Consistent Histories and Locality

[Morbert]

TL;DR Summary

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 $|\psi\rangle = a_\omega|+_\omega\rangle + a_\omega|-_\omega\rangle$ and the measurement apparatus is in the initial state $|\phi\rangle = \sum_\omega \omega |\omega\rangle$. 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.