Bell's theorem and QM: Peres' conclusion and terminology?

[Gordon Watson]

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In his text-book "Quantum Theory: Concepts and Methods", Asher Peres (1995) writes:

A: "Bell's theorem is not a property of quantum theory." - (p.162, Peres' emphasis).

B: "This conclusion can be succinctly stated: unperformed experiments have no results." - (p.168, Peres' emphasis).

Questions:

1. Is Peres' conclusion widely accepted within the mainstream QM community?

2. What are other mainstream conclusions (with sources if possible)?

3. What is the correct terminology, linking Bell's theorem to QM -- that goes something like this, as I recall -- "Bell's theorem cannot be formed from within QM?"

Thank you.

PS: Re #1 above: "For example, according to the so-called Copenhagen interpretation of quantum mechanics, one is simply not allowed to ask what happened in a situation where no measurement was made." (Rachel Hillmer and Paul Kwiat; April 16, 2007) at

http://www.scientificamerican.com/article.cfm?id=quantum-eraser-what-do-quantum-particles-really-do
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[eaglelake]

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In his text-book "Quantum Theory: Concepts and Methods", Asher Peres (1995) writes:

A: "Bell's theorem is not a property of quantum theory." - (p.162, Peres' emphasis).

B: "This conclusion can be succinctly stated: unperformed experiments have no results." - (p.168, Peres' emphasis).

Questions:

1. Is Peres' conclusion widely accepted within the mainstream QM community?

2. What are other mainstream conclusions (with sources if possible)?

3. What is the correct terminology, linking Bell's theorem to QM -- that goes something like this, as I recall -- "Bell's theorem cannot be formed from within QM?"

Thank you.

PS: Re #1 above: "For example, according to the so-called Copenhagen interpretation of quantum mechanics, one is simply not allowed to ask what happened in a situation where no measurement was made." (Rachel Hillmer and Paul Kwiat; April 16, 2007) at

http://www.scientificamerican.com/article.cfm?id=quantum-eraser-what-do-quantum-particles-really-do
..

Asher Peres was widely respected and admired, he published in the most respected academic journals, and he was a part of the mainstream physics community. But there does not seem to be any consensus among physicists about the interpretation of quantum mechanics. Even “the Copenhagen interpretation “, which is considered to be the “orthodox” version, means different things to different people.

Essentially, Bell’s theorem describes a classical experiment, not a quantum one. It assumes that the experiment is separable. Quantum events are non-separable, while separability is a distinguishing characteristic of classical physics. In that sense, Bell’s theorem is about classical physics. It is about an experiment that has several possible outcomes, which are mutually exclusive. In classical mechanics this is not a problem. For example, if you want to do determine the angular momentum of a classical particle, you just do the separate experiments that measure each component. Not so in quantum mechanics! The three experiments that measure the components are different and incompatible with each other. When we measure the x-component, we have no idea what the values of the other components are. Most importantly, the value of the x-component depends on the experiment designed to measure the x-component. The particle does not possesses an x-component of the angular momentum prior to its measurement. When we measure the x-component, we do not simultaneously perform the experiments for the other components and “unperformed experiments have no results.” Thus, we have no values from the unperformed experiments to be used in our calculations! If we insist on using the inferred values from unperformed experiments we often get contradictions and paradoxes. That is what happens in Bell’s theorem. Several results are used to obtain his inequality. But the experiment he describes can yield only one of those values. The other results are from unperformed experiments, and are, therefore meaningless in quantum mechanics, but Bell uses them as we would in a classical calculation. Consequently, quantum events violate Bell’s inequality while classical experiments satisfy it.

For a simpler example of non-separability in quantum mechanics, see Peres’ discussion of the triple Stern-Gerlach experiment described by Fig. 1.6 on p 16 of the Peres book you cite.
Best wishes

 

[JesseM]

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In his text-book "Quantum Theory: Concepts and Methods", Asher Peres (1995) writes:

A: "Bell's theorem is not a property of quantum theory." - (p.162, Peres' emphasis).

Without any context it's difficult to know what he means by "property of quantum theory." I doubt he would disagree with the notion that Bell's theorem proves that the predictions of QM are impossible to derive from any local realist theory, but the incompatibility of local realism and QM need not necessarily be seen as a "property of quantum theory", depending on your definition of what it means to say something is a "property" of a given theory.

 

[Gordon Watson]

Asher Peres was widely respected and admired, he published in the most respected academic journals, and he was a part of the mainstream physics community. But there does not seem to be any consensus among physicists about the interpretation of quantum mechanics. Even “the Copenhagen interpretation “, which is considered to be the “orthodox” version, means different things to different people.

Essentially, Bell’s theorem describes a classical experiment, not a quantum one. It assumes that the experiment is separable. Quantum events are non-separable, while separability is a distinguishing characteristic of classical physics. In that sense, Bell’s theorem is about classical physics. It is about an experiment that has several possible outcomes, which are mutually exclusive. In classical mechanics this is not a problem. For example, if you want to do determine the angular momentum of a classical particle, you just do the separate experiments that measure each component. Not so in quantum mechanics! The three experiments that measure the components are different and incompatible with each other. When we measure the x-component, we have no idea what the values of the other components are. Most importantly, the value of the x-component depends on the experiment designed to measure the x-component. The particle does not possesses an x-component of the angular momentum prior to its measurement. When we measure the x-component, we do not simultaneously perform the experiments for the other components and “unperformed experiments have no results.” Thus, we have no values from the unperformed experiments to be used in our calculations! If we insist on using the inferred values from unperformed experiments we often get contradictions and paradoxes. That is what happens in Bell’s theorem. Several results are used to obtain his inequality. But the experiment he describes can yield only one of those values. The other results are from unperformed experiments, and are, therefore meaningless in quantum mechanics, but Bell uses them as we would in a classical calculation. Consequently, quantum events violate Bell’s inequality while classical experiments satisfy it.

For a simpler example of non-separability in quantum mechanics, see Peres’ discussion of the triple Stern-Gerlach experiment described by Fig. 1.6 on p 16 of the Peres book you cite.
Best wishes

Thank you, eaglelake, for this very helpful and expansive reply; especially for the reference to p. 16.

There's a great deal that appeals to me in Peres' approach and analysis.

I very much like this phrase of yours: "Consequently, quantum events violate Bell’s inequality while classical experiments satisfy it."

Peres' makes an interesting comparison between quantum and classical experiments.

Personally, I am keen to understand the limits of local realism (L*R) -- by which I mean: going beyond many local realists, especially those who challenge (or doubt) the related experimental outcomes.

Your phrase, it seems to me, nicely positions Bell's theorem (BT) in the grand scheme of things. That's helpful as I wrestle with L*R and BT ... in that same grand scheme.
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With thanks again.

GW