- #126

- 3,507

- 26

I thought QM was not a deterministic theory.Definitely not. The Bohm interpretation of QM shows that--it is deterministic.

- Thread starter Pat71
- Start date

- #126

- 3,507

- 26

I thought QM was not a deterministic theory.Definitely not. The Bohm interpretation of QM shows that--it is deterministic.

- #127

- 3,507

- 26

- #128

atyy

Science Advisor

- 14,003

- 2,283

I thought QM was not a deterministic theory.

I'm not sure I'm going to get this right, because it is tricky. But here is my try.

It's unclear whether there is such a thing as a fundamentally indeterministic theory. QM itself is not deterministic, but if it can be embedded in a deterministic theory, then the determinism is not fundamental. Similarly, it is unclear if there is such a thing as a fundamentally deterministic theory, since stochastic theories can be well approximated by deterministic theories in certain regimes. Bohmian mechanics constructs an explicit embedding of non-relativistic QM into a classical indeterministic theory which can be embedded into a deterministic theory.

However, there is a different version of Bell's theorem in which it can be shown that if a theory does not allow faster than light communication and violates the Bell inequalities, then the theory must be indeterministic in some sense.

http://arxiv.org/abs/quant-ph/0508016

http://arxiv.org/abs/0911.2504

As far as I can tell, there are 3 different definitions of locality in Wiseman's recent papers.

(1) signal locality

http://arxiv.org/abs/0911.2504 (Eq 8)

(2) locality

http://arxiv.org/abs/0911.2504 (Eq 7)

http://arxiv.org/abs/1402.0351 (Eq 2)

(3) local causality

http://arxiv.org/abs/1402.0351 Eq (4)

Last edited:

- #129

- 3,507

- 26

Thanks for the references, the second paper, by Wiseman asserts: "Bell’s seminal 1964 paper shows that quantum correlations violate the conjunction of locality1 and determinism. However, there are quantum models that violate locality but maintain determinism (Bohmian mechanics is an example), andI'm not sure I'm going to get this right, because it is tricky. But here is my try.

It's unclear whether there is such a thing as a fundamentally indeterministic theory. QM itself is not deterministic, but if it can be embedded in a deterministic theory, then the determinism is not fundamental. Similarly, it is unclear if there is such a thing as a fundamentally deterministic theory, since stochastic theories can be well approximated by deterministic theories in certain regimes. Bohmian mechanics constructs an explicit embedding of non-relativistic QM into a classical indeterministic theory which can be embedded into a deterministic theory.

However, there is a different version of Bell's theorem in which it can be shown that if a theory does not allow faster than light communication and violates the Bell inequalities, then the theory must be indeterministic in some sense.

http://arxiv.org/abs/quant-ph/0508016

http://arxiv.org/abs/0911.2504

As far as I can tell, there are 3 different definitions of locality in Wiseman's recent papers.

(1) signal locality

http://arxiv.org/abs/0911.2504 (Eq 8)

(2) locality

http://arxiv.org/abs/0911.2504 (Eq 7)

http://arxiv.org/abs/1402.0351 (Eq 2)

(3) local causality

http://arxiv.org/abs/1402.0351 Eq (4)

The bolded part is specifically what I had in mind with my questions. Certainly this is not so clearly stated in the usual rendition of Bell's theorem where this subtle distinction about the relation of locality with the theorem is never made. If determinism is not fundamental it adds another layer of ambiguity to the already not clear cut meaning of the violation of the BE. Again I think that labeling a theory as "nonlocal" because it violates the BE without further qualifications as it's almost universally done when talking about Bell's theorem is highly misleading.

- #130

atyy

Science Advisor

- 14,003

- 2,283

Let's use the 3 definitions in post #58. Quantum mechanics is local and signal local, but it violates local causality, so it is in the third sense in which the violation of the Bell inequalities by quantum mechanics that renders it "nonlocal".Thanks for the references, the second paper, by Wiseman asserts: "Bell’s seminal 1964 paper shows that quantum correlations violate the conjunction of locality1 and determinism. However, there are quantum models that violate locality but maintain determinism (Bohmian mechanics is an example), andmodels that maintain locality but violate determinism (standard operational quantum theory is an example). Thus nothing can be concluded from Bell’s theorem about locality or determinism independently of each other."

The bolded part is specifically what I had in mind with my questions. Certainly this is not so clearly stated in the usual rendition of Bell's theorem where this subtle distinction about the relation of locality with the theorem is never made. If determinism is not fundamental it adds another layer of ambiguity to the already not clear cut meaning of the violation of the BE. Again I think that labeling a theory as "nonlocal" because it violates the BE without further qualifications as it's almost universally done when talking about Bell's theorem is highly misleading.

- #131

- 3,507

- 26

Agreed, but let's not say "nonlocal" as it lends itself to confusion, maybe "nonlocally causal"?Let's use the 3 definitions in post #58. Quantum mechanics is local and signal local, but it violates local causality, so it is in the third sense in which the violation of the Bell inequalities by quantum mechanics that renders it "nonlocal".

I highly recommend the last article by Wiseman:"The two Bell's theorems of John Bell", it really clarifies things.

- #132

- 3,507

- 26

- #133

atyy

Science Advisor

- 14,003

- 2,283

Yes. Even "local causality" can be confusing, since "signal locality" also provides a notion of causality, eg. http://arxiv.org/abs/quant-ph/9508009v1.Agreed, but let's not say "nonlocal" as it lends itself to confusion, maybe "nonlocally causal"?

I highly recommend the last article by Wiseman:"The two Bell's theorems of John Bell", it really clarifies things.

Older terms are "local determinism" or "local realism", but those are also confusing since it is not clear how indeterminism or non-realism can save local causality after the Bell inequalities are violated - non-realism can save locality before (but not after) the Bell inequalities are violated.

The one I like best is "local explainability", but that is not so common, although it is mentioned by http://arxiv.org/abs/0909.0015, and fits in with http://arxiv.org/abs/1311.6852.

- #134

atyy

Science Advisor

- 14,003

- 2,283

Well, terminology varies, but quantum mechanics and rigourous relativistic quantum field theory is simply not locally causal (unless one is using the less common definition of the term). The Bell theorem excludes this.

- #135

- 3,507

- 26

Well, rigourous relativistic quantum field theory will be not locally causal when(or if) it comes to existence some day.Well, terminology varies, but quantum mechanics and rigourous relativistic quantum field theory is simply not locally causal (unless one is using the less common definition of the term). The Bell theorem excludes this.

- #136

atyy

Science Advisor

- 14,003

- 2,283

It already exists in 1+1 and 2+1 spacetime dimensions. The hunt is on in 3+1D.Well, rigourous relativistic quantum field theory will be not locally causal when(or if) it comes to existence some day.

- #137

- 8,401

- 2,580

I looked at the paper by Wiseman (here: http://arxiv.org/pdf/1402.0351v2.pdf) where he makes the distinction between locality and local causality, but I didn't say a statement of the definitions that showed how they were different. Equation (2) (Page 6) gives a definition of local, and equation (4) (Page 14) gives a "criterion" (not a definition, because it's not if and only if) for local causality. But they're the same equation! So what's the difference?Let's use the 3 definitions in post #58. Quantum mechanics is local and signal local, but it violates local causality, so it is in the third sense in which the violation of the Bell inequalities by quantum mechanics that renders it "nonlocal".

- #138

atyy

Science Advisor

- 14,003

- 2,283

Locality (Eq 2) doesn't have Alice's measurement outcome on the LHS, whereas local causality (Eq 4) does. So Eq 2 is just the reduced density matrix, which means that Bob's results don't depend on what Alice does. But Eq 4 is the nonlocal correlation, which means that if Bob knows Alice's results, he can sort his results and find perfect correlation.I looked at the paper by Wiseman (here: http://arxiv.org/pdf/1402.0351v2.pdf) where he makes the distinction between locality and local causality, but I didn't say a statement of the definitions that showed how they were different. Equation (2) (Page 6) gives a definition of local, and equation (4) (Page 14) gives a "criterion" (not a definition, because it's not if and only if) for local causality. But they're the same equation! So what's the difference?

- #139

- 3,507

- 26

The difference is what I was referring to in the second paragraph of #110, it is explained in the paper since the second equation is <if> instead of <iff> like the first one, so local causality is weaker than locality. I think this distinction is obscured in many popular and also textbook(since people apparently knowledgeable about the theorem ignores this distinction) accounts of the theorem leading to empty debates and lots of unnecessary confusion. The discussions about BT I've witnessed so far (in PF and elsewhere) use the the strong definition without qualification in the place of the weak one wich is the appropriate according to scholars experts in the theorem.I looked at the paper by Wiseman (here: http://arxiv.org/pdf/1402.0351v2.pdf) where he makes the distinction between locality and local causality, but I didn't say a statement of the definitions that showed how they were different. Equation (2) (Page 6) gives a definition of local, and equation (4) (Page 14) gives a "criterion" (not a definition, because it's not if and only if) for local causality. But they're the same equation! So what's the difference?

It would be interesting to know if Binney is using the stron or weak sense of locality when making his assertions, maybe in the light of it his view would be less controversial.

- #140

- 499

- 37

What difference would it make? His theory doesn't work because his geometrical calculation is wrong, not because of any assumptions about locality.It would be interesting to know if Binney is using the stron or weak sense of locality when making his assertions, maybe in the light of it his view would be less controversial.

- #141

- 3,507

- 26

I haven't found anything about Binney's geometrical calculations in the thread and Binney has no theory that I know of. Reading again the first posts Binney's quotes seem perfectly compatible with the indeterministic and local QM view of Bell's theorem, and all the comments about his "not even considering nonlocality" look like misled over-reactions, did you not read the Wiseman paper linked by atyy?What difference would it make? His theory doesn't work because his geometrical calculation is wrong, not because of any assumptions about locality.

- #142

atyy

Science Advisor

- 14,003

- 2,283

To be honest, I didn't join the discussion till now because I have no idea what Binney is saying, let alone whether it is right or wrong, so I don't know if Binney is simply using locality as defined by Wiseman. Locality as defined by Wiseman is uncontroversially a property of quantum mechanics.I haven't found anything about Binney's geometrical calculations in the thread. Reading again the first posts Binney's quotes seem perfectly compatible with the indeterministic and local QM view of Bell's theorem, and all the comments about his "not even considering nonlocality" look like misled over-reactions, did you not read the Wiseman paper linked by atyy?

- #143

- 499

- 37

I agree he does not set out his calculation, but he doesI haven't found anything about Binney's geometrical calculations in the thread and Binney has no theory that I know of. Reading again the first posts Binney's quotes seem perfectly compatible with the indeterministic and local QM view of Bell's theorem, and all the comments about his "not even considering nonlocality" look like misled over-reactions, ...

Post #25 is my calculation

Unfortunately, although it produces a result, it is the wrong result. For small angles, the overlap of two hemispheres is proportional to the overlap. The quantum correlation is proportional to the overlap squared. Of course, if

- #144

- 499

- 37

Post #25

Oops! Just say "cosine rule"not the required cos^((b-a)/2) rule

- #145

- 3,507

- 26

There are two key points in what he says that I'm guiding my opinión on, he says literallythat no hidden variables can explain violations of BI, wich I take as a clear rejection of determinism, and in the example used by Derek in #25 he doesn't say one can predict or calculate anything based simply on anything fixed at the outset, if one did like Derek did would find wrong results but he only talks about "consistence", by which I understand he means that the indeterminism he endorses allows the principle of locality to hold.

- #146

- 499

- 37

They're consistent with there being a g in my middle name too but that is just as irrelevant.

There are two key points in what he says that I'm guiding my opinión on, he says literallythat no hidden variables can explain violations of BI, wich I take as a clear rejection of determinism, and in the example used by Derek in #25 he doesn't say one can predict or calculate anything based simply on anything fixed at the outset, if one did like Derek did would find wrong results but he only talks about "consistence", by which I understand he means that the indeterminism he endorses allows the principle of locality to hold.

- #147

- 3,507

- 26

Do you see the difference between claiming one can calcule the results of Bob from knowing that the hemisphere containing the positron's spin is fixed at the outset vs claiming that "a posteriori" (after the fact) the results are consistent with it being fixed at the outset and unaffected by Alice's measurement?They're consistent with there being a g in my middle name too but that is just as irrelevant.

Last edited:

- #148

- 8,401

- 2,580

Thanks! I stared at the two equations and didn't see that difference.Locality (Eq 2) doesn't have Alice's measurement outcome on the LHS, whereas local causality (Eq 4) does. So Eq 2 is just the reduced density matrix, which means that Bob's results don't depend on what Alice does. But Eq 4 is the nonlocal correlation, which means that if Bob knows Alice's results, he can sort his results and find perfect correlation.

But now I'm having the opposite problem. It seems to me that if locality is violated that that would imply the possibility of signaling. If Bob's result depends on Alice's detector setting, then wouldn't Alice be able to signal to Bob by varying her setting?

Ah, nevermind. I see the difference: Equation 2 is this:

[itex]P_\theta(B|a,b,c,\lambda) = P_\theta(B|b,c,\lambda)[/itex]

If that is violated, then Alice's setting affects Bob's result, but only if [itex]\lambda[/itex] is kept

- #149

- 499

- 37

Yes.Do you see the difference between claiming one can calcule the results of Bob from knowing that the hemisphere containing the positron's spin is fixed at the outset vs claiming that "a posteriori" (after the fact) the results are consistent with it being fixed at the outset and unaffected by Alice's measurement?

- #150

- 499

- 37

I mean the Binney correlation is proportional to the overlap!the overlap of two hemispheres is proportional to the overlap. The quantum correlation is proportional to the overlap squared.