Hi Travis,

I don’t have anything to add to my reply under my article about why I think Bell gives his own definition of `locality’, and uses the referencing of Einstein as an appeal to authority to justify the reasonableness of making an assumption like this.

In my formal reply I will give the quotes and both our opinions, and readers can…[Read more]

Matt, re: #1866, good, it seems like we’re basically on the same page. I suspect there remains some lingering disagreement having to do with whether Bell (in ’64) meant to define locality with his Einstein quotations and/or how similar the Einstein quotation (what Howard calls “no telepathy”) is to (Bell’s later formalized) “local causality”.…[Read more]

Hi Matt,

I agree with some your comments here. But:

1. Your discussion about DAGs is not really relevant to the physics community in 1964. Pearle’s first book was only published in the 1980s. No-one in physics was thinking this way in the 1960s. And in any case, the DAG model of causality is one that orthodox quantum mechanics fails to obey. So…[Read more]

Hi Howard,

I can’t deny that the “operationalist” in me jumps to the parameter independence conclusion when reading any of your four quotations. Indeed that is why I didn’t question your interpretation until I read Travis’ paper. But, outside of the deterministic case, that interpretation requires a certain style of thinking about causation in…[Read more]

Sorry, another comment: Travis admits that Bell’s words in the EPR paragraph cannot be read as being a statement of local causality. That is why he says the paragraph “leaves something to be desired,” that it “disappoints” and is “problematic”. If it was all plausible that Bell’s words could be interpreted as being “local causality” then Trav…[Read more]

Hi all,
Just a quick comment to say that, as per my original paper, and my reply paper, I do not at all agree that
“… we can only speculate on how the 1964 Bell would have formally defined locality in a stochastic hidden variable theory. Since both parameter independence and local causality both reduce to exactly your equation (3) in the…[Read more]

Hi Travis,

I guess B’ was (and still is) usually what drives people to B, so that “refuting” B’ certainly undermines the case for B, which I think is what Einstein was getting at in your quote.

Of course I agree that the EPR paper contains a valid argument from their background assumptions + perfect correlations to determinism, and that Bell…[Read more]

Hi Matt. Yes, I agree with you. Refuting B’ (i.e., refuting Bohr’s “completeness doctrine”) and refuting B (i.e., establishing deterministic hidden variables) are distinct, though of course closely-related. (In case it’s not obvious, here by “refuting” I mean “subject to the assumption of locality”. Post-Bell — i.e., once it is established…[Read more]

Travis,

I agree that Bell was probably taking the Einstein quote to be the definition of locality, and that it is stronger than your equation (3), as it applies to any “real factual situations”, not just pre-determined measurement outcomes. However, to my mind the quote is not totally unambiguous in all cases (particularly when probabilities are…[Read more]

Thanks for the comments, Matt. I’m of course happy to hear that you found the paper thought-provoking, and in particular happy to hear that it helped you realize that there is no basis for thinking Bell meant Parameter Independence by “locality”. As should be clear, I completely agree with what you say about the “mathematically rigorous part of…[Read more]

Hi Travis,

This is a belated comment to say thanks for your thought-provoking paper.

In particular, you paper has changed my mind on one point: it is wrong to say, as Howard did, that the theorem Bell proved in 1964 uses [what is now often called] parameter independence. Bell’s locality assumption is more accurately captured by your equation 3,…[Read more]

Dear Roderich,

Again, relative to your #1857. Many people have the mistaken notion that spin half can contain large amounts of information because they visualize the quantum state as a classical arrow with a precise direction, or a classical spinning top with a precise axis of rotation. While such pictures are useful, they can mislead. In…[Read more]

Dear Roderich,

Thank you for #1857. Let me take up the second topic first: properties of macroscopic systems. Since you believe that quantum theory applies at the macroscopic level, you need some way to represent properties on a Hilbert space, assuming you are not using hidden variables. I use projectors, because these are the ways properties…[Read more]

Indeed I do believe (not merely suspect) that statements about probability and fixity must be relativized in the way I suggested. I question your use of the word “pre-determines”. Certainly Alice’s outcome (ideally) lies on a spacelike hypersurface whose future domain of dependence includes Bob’s outcome. But points on that hypersurface outside…[Read more]

Dear Richard,

Indeed one might suspect that statements about probability, or even fixity, must be relativized in the way you suggest. So let me go through the reasoning in more detail. The state-of-affairs (i.e., the “real, factual situation,” the “beables”) on that hypersurface includes Alice’s outcome, so it pre-determines Bob’s outcome (as Bob…[Read more]

Dear Bob,

Let me first address the Carol-Donald issue. I was, in fact, paying attention to the distinction you emphasize; let me elaborate some more. Let n_k be the unit vector in the direction in which Carol has prepared the spin of particle k. She predicts that if one were to make a Stern-Gerlach experiment on particle k in the direction n_k,…[Read more]

Thus: to exercise my gratefully-received author’s last-word prerogative.

I have a better understanding of where you’re coming from now Travis (I also managed to skim very quickly some parts of your paper—which I shall return to properly in hopefully not too long—and that helped me see better where some of our differences are emerging).

I…[Read more]

Roderich,

In response to your 1835 you ask (re my 2,3)

“I am happy to change my statement to “Bob’s outcome was already fixed on some spacelike hypersurface before his experiment.” Would that take care of your concern?”

No, this does not address my concern. In a relativistic spacetime fixity, like chance, should not be relativized to a space…[Read more]

Dear Roderich,

I find your reply to my comment interesting, but I wonder if you could elaborate on the following. My use of a subspace for a quantum property goes back to von Neumann, and I employ it at the microscopic level or spin half and at the macroscopic level, because I believe that quantum mechanics applies at all length scales, “from…[Read more]

Thank you to all of the commentators for your remarks!

To Dieter at 1674:

You may be surprised but I completely agree with you that Everett’s many-worlds proposal is a realist theory. In my paper, I considered the conditions (R1) through (R4) for their potential relevance to Bell’s theorem, not for categorizing interpretations of quantum…[Read more]