I agree with your first paragraph.

“Local determinism” (LD) indeed encompasses everything you need for the 1964 Bell’s theorem [minimal]. I was attempting to reserve DL just for the formulation of locality once determinism is already in place. I think it makes phrases like “any reasonable “localist” notion that manifestly reduc…[Read more]

]]>I can’t help wondering if a few tweaks to Howard’s nomenclature might help bridge much of the remaining divide. How about something like this:

**Deterministic Locality (DL):** A somewhat clunky name for Travis’ equation 3.

**A 1964 Bell’s theorem:** any theorem of the form “There exist quantum phenomena for which there is no theory satisfying…[Read more]

Of course nobody would have put it quite like I did in 1964. But the DAG is an attempt to formalise fairly natural and long-standing way of thinking about causality (as evidence: two different formulations based on functions and probabilities respectively, turn out to be completely equivalent), the basic ideas of which (e.g.…[Read more]

]]>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]

]]>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]

]]>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]

]]>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]

]]>How to make sense of the wave function?

I currently think the epistemic approach has the best hope of doing this. Even if one constructs a good psi-ontic interpretation, it seems unlikely to make sense of the wave-function if that means provide natural explanations for it’s key properties (living in configuration space, collapse, etc).

]]>Do we…

I’ve agreed that more work is required to clarify exactly what Bob’s strategy is in the original scheme and whether or not this is equivalent to my “recap”. Thanks for your additional ideas on this matter.

But as I have tried to make clear, the operational argument does not depend in any way on what the protective measurement…[Read more]

]]>I can tell you how I currently see this issue. As we’ve mentioned, the adiabatic scheme is present in the Gaussian toy theory. Recall that the ontology of that toy theory is just that of classical particle mechanics. This basically turns out to move the particle around in such a way that, for any observable allowed in the theory, the…[Read more]

]]>Getting inaccurate expectation values is something that may or may not happen to *Bob*. Charlie just sits there doing projective measurements in a fixed basis over and over again, right?

Regards,

Matt

As the other Matt has already mentioned, the existence of psi-epistemic models of protective measurement makes your argument difficult to swallow. But let me focus here on two more specific questions here:

1) Why couldn’t somebody also run your argument using the tomography-of-protector then projective measurement-of-system scheme?

2)…[Read more]

]]>The best toy model for thinking about weak measurements is the Gaussian theory, because then you already have continuous variables to act as your pointer, the pointer can be prepared in a Gaussian state, and the “von-Neumann measurement” interaction is present in the theory.

A nice example for imaginary weak values is to prepare the…[Read more]

]]>I’m afraid I don’t quite get your question. Which contexts are you talking about?

Cheers,

Matt

We definitely need to think more about which schemes are or are not equivalent to the original ones. (There is also a question of what equivalence means exactly – for example if one scheme requires classical post-processing of the data whilst another does the same processing “as it goes along”, does that necessarily mean they are not…[Read more]

]]>What we do or don’t know has no bearing on which POVMs *exist*. Of course it may affect our *choice* of POVM – if we already know what basis the system was prepared in, we can measure it in that basis and determine the correct state. I don’t think anybody would argue that this establishes the reality of the wave-function. The claim is…[Read more]

Thanks to everyone for the stimulating responses that I think will, in the true spirit of a workshop, lead to improvements in the paper whenever it finally appears!

Matt

]]>The claims you refer to apply only when one considers the totality of Bob and Charlie’s actions as a measurement procedure on the system from Alice. (Imagine putting Bob and Charlie in a huge black box, that has an input for the quantum system and a classical output of Bob’s estimate of the state.)

Since an arbitrarily sequence of…[Read more]

]]>You might be interested to know that your example is pretty much exactly what protective measurement amounts to when carried out within the Bartlett, Rudolph, Spekkens model.

Yours,

Matt

We should be able to reach agreement at least on this narrow point: Thinking of the protection-by-measurement (aka Zeno) scheme, does the protection amount to repeated applications of the channel given by eq. (1) in my notes?

(How this compares to the protection in the Hamiltonian-based scheme is probably a question for another day.…[Read more]

]]>If there is no difference, then my…[Read more]

]]>Having returned to one of the original papers, I can see that you’re right that my “recap” of protective measurement does not quite agree with the original scheme, in which the “protecting” measurements are done *during* Bob’s measurement rather than only between them. Perhaps I heard about this scheme elsewhere and somehow I confused it…[Read more]

Thanks for your comment. Just to be clear about something I didn’t make explicit in the notes, I’m certainly not trying to argue that protective measurement is incompatible with the reality of the wave-function, and indeed in interpretations in which the wave-function is (always or sometimes) real it may well be a perfectly good method…[Read more]

]]>Thanks for the interesting remarks. Given that ontic and epistemic are fundamentally different categories, would you agree that, generally speaking, it would be surprising to find something ontic and something epistemic represented by the same mathematics?

If you do not agree: can you think of an example of this occurring outside of quantum…[Read more]

]]>Without wanting to put words in anyone’s mouth, I took Shan’s second point to be that if we can establish the reality of the expectation value of an arbitrary observable, then we have established the reality of the expectation values of all observables, and the latter is (more than) sufficient to reconstruct the wave function.

Yours,

Matt

Thanks for your comments so far, I think I now understand your position a bit better. Obviously I’m more than a little late to the party, and my question isn’t about the wave function *per se*, but if you get a chance to respond to the following at some point, I’d be interested in your thoughts.

You’ve said that “quantum theory does…[Read more]

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