A Consistent Histories and Locality

[PeterDonis]

I don't understand the reasoning behind the experimental fact

The experimental fact is what I described in post #71.

Everyone agrees that the full set of measurements on 1&4 show no special correlations.

Meaning, if you take the entire data set, not splitting it up into subsets based on the 2&3 results. Yes.

And that there is a subset of 25% of them show correlations that violate Bell's inequality no matter what is done on the rest of the system.

NO. Go read my post #71 again, carefully.

 

[PeterDonis]

the conclusion that if you don't do the BMS on 2&3 will change the outcome at 1&4 is unclear to me.

"Don't do the BMS" means "don't allow the swap to take place at the BMS". But photons 2&3 go through the BMS and get measured afterwards in all the runs, not just the ones where a swap takes place.

 

[PeterDonis]

Since we haven't done the BMS how do we know which subset of result at 1&4 to look at?

You pick out the four subsets corresponding to the four possible combinations of photon 2&3 measurement results: HH, HV, VH, VV. Those measurement results are there on every run, whether a swap takes place or not.

 

[Morbert]

You pick out the four subsets corresponding to the four possible combinations of photon 2&3 measurement results: HH, HV, VH, VV. Those measurement results are there on every run, whether a swap takes place or not.

I think I see the point of disagreement: We have four subsets HH, HV, VH, VV when no swap occurs. We have four subsets HH', HV', VH', VV' when a swap occurs (or at least HH' and VV'). I don't think it's the case that HH = HH' and VV = VV'

From Ma:

The Bell-state measurement (BSM) corresponds to turning on the switchable quarter-wave plates. In this case, the phase of the interferometer is π/2 and the interferometer acts as a 50/50 beam splitter. Therefore, the two photons interfere and are projected onto a Bell state by polarization-resolving single-photon detections.

The operation "quarter wave plates off and then polarization measurement" will select a different four subsets from "quarter wave plates on and then polarization measurement"

As this is converging with the other thread I might give my responses there

 

[PeterDonis]

I don't think it's the case that HH = HH' and VV = VV'

I have not claimed that it is. Nor has @DrChinese. Nothing in what either of us has said requires this. You are attacking a straw man.

Again, if you know of an interpretation of QM where the claim you are stating here is relevant, what is it, and what reference do you have to support it?

 

[Morbert]

I have not claimed that it is. Nor has @DrChinese. Nothing in what either of us has said requires this. You are attacking a straw man.

Again, if you know of an interpretation of QM where the claim you are stating here is relevant, what is it, and what reference do you have to support it?

Right now, I am making an interpretation-free statement about the experiment described in the Ma paper

These two measurements [BSM and SSM] are mutually exclusive (complementary in the Bohrian sense) in the same way as measuring particle or wave properties in an interference experiment.

If the subsets identified by the BSM are different from the subsets identified by the SSM (which everyone agrees) then we cannot conclude the BSM has a nonlocal influence without some further interpretational commitment.

@DrChinese disagrees, and believes we are compelled by standard QM to conclude nonlocal influence.

 

[PeterDonis]

If the subsets identified by the BSM are different from the subsets identified by the SSM (which everyone agrees)

Of course they are, since the two subsets represent different sets of actual, physical runs of the experiment. It makes no sense to even ask whether they are "the same".

then we cannot conclude the BSM has a nonlocal influence without some further interpretational commitment.

Obviously you need some "interpretational commitment" since the basic math of QM, without any interpretation, makes no claim whatever about "nonlocal influence".

@DrChinese disagrees, and believes we are compelled by standard QM to conclude nonlocal influence.

@DrChinese is saying that on his preferred interpretation, there is "nonlocal influence"--because his preferred interpretation is basically a "nonlocal realist" interpretation, where each individual run is described by a quantum state, and the final state of the 4-photon system is different for runs where a swap occurs vs. runs where no swap occurs, and since that state involves spatially separated entangled subsystems, it is inherently nonlocal, and so is any change that is made to it by any operation done during the experiment.

There is at least one interpretation where no such claim can be made, namely, a statistical interpretation such as the one used by Ballentine, in which the quantum state never describes individual runs, it only describes ensembles. Such an interpretation makes no claim about "nonlocal influence" because it makes no claim at all about what is happening in individual runs. It only makes claims about statistics.

I am still not clear about exactly what the Consistent Histories interpretation claims--whether it makes claims about what is happening in each individual run or not, and if it does, whether its claims involve any kind of "nonlocal influence".

 

[gentzen]

I am still not clear about exactly what the Consistent Histories interpretation claims--whether it makes claims about what is happening in each individual run or not, and if it does, whether its claims involve any kind of "nonlocal influence".

I guess you can try to go beyond a minimal statistical interpretation with the CH formalism. Hartle and Gell-Mann wanted this, and did try.
Griffiths mentioned (I guess in his SEP article) that some people extended the frameworks such that later projectors and decompositions are allowed to depend on results of earlier „measurements“. I never found the time to study those.

However, Griffiths himself never tries such complicated stuff in his book or in his papers which I have read. There is also a positive side to this, namely that I always found his stuff easy to read (and understand/make sense of), which is not always true for Hartle and Gell-Mann.

Our discussions here reveal another way in which one could try to go beyond a minimal statistical interpretation, which „might“ only be slightly more complicated than the basic CH formalism: „halt“ at an intermediate point (in „logical time“ in the experiment) while some future measurement settings are still open, and hence only give a „partial“ framework that can still be extended to model the measurement settings which „will“ actually be chosen in „the future“. In entanglement swapping experiments, this could be after the swap, but before the measurements verifying the entanglement, for example.

 

[Morbert]

I guess you can try to go beyond a minimal statistical interpretation with the CH formalism. Hartle and Gell-Mann wanted this, and did try.

CH is not a statistical interpretation. It lets the physicist make claims about individual runs. This not just the opinion of Hartle and Gell-Mann. This is explicitly stated by Griffiths and Omnes. See my post #70 in this thread.

I am still not clear about exactly what the Consistent Histories interpretation claims--whether it makes claims about what is happening in each individual run or not, and if it does, whether its claims involve any kind of "nonlocal influence".

CH is firstly a formalism for computing probabilities without recourse to measurement as a fundamental concept, or to an external classical environment separated by a Heisenberg cut. The traditional procedure of unitary evolution + state reduction is replaced by sets of histories and their probabilities. It follows closely from Feynmann's sum-over-histories formalism.

Whether these histories describe actually existing properties of microscopic systems, or whether they are just tools for reliably reasoning about experiments is where CH proponents diverge. Hartle, Gell-Mann, and Griffiths interpret histories as the former.

 

[gentzen]

I guess you can try to go beyond a minimal statistical interpretation with the CH formalism. Hartle and Gell-Mann wanted this, and did try.

CH is not a statistical interpretation. It lets the physicist make claims about individual runs. This not just the opinion of Hartle and Gell-Mann. This is explicitly stated by Griffiths and Omnes. See my post #70 in this thread.

If you claim to be able to go beyond a minimal statistical interpretation, then you should better be able to model situations that no minimal statistical interpretation can interpret.

In that case, considering an infinite collection of copies of the solar system would certainly then be odd

This is an argument against an ensemble interpretation of probability, but not necessarily an argument against a statistical interpretation of QM.

If I have to wait for the end of time before my formalism can give me probabilities for the different possible histories of the universe, then it is a hard call to claim that those probabilities would apply to a single system.

However, since you misinterpreted the "... wanted this, and did try" from my post which you quoted as "just the opinion of ...", I don't really expect that you tried to understand the parts of my post which you didn't quote.

 

[DrChinese]

1. I think I see the point of disagreement: We have four subsets HH, HV, VH, VV when no swap occurs. We have four subsets HH', HV', VH', VV' when a swap occurs (or at least HH' and VV'). I don't think it's the case that HH = HH' and VV = VV'

From Ma:
The operation "quarter wave plates off and then polarization measurement" will select a different four subsets from "quarter wave plates on and then polarization measurement"

2. As this is converging with the other thread I might give my responses there

1. Is HH = HH' and VV = VV' ?

Well of course this is true, answer YES. It has to be, this is physically dependent on the polarization characteristics of a beam splitter. No amount of interference or interaction between 2 photons overlapping in a beam splitter is going to change H to V (or vice versa). There is no evidence otherwise, and there is no theory to support that speculative idea. It is easily testable, although I have never seen such an experiment. (Of course, there are many experiments one might perform to confirm the predictions of QM that have never been performed.)

Next, you ask: Are the selected [4 fold] subsets the same? Answer is of course, NO, as the authors say in your quote. That's because the swap induces a change in the 1 & 4 pairs - they are correlated in a specific Bell state, when they weren't before.


2. And I answered your equivalent question in more detail over there in this post.

 

[DrChinese]

1. Fine, I am ok with the terms. But I don't understand the reasoning behind the experimental fact. So let me ask you this. Everyone agrees that the full set of measurements on 1&4 show no special correlations.

2. And that there is a subset of 25% of them show correlations that violate Bell's inequality no matter what is done on the rest of the system.

3. If you perform the experiment and do a BMS on 2&3 in 25% of the cases the result will be a projection to the phi minus state, and this subset of trials will match the subset of Bell inequality violating results of 1&4. So far I understand.

4. But then the conclusion that if you don't do the BMS on 2&3 will change the outcome at 1&4 is unclear to me. Since we haven't done the BMS how do we know which subset of result at 1&4 to look at? If I understand you correctly you say that we measure the 2&3 in a different basis and look at the partition for the full set into the four subsets according to the four possible outcomes. But why? We cannot say that one of them would have been the subset with the phi minus state had we done the BMS on 2&3.

5. I don't think that any interpretation claims that it is local in the sense of Bell inequality violations. The violations are a mathematical consequence of the theory, so no interpretation can avoid it. I think that all they claim is that they are local in the sense of lack of influence at a distance.

1. If you ignore what we are testing in the experiment, which is 4-fold coincidences, then yes: 1 & 4 have 0 correlation.

2. No, the only such subsets are ones that you hand pick. There is a subset that show correlations (Bell inequality violations like you describe) WHEN a BSM is performed and we select on an identifiable Bell state.

3. Good.

4. If you flip a switch in your living room, and then correlations appear in the HH/VV subset in the kitchen that were not there before: how would you NOT guess that flipping the switch in the living room was the cause of the results in the kitchen?

Of course, you already assume there are no "nonlocal" anythings. So that leaves you in an "unclear" mindset, I get that. I am asking you to drop your assumption and see where it leads. And why do I ask that? Because that is the purpose of the experiment, to demonstrate that in an objective manner: there are "nonlocal" somethings.

5. If you re-read this, I think some of this is self-contradictory. There are many interpretations denying nonlocality in any form (i.e they are local interpretations).

On the other hand: if it looks like a duck, and quacks like a duck: it's a duck. And these ducks not only look like a duck (with a theoretical lack of the usual limits on locality); they quack like a duck (as shown by these amazing experiments). My apologies to any ducks who might take offense at the analogy.

 

[Morbert]

If I have to wait for the end of time before my formalism can give me probabilities for the different possible histories of the universe, then it is a hard call to claim that those probabilities would apply to a single system.

Why would you have to wait until the end of time? A history set bound by some time is equivalent to a maximally coarse-grained future, and extending a history set to some later time in the future is equivalent to a refinement. A physicist is free to consider whatever framework is most useful, so they can just use the course-grained set that limits assertions to times relative to the experiment.

 

[Morbert]

@DrChinese I will continue our convo re/ partitioning in the other thread

 

[gentzen]

Why would you have to wait until the end of time? A history set bound by some time is equivalent to a maximally coarse-grained future, and extending a history set to some later time in the future is equivalent to a refinement. A physicist is free to consider whatever framework is most useful, so they can just use the course-grained set that limits assertions to times relative to the experiment.

Because if you want to go beyond the most basic CH formalism, you have to investigate what actually happens when you do this:

Our discussions here reveal another way in which one could try to go beyond a minimal statistical interpretation, which „might“ only be slightly more complicated than the basic CH formalism: „halt“ at an intermediate point (in „logical time“ in the experiment) while some future measurement settings are still open, and hence only give a „partial“ framework that can still be extended to model the measurement settings which „will“ actually be chosen in „the future“.

One thing to investigate is whether there is a nice characterization of the allowed continuations of a „partial“ framework. Your characterization as the refinements of the maximally coarse-grained future is good. It is simple enough that Griffiths could have used it somewhere (i.e. not just Hartle/Gell-Mann).

Nevertheless, it would be interesting whether there is also a more explicit characterization, say as some way to compute a density matrix and a maximally coarse-grained set of projectors (at the intermediate point in time) (as a sort of maximal simplified „partial“ framework) with the same allowed continuations.

 

[bhobba]

What do you mean by „descriptions of the same reality“?

First, so others understand CH, Griffiths has been kind enough to make his book on Consistent Quantujm Theory (I purchased it ages ago) available for free:
https://quantum.phys.cmu.edu/CHS/histories.html

I think Gleason's Theorem adequately explains the Born rule. Think of the two axioms in Ballentine (that reminds must get a new copy - mine is falling to pieces). Gleason connects the second to the first.

I want to address 'descriptions of the same reality' in this post.

Think of LET and the geometrical description of Minkowski, which most people use today. Both theories can not be distinguished in an inertial frame, yet virtually anyone exposed to it prefers the geometrical description. It is more straightforward, beautiful, and based on symmetry principles. LET, with its aether wind, breaks the isotropy of an inertial frame (the symmetry definition is found in books like Lanadau Mechanics) and can't then be the basis of mechanics. Usually, an inertial frame is defined as one that Newton's first law holds, but the definition of a frame where each point, direction, or instant of lime has the same laws of physics is better at a more advanced level. From a modern perspective, Minkowski is preferred in many ways. The point is that descriptions of reality are often chosen from several differing ones depending on other factors such as ease of generalisation and that elusive thing - scientific tact, which, of course, can vary between scientists.

We do not discuss philosophy here, but to be clear, I am not advocating that reality is a social construct because, in science, we have correspondence with observation (experiment, etc., precisely as Feynman says in his famous video), where unless specified otherwise, observation has a usual common-sense meaning.

Thanks
Bill