Consistent Histories and Locality

[Morbert]

TL;DR

Continuation of a discussion in a previous thread

Griffiths only talks about statistical properties. This is not what most people (including me) mean by realistic. In fact, I claim that CH itself can only talk about statistical properties. This is a nontrivial claim, and it could be wrong. But not in the way Griffiths argues against it, by simply ignoring the issue.

I don't understand this accusation. Given a single system prepared in some state $\psi = \sum c_i|i\rangle$, the probability $\mathrm{tr} |\psi\rangle\langle\psi|i\rangle\langle i|$, according to Griffiths, is the probability that the system has the property $i$. This is in contrast to statistical interpretations that present QM as a theory about infinite ensembles rather than single systems.

 

[Morbert]

My head is spinning.

I didn’t see the non-hidden variable mechanism that would then need to exist in CH. (We see that in MWI. We see that in retrocausal type explanations.) On the other hand, in your post #69: you say CH is realistic, but denies hidden variables. I am not sure how it can be realistic, which implies a pre-existing and determinate outcome for measurements at all angles independent of a setting elsewhere.

And he does accept a form of “proper” nonlocality. But I am very open to better understanding what is being presented, because it doesn’t seem to fit together as I read it.

These papers might be useful https://arxiv.org/abs/1105.3932 , https://arxiv.org/abs/1704.08725

While, according to Griffiths, measurements reveal pre-existing properties of systems, this doesn't mean we can write down some comprehensive state $\lambda$ describing all properties a system has because, unlike in classical physics, there is no maximally refined sample space covering all properties of the system.

 

[gentzen]

I don't understand this accusation. Given a single system prepared in some state $\psi = \sum c_i|i\rangle$, the probability $\mathrm{tr} |\psi\rangle\langle\psi|i\rangle\langle i|$, according to Griffiths, is the probability that the system has the property $i$.

Let us first agree that CH is consistent, and that Goldstein was wrong when he claimed that CH us inconsistent, and accused the framework rule to simply forbid to talk about it, without removing the inconsistency.

Therefore, Griffiths is not free to simply declare that probabilities predicted by CH are the probability of a single system to have the property $i$. Only the entire framework is allowed to be interpreted, not a single isolated part like the preparation without the remaining context.

My claim is that the interpretation of the probabilities for the framework are only statistical, i.e. not for single systems.

This is in contrast to statistical interpretations that present QM as a theory about infinite ensembles rather than single systems.

In the end, A. Neumaier and me had the same disagreement with vanhees71. The problem is the nature of predictions which apply to single systems. Just because you say „my probabilities talk about a single system“ doesn‘t make this true.

 

[Morbert]

Let us first agree that CH is consistent, and that Goldstein was wrong when he claimed that CH us inconsistent, and accused the framework rule to simply forbid to talk about it, without removing the inconsistency.

Therefore, Griffiths is not free to simply declare that probabilities predicted by CH are the probability of a single system to have the property $i$. Only the entire framework is allowed to be interpreted, not a single isolated part like the preparation without the remaining context.

My claim is that the interpretation of the probabilities for the framework are only statistical, i.e. not for single systems.

A framework is just a sample space, which exists in both classical and quantum theories. In quantum theories there isn't a unique sample space for which all other sample spaces are coarse grainings, but that doesn't prevent statements like "There is a probability p that system A has a property X"

In the end, A. Neumaier and me had the same disagreement with vanhees71. The problem is the nature of predictions which apply to single systems. Just because you say „my probabilities talk about a single system“ doesn‘t make this true.

It's not about being true or false. It's about consistency and sufficiency of interpretation. To insist probabilities yielded by quantum theories must be fundamentally about samples or ensembles, you would presumably have to argue that bayesian or propensity interpretations of probabilities are inconsistent or deficient.

 

[gentzen]

A framework is just a sample space, which exists in both classical and quantum theories.

All statements within CH have to be inside of some framework. Especially, taking about the preparation and properties $i$ of that preparation as if it were independent of a framework is not allowed.

This goes both ways, for Goldstein who cannot use this to prove CH inconsistent, but also for Griffiths who cannot use this to claim that CH is realistic.

In quantum theories there isn't a unique sample space for which all other sample spaces are coarse grainings, but that doesn't prevent statements like "There is a probability p that system A has a property X"

Careful, Copenhagen has its own ways to make such statements sometimes valid. But CH is more strict about which statements are allowed and forbidden, therefore it is not enough that such statements are not always strictly invalid.

It's not about being true or false.

As long as people like vanhees71 believe that the minimal statistical interpretation can make statements about single systems, I prefer the clarity of saying that this is simply not true.

It's about consistency and sufficiency of interpretation.

CH is consistent. Whether Bohmian mechanics is sufficient for all scenarios where QM or QFT apply is disputed. But it is not important for our current discussion whether CH is much better than Bohmian mechanics in this respect. I hope we can both agree that there are many scenarios where CH is sufficient.

Where we disagree is whether CH is realistic. I claim that CH is not realistic in the sense that Bell, DrChinese, and many other people understand that concept.

To insist probabilities yielded by quantum theories must be fundamentally about samples or ensembles, you would presumably have to argue that bayesian or propensity interpretations of probabilities are inconsistent or deficient.

The Bayesian interpretation of probabilities doesn‘t help either to turn some non-realist interpretation of QM into a realist one.

 

[DrChinese]

... according to Griffiths, measurements reveal pre-existing properties of systems, this doesn't mean we can write down some comprehensive state $\lambda$ describing all properties a system has because, unlike in classical physics, there is no maximally refined sample space covering all properties of the system.

If I can predict the precise outcome of any polarization measurement on a photon that has not been locally disturbed, altered or otherwise examined during its existence: How does the above make sense?

(Admittedly we can't make a statement about all properties simultaneously.)

My claim is that the interpretation of the probabilities for the framework are only statistical, i.e. not for single systems.

If I can predict the precise outcome of any polarization measurement on a photon that has not been locally disturbed, altered or otherwise examined during its existence: How is this "only statistical"?

I can do this for each and every identifiable Bell state resulting from a swap. That doesn't seem statistical to me.

 

[DrChinese]

These papers might be useful https://arxiv.org/abs/1105.3932 , https://arxiv.org/abs/1704.08725

While, according to Griffiths, measurements reveal pre-existing properties of systems, this doesn't mean we can write down some comprehensive state $\lambda$ describing all properties a system has because, unlike in classical physics, there is no maximally refined sample space covering all properties of the system.

Thanks for the references. I will work through them a bit closer to see if I can understand how "pre-existing" properties could possibly be made to yield the usual correlations for entangled photons: cos^2(A-B) where A=Alice's future angle setting and B=Bob's future angle setting.

I can't see how that is possible in a realistic interpretation. And not surprisingly, there is not a single specific example of how that could work. I would sure like to see one that reproduces both the quantum expectation for A<>B and A=B!

 

[gentzen]

If I can predict the precise outcome of any polarization measurement on a photon that has not been locally disturbed, altered or otherwise examined during its existence: How is this "only statistical"?

As I wrote in the other thread, those cases are not „only statistical“. It is the other cases where CH can only talk about statistical properties.

I can do this for each and every identifiable Bell state resulting from a swap. That doesn't seem statistical to me.

You can only do this for certain frameworks. And typical Bell inequality violation experiments cannot be described in those frameworks. But because you are not allowed to mix incompatible frameworks in CH, you cannot conclude anything from the possibility of those exact predictions.

 

[Demystifier]

I claim that CH is not realistic in the sense that Bell, DrChinese, and many other people understand that concept.

Yes, that's definitely true. CH is an attempt to give a realist interpretation of quantum complementarity. While many other interpretations say that complementarity (i.e. dependence on the framework) is really a dependence on the measurement setting, CH insists that complementarity has intrinsic ontological meaning independent on measurement. Some CH proponents say that CH is the Bohr's interpretation done right. To people with a kind of thinking similar to Bell's, that's a way too weird notion of ontology.

On top of that, CH in the Griffiths version adds a non-classical logic as a correct way of thinking about different frameworks, which is why Goldstein et al call it inconsistent, from the perspective of classical logic.

 

[Demystifier]

I can't see how that is possible in a realistic interpretation.

It's not, if the word "realistic" is interpreted in your way. But CH interprets the word "realistic" in a very different way.

 

[Demystifier]

Let us first agree that CH is consistent, and that Goldstein was wrong when he claimed that CH us inconsistent, and accused the framework rule to simply forbid to talk about it, without removing the inconsistency.

CH claims that reality depends on the framework. If we stretch this principle a bit, there is a framework, the framework of classical logic, in which Goldstein is right that CH in the Griffiths's version is inconsistent.

 

[Morbert]

If I can predict the precise outcome of any polarization measurement on a photon that has not been locally disturbed, altered or otherwise examined during its existence: How does the above make sense?

Consider a measurement on the photon with a random choice of aspect $\omega$ and measurement outcome $\{1_\omega,0_\omega\}$. The photon is in the initial state $|\psi\rangle = a_\omega|+_\omega\rangle + b_\omega|-_\omega\rangle$ and the measurement apparatus is in the initial state $|\phi\rangle = \sum_\omega c_\omega |\omega\rangle$. We can model this scenario with the time-evolution $\mathcal{U}$$$\begin{eqnarray*}\mathcal{U} &=& \sum_\omega U^{(\omega)}|\omega\rangle\langle\omega|\\U^{(\omega)}(t_0,t_1)|\psi\rangle|\omega\rangle &=& |\psi\rangle|\omega\rangle\\U^{(\omega)}(t_1,t_2)|\psi\rangle|\omega\rangle &=& a_\omega|+_\omega\rangle|1_\omega\rangle+b_\omega|-_\omega\rangle|0_\omega\rangle \end{eqnarray*}$$First, we can construct histories $\{C_\alpha\}$ reflecting the ordinary quantum description of this experiment. $$C_\alpha = \left[\psi,\phi\right]\odot\left[\omega_\alpha\right]\odot\left[W_\alpha\right]$$where $\left[W_\alpha\right]$ is either $\left[1_{\omega_\alpha}\right]$ or $\left[0_{\omega_\alpha}\right]$, depending on $\alpha$. These histories describe the preparation at $t_0$, the choice of aspect at $t_1$, and the outcome at $t_2$. The probability of a history occurring is $\mathrm{Pr}(C_\alpha) = \mathrm{tr}C_\alpha^\dagger\left[\psi,\phi\right]C_\alpha$. If, instead, we are concerned with a "realistic" description, where the measurement reveals a pre-existing property $\{+_\omega,-_\omega\}$, we can construct the histories $$C_\alpha = \left[\psi,\phi\right]\odot\left[\omega_\alpha\right]\odot\left[\lambda_\alpha\right]\odot\left[W_\alpha\right]$$ where a measurement outcome $W_\alpha$ reveals the property $\lambda_\alpha$. We'll get the same probabilities as before. Note that unlike Bell's hidden variables, the microscopic properties $\{\lambda_\alpha\}$ don't permit a joint probability distribution like $\mathrm{Pr}(\lambda, \omega)$. So "realistic" in the sense of measurements revealing pre-existing properties, but not hidden variables, and hence not running afoul of Bell's theorem.

 

[Morbert]

CH claims that reality depends on the framework. If we stretch this principle a bit, there is a framework, the framework of classical logic, in which Goldstein is right that CH in the Griffiths's version is inconsistent.

It's not that reality depends on the choice of framework. It's that a description of reality requires multiple frameworks, with the logic of propositions about reality being specific to frameworks. This framework dependence is true in classical theories too. The difference being in classical theories we can always identify a unique framework for which all other frameworks are coarse-grainings.

This is quite opposite to the common misunderstanding of CH where we can decree whatever we like to be true by choosing the right framework.

 

[Morbert]

Where we disagree is whether CH is realistic. I claim that CH is not realistic in the sense that Bell, DrChinese, and many other people understand that concept.

This might be true. It is certainly true for Bell. "Measurements reveal pre-existing properties" is a weaker condition than what Bell addresses.

Your other objections seems to amount to pointing out that CH does not render alternative interpretations incorrect. This is also true. All that can ultimately be shown is that CH is a coherent, unambiguous, and robust interpretation of any quantum theory.

 

[gentzen]

CH claims that reality depends on the framework. If we stretch this principle a bit, there is a framework, the framework of classical logic, in which Goldstein is right that CH in the Griffiths's version is inconsistent.

What do you by „the framework of classical logic“? The technical meaning of „framework“ in CH does not talk about stuff like intuitionistic logic. Morbert tried to make sense of your remark, and came up with:

The difference being in classical theories we can always identify a unique framework for which all other frameworks are coarse-grainings.

Is this what you mean? Or was it just a play of words never intended to make technical sense?

 

[Demystifier]

Or was it just a play of words never intended to make technical sense?

Yes.

 

[Demystifier]

It's not that reality depends on the choice of framework. It's that a description of reality requires multiple frameworks, with the logic of propositions about reality being specific to frameworks. This framework dependence is true in classical theories too. The difference being in classical theories we can always identify a unique framework for which all other frameworks are coarse-grainings.

In other words, used e.g. by some Bohmian-type realists, in classical theories there is primitive ontology, while the CH interpretation lacks primitive ontology.

 

[gentzen]

This might be true. It is certainly true for Bell. "Measurements reveal pre-existing properties" is a weaker condition than what Bell addresses.

Good. I guess/hope this is enough to not confuse DrChinese unnecessarily.

Your other objections seems to amount to pointing out that CH does not render alternative interpretations incorrect. This is also true.

I am not sure what to make of this. I certainly tried to prevent an unproductive discussion with DrChinese, caused by a „niche“ interpretation of „realistic“ and a missing sensibility of non-statistical properties, or maybe better „non-ensemble“ single system properties.

But I also brought up Bohmian mechanics and Copenhagen, so maybe you are referencing to that. Maybe more importantly, when I found out that Barandes only talks about statistical properties in his latest paper

And his "Causally Local Formulation" turns out to be just the well known "no signaling" property of QM

I got quite disappointed and worried, why he „lost his track“. But it is worse for Barandes (who is explicitly concerned with primitive ontology) than for CH (where the formulation itself „needs no ontology“).

All that can ultimately be shown is that CH is a coherent, unambiguous, and robust interpretation of any quantum theory.

We definitively agree in this point, except that it may not be „all that can ultimately be shown“.

 

[Morbert]

Good. I guess/hope this is enough to not confuse DrChinese unnecessarily.

I am not sure what to make of this. I certainly tried to prevent an unproductive discussion with DrChinese, caused by a „niche“ interpretation of „realistic“

See this post where the meaning was clarified.

and a missing sensibility of non-statistical properties, or maybe better „non-ensemble“ single system properties.

I still don't understand this. This sensibility isn't missing in CH. One of the primary motivations for CH was its applicability to single systems like the universe.
https://www.webofstories.com/play/murray.gell-mann/163

 

[DrChinese]

These papers might be useful : https://arxiv.org/abs/1704.08725

1. "... let us now turn to the source of the mistaken notion that the quantum world is somehow pervaded by nonlocal influences, which even their proponents admit cannot be used to transmit information, and are hence experimentally undetectable."

Whoops! In the Ma experiment, the nonlocal influence is clearly detectable. See figure 3a versus 3b. But yes, we all otherwise agree that these influences cannot be used to transmit information.


2. "Einstein locality: Objective properties of isolated individual systems do not change when something is done to another non-interacting system."

In the Ma experiment and many others of a similar vein, this is precisely what is violated. Objective properties of distant systems change, or at least apparently so. "Apparently" here meaning that the most obvious conclusion is that the experimenter can freely choose to change an observable statistical resultset. But there are of course interpretations that can address that (Bohmian Mechanics for example). Most are nonlocal or retrocausal.

 

[DrChinese]

It's not, if the word "realistic" is interpreted in your [DrChinese] way. But CH interprets the word "realistic" in a very different way.

Point taken, Demystifier, thanks. But...

"Measurement reveals pre-existing properties" or "appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place" (quoted from the abstract here) sounds realistic in the same sense I mean.

And yet the only elements used to make a 100% certain quantum prediction for distant observations is the relative (nonlocal) settings of both measurements. So do the observed quantum properties exist and have those values prior to the measurement settings? Or do the values change as the distant relative settings change?

In other words: I can make up a definition of "realistic" that differs from how Bell uses that concept. Then I claim QM is realistic in my sense but not in Bell's. But aren't I obligated to address how my definition applies to various experiments directly probing the matter? Or do I get off scot-free because I merely claim my definition works?

So I am asking for a simple application of any CH definition of realism as it applies to this loophole free test where settings are changed midflight, and the systems (1.3 km apart) do not have time to communicate after the settings* are determined. What, exactly, pre-exists before the measurement takes place? Keeping in mind that the A and B electrons being spin-measured have absolutely no relationship to each other at the beginning of each run. (They are not part of a single quantum system after reset, they become entangled later on a another distant spot C.)

Can anyone please explain? Because I don't think there is a meaningful difference in "DrChinese (or Bell) realistic" vs. "CH realistic". Certainly nothing that justifies claiming that QM is "CH" realistic and Einstein local.


*For sake of this discussion, let's pretend the settings are always the same for A and B when measuring the electron spins, even though they vary from run to run. That way we always get perfect correlation.

 

[Morbert]

And yet the only elements used to make a 100% certain quantum prediction for distant observations is the relative (nonlocal) settings of both measurements. So do the observed quantum properties exist and have those values prior to the measurement settings? Or do the values change as the distant relative settings change?

In other words: I can make up a definition of "realistic" that differs from how Bell uses that concept. Then I claim QM is realistic in my sense but not in Bell's. But aren't I obligated to address how my definition applies to various experiments directly probing the matter? Or do I get off scot-free because I merely claim my definition works?

Maybe my post #17 was not relevant to what you are asking about. What is meant here by 100% certain quantum predictions? Some preparation and measurement where the probability of a specific outcome is 1?

 

[DrChinese]

Maybe my post #17 was not relevant to what you are asking about. What is meant here by 100% certain quantum predictions? Some preparation and measurement where the probability of a specific outcome is 1?

Yes, that's my intention. The idea is that the outcomes are specific and identical, let's say both a +1 outcome at 19 degrees (I just picked this out of thin air). Or both -1 at 56 degrees (also out of thin air). Variations of that can be tested with the cited Hensen experiment (although they use different angle settings, the expectation values match QM; and CH must too).

So by what standard can Griffiths say "appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place" and it NOT mean the same thing as Bell or myself? He is apparently drawing some distinction between: a) "hidden variables" (those don't exist); and b) "true" realism (which because it is different than Bell realism, means that Bell inequalities don't apply).

Well, my example does not rely on Bell or CHSH. It is back to EPR-type reasoning (elements of reality). So either the measurement outcome of A is independent of the setting at distant B; or it isn't. Which? Because if they match, the question immediately becomes: how do 2 independently oriented electrons suddenly match spins without violating the very Einsteinian locality that is central to CH? Given they had those "quantum properties" prior to measurement, also according to CH.

 

[gentzen]

possessed by the measured system

The trick is what is meant by measured system. In Copenhagen, this would be the state before measurement (i.e. the analog of an initial state in a deterministic theory) and the system dynamics, typically given by a Hamiltonian. But in CH, the framework is also part of the measured system.

That is the context of that statement. However, for Einstein locality, Griffiths tried to show more, and was more liberal with respect to the framework. But his calculations are just for statistical properties, i.e. basically the no signaling property, or at least not significantly more.

 

[DrChinese]

And just to drop another point:

"Reichenbach's Common Cause Principle is the claim that if two events are correlated, then either there is a causal connection between the correlated events that is responsible for the correlation or there is a third event, a -so called (Reichenbachian) common cause, which brings about the correlation."-Miklos Redei

Since Redei (see here, 2003) holds locality (what he calls "local primitive causality") true by assumption (which he claims is justified, i.e. "this condition has been verified in many concrete models"). Using that assumption, he is able to "prove" cause precedes effect in basic entanglement setups (such as PDC).

On the other hand: If you believe the above Common Cause Principle is true (as he does), then Delayed Choice Entanglement Swapping experiments prove that cause need not precede the effect. That's because the causal agent unambiguously occurs in the future, and not in the past.

---

Note yet again: There is no consideration of Delayed Choice Entanglement Swapping experiments in his 2003 paper, because those had not been widely published and discussed until about 2008. And also not surprisingly: none of Redei's later papers in the arxiv ever acknowledge the existence of swapping experiments. Therefore he merrily proceeds to prove mathematically something that is disproven by experiment. My point is... don't be like Redei!

 

[DrChinese]

DrChinese said:
"possessed by the measured system" [quoting Griffiths]

The trick is what is meant by measured system. In Copenhagen, this would be the state before measurement (i.e. the analog of an initial state in a deterministic theory) and the system dynamics, typically given by a Hamiltonian. But in CH, the framework is also part of the measured system.

Griffiths specifically added "before the measurement took place", which you left off of the quote. That's realism as he defines it himself, and close enough to how I define it not to see a difference. If there is such realism, there cannot be locality. Such locality would NOT be excluded because of Bell's Theorem; it would be excluded by experiment.

 

[gentzen]

That's realism as he defines it himself, and close enough to how I define it not to see a difference.

This is irrelevant, whether you believe you know Griffiths and CH better than me. There is a context in which those statements are correct, and this context doesn‘t change just because you highlight some word in bold.

 

[DrChinese]

This is irrelevant, whether you believe you know Griffiths and CH better than me. There is a context in which those statements are correct, and this context doesn‘t change just because you highlight some word in bold.

I don’t think I know it better than you, I am the one asking.

Is there a preexisting value for A and B (or relationship between them) prior to their measurement? I’m trying to get specific details of what Griffith is asserting. I don’t understand why you truncated my Griffiths quote where you did, because the “prior” nature is fundamental to my question. If you agree/disagree a future action can affect (or appear to affect) a past outcome, tell me either way yes or no.

I am presenting specific experimental evidence that appears diametrically opposite to CH. I am trying to walk through using standard terminology. Words/phrases like “frameworks” (not present virtually anywhere else) and “ill defined concepts of measurement” (which seems pretty well described in actual experiments) make the discussion more difficult.

I am simply trying to map CH ideas to entanglement swapping, which I have yet to see mapped. All I have seen is general dismissals without addressing substance.

 

[gentzen]

Words/phrases like “frameworks” (not present virtually anywhere else) … make the discussion more difficult.

It makes no sense to talk about CH without its „framework“ concept:
https://plato.stanford.edu/entries/qm-consistent-histories/#PDIsFramSingFramRule

A central principle of the histories approach is that quantum propositional reasoning must always employ a single PDI, referred to as a framework. While the choice may be implicit, it is often helpful to make it explicit when carrying out a logical argument. The single framework rule states that any logical argument must use a particular framework; combining results from two incompatible frameworks is illegitimate.

If you agree/disagree a future action can affect (or appear to affect) a past outcome, tell me either way yes or no.

It is unclear whether CH can even talk about this, in the way you „want“ to talk about those things. When it comes to Einstein locality, Griffiths tries hard to do this, but I am not convinced that he succeeded.

When it comes to pre-existing properties revealed by measurements, there is little point in trying to go beyond the single framework rule in CH, because otherwise it would be simple to show that CH is inconsistent, if that were allowed.

 

[DrChinese]

It makes no sense to talk about CH without its „framework“ concept:
https://plato.stanford.edu/entries/qm-consistent-histories/#PDIsFramSingFramRule


When it comes to pre-existing properties revealed by measurements, there is little point in trying to go beyond the single framework rule in CH, because otherwise it would be simple to show that CH is inconsistent, if that were allowed.

Thanks for the reference.

Griffiths specifically talks about spin x not being a compatible framework with spin z. Ok, accepted. But that makes discussion of 4 fold measurements on photons 1/2/3/4 a compatible framework, because no counterfactual statements are discussed. Only physically realizable measurements. We are looking at polarization: 1&4 is L/R measured early, 2&3 is V/H measured late. Distances between measurements can be arbitrarily large.

So the question is: does this consistent framework indicate a failure of locality, as it appears to be in the experiment? No counterfactual or inconsistent reasoning is employed. And Bell is not a factor. Just actual results.

I say CH forbids this type of swap by its stated premises. In contradiction to the experiment.