #56, or provide an alternate classical explanation for the correlation.

I personally DO NOT NEED A CLASSICAL EXPLANATION OF ANYTHING :::: NOW THAT I HAVE VANESCH'S MATHS.

NB: THAT IS NOT me SHOUTING AT YOU. THAT IS ME SHOUTING TO THE ROOF-TOPS AND MY (sorry -- meant to turn caps off) friends that I have learned something good.


PS: I am making a big mistake in rushing all this stuff when i am so busy. I do feel that I owe you answers. But please consider them in the spirit of community dialogue and my personal learning. There is not a question I will not answer honestly; just maybe not good wording, especially when rushing.

Is this now OK please?

wm

 

[JesseM]

I personally DO NOT NEED A CLASSICAL EXPLANATION OF ANYTHING :::: NOW THAT I HAVE VANESCH'S MATHS.

Vanesch's math does not in any way support your conclusion that commonsense local realism (which is what I meant by the word 'classical') is compatible with QM, if you think it does, you need to explain why you think so (see my previous post #147). In fact, the probabilities vanesch calculates are absolutely incompatible with common-sense local realism, the only way for common-sense local realism to be true would be if the probabilities he calculated were incorrect. Bell's theorem shows this.

If you disagree that Bell's theorem proves that the quantum predictions derived by vanesch's math are absolutely incompatible with commonsense local realism (a conclusion I am sure vanesch and Doc Al and DrChinese would all agree with), then if you are interested in learning why everyone disagrees with you rather than just declaring everyone wrong, you need to cooperate with our attempts to try to walk you through Bell's theorem. If you're not interested in learning, but just in promoting your incorrect ideas, you should take it to theory development.

 

[wm]

Gosh!

What exactly have I "misunderstood"? WHY DO YOU THINK THIS? Vanesch just gave a recipe for calculating things in QM, the recipe itself is not based on local or nonlocal signals between events, it doesn't explain anything about why you see the correlations you do between measurements on entangled particles. However, if you take the results given to you by the recipe, and then you take Bell's theorem, it is clear that logically the results DO absolutely rule out common-sense local realism.

You seem to be confusing these two statements:

-Vanesch's calculations do not in themselves say anything either way about nonlocality vs. locality

-Vanesch's calculations are equally compatible with nonlocality and (common-sense) locality

But they are NOT equivalent--the first is true while the second is totally false! Logically the results are completely incompatible with common-sense local realism, it's just that this is not immediately obvious from looking at the calculations, you have to provide some additional logical arguments which go by the name of "Bell's theorem". But it is an invalid interpretation, definitively ruled out by quantum predictions. Bell's theorem shows this. Yes, no mainstream physicist would accept it as a valid "interpretation", because it does not make logical sense. You would see this if you actually made an effort to understand Bell's theorem, which is why I have been trying to walk you through it. If you're not trying to understand it, then this is equivalent to advancing the "interpretation" that perpetual motion is possible without listening to people's attempts to explain why it is ruled out by the laws of thermodynamics. No, because you have given no explanation for why you think vanesch's math somehow supports your idea. It doesn't, all vanesch's math gives is a recipe for calculating the probabilities, and then Bell's theorem proves that these probabilities are absolutely incompatible with common-sense local realism.

vanesch gives me much personal comfort BECAUSE his QM maths I will be able to happily understand and live with.

Please, me not being rude; define Bell's theorem that you want me to swear to. I am not avoiding here but I have no idea how to answer.

I believe in LOCAL QM; shall I be thrown out for that?

I think my saints (my co-conspirators) might be Bell, Einstein, Cramer (bit re-interpreted), Peres, Rovelli, Ballentine, Griffiths, Haag, Froehner, Kracklauer, Mayants, Jaynes, Hestenes, Harrison, Gottfried, parly vanesch (because I think we might be able to agree, due his maths) +++++++++ (though I know little of them and I'm not a full-member of MWI -- see hurkyl comment early on; it seems to fit me ok but I'm not studied it much). Some gurus here seem to be ok in ideas too.

Am I fallen into a group of terrorists? Should I head voluntarily for Guantanamo Bay?

wm