John Bell Workshop 2014

[Richard Healey]

In papers published in the 25 years following his famous 1964 proof John Bell refined and reformulated his views on locality and causality. Although his formulations of local causality were in terms of probability, he had little to say about that notion. But assumptions about probability are implicit in his arguments and conclusions. Probability does not conform to these assumptions when quantum mechanics is applied to account for the particular correlations Bell argues are locally inexplicable. This account involves no superluminal action and there is even a sense in which it is local, but it is in tension with the requirement that the direct causes and effects of events are nearby. Full text

[Quantum Speculations]

Hi Richard,

I have a short comment on your very intriguing paper. It seems that in your formulation of QM there is still the collapse of the wave function, though the wave function is not ontic. Then it seems that my new proof of the quantum nonlocality also applies to your theory. My proof does not depend on the meaning of the wave function, but depend on the existence of the collapse of the wave function.

Best,
Shan

[Richard Healey]

Shan,

Thank you for your comment. As you point out, on my understanding a wave function does not describe or represent the physical state of a system to which it is assigned. Moreover, a system may be assigned more than one wave function at once, since each assignment is relative to the physical situation of a hypothetical assigner. In the example you use in your own argument, the wave function to be assigned to the distant photon relative to the physical situation immediately in the future light cone of the nearby measurement of polarization with respect to a (or to a’) differs from the wave function to be assigned relative to the immediate past light cone of the measurement on the distant photon, even if these assignments are made at the same time in the lab. frame. So while the result of the polarization measurement with respect to a or to a’ requires reassignment of the distant photon’s wave function relative to the situation of the one making the nearby measurement, it does not require any change in that photon’s wave function relative to anyone about to make a measurement of its polarization. The polarization measurement with respect to a or to a’ induces no collapse in the other photon’s wave function for two reasons: first, there is no single wave function capable of collapsing (or not collapsing); and second, even if it does occur, reassignment of a wave function relative to the physical situation of a hypothetical agent (if required) does not represent any physical change in the system to which the wave function is being assigned—it couldn’t, because a wave function does not represent the physical state of that system.
Here I think I agree with Shelly’s objection to your argument.

[Quantum Speculations]

Hi Richard,

Many thanks for your kind reply! I will consider my argument more deeply. But I still have a question for your reply. I think the existence of precise anticorrelation requires that the wave function of the photon on every side need to be collapsed as in standard quantum mechanics. I would like to know what you think about this point.

Best,
Shan

[Richard Healey]

Shan,

I take myself to be clarifying standard quantum mechanics, not modifying it, so I don’t think there is any physical collapse on “measurement”—merely the periodic reassignment of wave function required as the physical situation of a hypothetical agent changes and so gives access to new information about “the result”.
Immediately in the past light cone of her measurement event Alice should assign an entangled wave function to the photon pair and the corresponding reduced density operator to her own photon. At the same time in the lab. frame (in which Alice’s measurement occurs first) Bob should assign a pure polarization state to Alice’s photon, reflecting the outcome of his measurement on his photon (which he takes to have been absorbed into his apparatus, and so no longer to be assigned a quantum state.)

[Richard Healey]

Shan,

I take myself to be clarifying standard quantum mechanics, not modifying it, so I don’t think there is any physical collapse on “measurement”—merely the periodic reassignment of wave function required as the physical situation of a hypothetical agent changes and so gives access to new information about “the result”.
Immediately in the past light cone of her measurement event Alice should assign an entangled wave function to the photon pair and the corresponding reduced density operator to her own photon. At the same time in the lab. frame (in which Bob’s measurement occurs first) Bob should assign a pure polarization state to Alice’s photon, reflecting the outcome of his measurement on his photon (which he takes to have been absorbed into his apparatus, and so no longer to be assigned a quantum state.)

[editor]

Hi Richard,

Thanks again for your further clarification!

Best,
Shan

[Robert Griffiths]

Dear Richard,

Busy over year end, so only got to your post recently. Two comments

First, I couldn’t see why agents were really needed for the discussion unless one insists, like some do, that probabilities must be interpreted that way. Everything you said, it seemed to me, could very well be expressed in terms of conditional probabilities based on various types of information present or absent in the condition. Am I correct that this would be satisfactory (i.e., I would not be missing some crucial point) for someone like me who doesn’t see the much advantage in following de Finetti? (I assure you I don’t want to pick fights with with his disciples.)

Second, I didn’t see where quantum theory had much to do with anything you were talking about, other than you wrote down the quantity that violates the CHSH bound. To be more specific, imagine a classical universe in which the dynamics are stochastic; wouldn’t everything you said, at least leaving out the actual probabilities, be just as applicable there? Or consider the macroscopic analogy often used in some way to illustrate EPRB: Charlie sends Alice and Bob slips of paper of different colors after mixing up the envelopes so that neither he nor they knows which is which. Most of your discussion would seem to apply to that just as well to that as to correlated photons.

Bob Griffiths

[GianCarlo Ghirardi]

Dear Prof. Griffiths,
I would like to stress that the example with the colored cards would satisfy Bell’s inequality.
GianCarlo Ghirardi

[Robert Griffiths]

8 Jan. 2015

Thank you, Prof. Ghirardi. That is precisely my point. I don’t see where
quantum mechnaics plays any essential role in Healey’s discussion. Have I missed something? Bob Griffiths

[Richard Healey]

Bob,

I found out only today about your comments: for some reason I am receiving only selective notifications of comments’ postings.

Section 2 of my paper is indeed independent of quantum theory, as are the arguments of Bell it addresses.

But quantum theory plays a major role in sections 3-6. Section 5 outlines a view of quantum theory, while section 6 applies quantum theory, so viewed, to what Bell called the EPR-Bohm scenario to show how quantum theory explains violations of CHSH inequalities with no superluminal causal influences: this is something we cannot explain without using quantum theory, and there are those who maintain we cannot explain it even using quantum theory (even though everyone agrees we can use quantum theory to predict correlations in violation of CHSH inequalities).

Section 3 is mainly about the relation between general probabilities supplied by a theory and chances of particular events in a relativistic space-time, but it uses quantum theory as an important illustrative example in which general probabilities are supplied by applications of the Born rule. This example is important because of its bearing on the arguments of Bell analyzed in section 2.

Section 4 is mainly about the relation between chance and causation. But again this has an important payoff when it comes to assessing the claim that violation of CHSH inequalities entails violation of Bell’s Local Causality condition.

My paper argues for two main theses, one negative, the other positive:
1. Once one understands the relations between probability, chance and causation, one can see why violation of CHSH inequalities does not entail instantaneous action at a distance.
2. Once one understand quantum theory, one can see how we can use that theory to explain violation of CHSH inequalities while denying this violation involves any instantaneous action at a distance.

As I make clear in the last paragraphs on page 13 and 16, neither chance nor quantum theory is about agents, and we can talk of chance and apply quantum theory to calculate chances of events that might occur in a world without agents. But if there were no physically situated agents in a world then no-one in that world would need to talk of chances or to apply quantum theory.

I can’t answer your question about a universe with classical stochastic dynamics without more details as to what I am supposed to be imagining. But I suspect that the scenario you have in mind would yield a unique chance of an event like Alice’s next polarization recording, in which case Bell’s Local Causality condition could be unambiguously applied to that chance. Quantum theory yields no such unique chance—see section 3 of my paper.

[Author]

Posts