Incompleteness of Griffiths' consistent histories interpretation

[PeterDonis]

The argument is similar to this paper of Smolin https://arxiv.org/abs/1201.2632.

This paper is not proposing an interpretation of QM but what amounts to a different theory. As such, it's not really in scope for discussion in this forum.

 

[Fra]

No, you don't. An observer does not observe everything, nor do we need an exact model of the entire universe in order to construct a model that is a reasonable approximation of a restricted subsystem, such as an observer and some particular object they are observing.

Note that tracing over the rest of the universe does not require you to know its state. Indeed, it presupposes that you don't know its state, because tracing means basically averaging over all possible states that the rest of the universe could have. You wouldn't have to do that if you knew the exact state of the entire universe. But of course we don't and we never will.

I actually agree with what you write, but i think the discussion is to what extent the paradigm of QM foundations, actually implement the inference method we de facto use. It's here I see a inconsistency problem or incompleteness depending on how one views it.

/Fredrik

 

[PeterDonis]

the discussion is to what extent the paradigm of QM foundations, actually implement the inference method we de facto use

QM foundations is not about using QM in a practical sense. In a practical sense, QM does use the method I described. But QM foundations is about QM as a "theory of everything", i.e., it's not enough to just make practical use of it, there has to be a logically complete foundation for everything, not just a "for all practical purposes this works". At least, that is what the people working in the field of QM foundations give as their reason for whatever foundational program they advocate.

 

[Fra]

QM foundations is not about using QM in a practical sense. In a practical sense, QM does use the method I described. But QM foundations is about QM as a "theory of everything", i.e., it's not enough to just make practical use of it, there has to be a logically complete foundation for everything, not just a "for all practical purposes this works". At least, that is what the people working in the field of QM foundations give as their reason for whatever foundational program they advocate.

I can't disagree with this.

/Fredrik

 

[Demystifier]

Only the fundamental entities should need to appear in the formal definition of the theory. Yet no one has found a formalization of QM that does that.

I disagree, many interpretations of QM offer a formalization without a mention of measurement. Examples include consistent histories (which is the topic of this thread), many worlds, Bohmian mechanics, GRW, and many more.

 

[PeterDonis]

many interpretations of QM offer a formalization without a mention of measurement. Examples include consistent histories (which is the topic of this thread), many worlds, Bohmian mechanics, GRW, and many more.

Of these, the first and second cannot make any predictions without making use of the concept of measurement, so they are useless without that concept (which is not formalized in either).

I could see Bohmian mechanics being sort of able to make predictions without a concept of measurement, as long as one is willing to accept that all of the predictions are about particle positions only, and any talk of any other observable (which would include most talk about "measurement") is really disguised talk about particle positions.

GRW is a different theory from standard QM, so it's not the kind of thing I was talking about.

 

[Demystifier]

But you cannot formally define, what a measurement is. It's what's done in the lab and changes with the advance of technology. It's physics, not pure math!

Maybe, but fundamental principles of classical mechanics can be stated without mentioning measurement. If that's possible for classical mechanics, there is no a priori reason that it should be impossible for quantum mechanics. Yet, the standard "minimal" formulation mentions measurement in its fundamental principles. For many physicists it is a sign that the "minimal" formulation misses something, which is why they study non-minimal formulations.

 

[Demystifier]

Of these, the first and second cannot make any predictions without making use of the concept of measurement, so they are useless without that concept (which is not formalized in either).

I could see Bohmian mechanics being sort of able to make predictions without a concept of measurement, as long as one is willing to accept that all of the predictions are about particle positions only, and any talk of any other observable (which would include most talk about "measurement") is really disguised talk about particle positions.

GRW is a different theory from standard QM, so it's not the kind of thing I was talking about.

May I ask, which interpretation of QM do you prefer? I know that you want to stay neutral and unbiased regarding the interpretations, which I appreciate, but at some subjective level I'm sure that even for you some interpretations look more plausible or intuitive than the others.

 

[Morbert]

Doesn't this make consistent histories even more incomplete? If composition of statistically independent quantum systems is important enough to justify using the stronger consistency condition, then it should also be important enough to warrant some substantial discussions of their role in that quantum logic.

Could you expand on this? I.e. What do you think is the significance of the Diosi paper re/ incompleteness of CH? I've checked the citations and the CH people like Gell-Mann and Hartle and Griffiths all mention it, describing medium decoherence as "the weakest of known conditions that are consistent with elementary notions of the independence of isolated systems"

 

[gentzen]

Could you expand on this? I.e. What do you think is the significance of the Diosi paper re/ incompleteness of CH?

The Diosi paper is a strong indication that a closer investigation of (tensor) products should have been done, or rather that issues which occur in the context of (tensor) products had been neglected before. Which issues exactly I cannot say, because I have not done that investigation either. Maybe this is related to what Griffiths writes in the section "8.4 Open issues" (or maybe not):

8.4.1 Entangled histories
Whereas the principles of quantum stochastic dynamics summarized in Sec. 3 are both consistent and provide what seems to be a quite adequate foundation for all the sorts of calculations taught in textbooks and used in current research papers, they are incomplete in the following sense. Most discussions of histories and all discussions of consistency conditions known to the author employ a sample space of product histories: at each time in the history tensor product space a projector represents a property of the system at that particular time. But the tensor product space representing a composite quantum system—two or more subsystems—at a single time also contains what are called entangled states, which cannot be thought of as assigning a particular property to each subsystem; e.g., the singlet state (34). Consequently, the tensor product space of histories also includes states which are, so-to-speak, entangled between two or more times.
What is their physical significance? Could they serve a useful role in describing some sort of interesting time development? And how, assuming it to be possible, are probabilities to be assigned in the case of a closed quantum system? It is not obvious how consistency conditions as presently formulated, see (15), can be extended to this case, since the temporal ordering of events plays a crucial role. Thus this is thus an open question.

 

[vanhees71]

Formally means in formal mathematical terms.The fundamental entities (such as point particles in classical mechanics) are simple and their complete collection of properties is postulated (in classical mechanics as irreducible Poisson representations of the Galilei or Poincare group).

For a formally complete description, everything more complicated (macroscopic objects, observer, observations) must be defined mathematically in terms of the states of the fundamental entities.

This is the case in classical mechanics but not in quantum mechanics. In the latter case, the missing piece is the content of the measurement problem.And since measurements are not among your fundamental entities, one must also tell how they are built from the fundamental entities by deriving some kind of "effective theory".

But that's done, or what do you think condensed-matter physics is about?

On the level you define point particles in classical mechanics elementary particles are also defined in QT, i.e., as irreducible (ray) representations of the Galilei or Poincare group. Where is the difference between classical and quantum "axiomatics" here?

 

[vanhees71]

QM foundations is not about using QM in a practical sense. In a practical sense, QM does use the method I described. But QM foundations is about QM as a "theory of everything", i.e., it's not enough to just make practical use of it, there has to be a logically complete foundation for everything, not just a "for all practical purposes this works". At least, that is what the people working in the field of QM foundations give as their reason for whatever foundational program they advocate.

Well, ok. We don't have such fictions yet ;-).

 

[A. Neumaier]

But that's done, or what do you think condensed-matter physics is about?

It is not done, or at most half. Currently there is no definition of the measurement process in terms of condensed-matter physics. If one tries, one necessarily ends up with my thermal interpretation since condensed-matter physics is exclusively about expectations! But there is still the gap of deriving Born's rule from the thermal interpretation...

On the level you define point particles in classical mechanics elementary particles are also defined in QT, i.e., as irreducible (ray) representations of the Galilei or Poincare group. Where is the difference between classical and quantum "axiomatics" here?

This is described in my online book

• A. Neumaier and D. Westra, Classical and Quantum Mechanics via Lie algebras, 2011, arXiv:0810.1019

In classical mechanics we have representations by canonical transformations of the commutative Poisson algebra of observables.

In quantum mechanics we have representations by unitary transformations of the noncommutative operator algebra of observables.

The quantum operator algebra is the deformation of the classical Poisson algebra obtained via the Moyal product. The classical Poisson algebra is the limit $\hbar\to 0$ of the quantum operator algebra.

 

[A. Neumaier]

Well, ok. We don't have such fictions yet ;-).

That's why it is still an active research area...

 

[PeterDonis]

which interpretation of QM do you prefer?

Since this is the interpretations subforum, I can answer this question. Unfortunately, though, my answer is "mu": I don't prefer any of the interpretations that we currently have. I think we have not yet discovered a workable interpretation of QM, and the best we can do in our current state of knowledge is to "shut up and calculate" and hope someone discovers a better interpretation in the future.

 

[vanhees71]

But that's the answer! The shutup-and-calculate interpretation (or a bit more seriously called minimal statistical interpretation) is all that's needed to use QT as a physical theory.

 

[Morbert]

And since measurements are made using macroscopic objects, we should be able to build measurements out of fundamental entities as well. Then "measurements" would not need to appear in the formal definition of the theory, any more than "macroscopic objects" do. Only the fundamental entities should need to appear in the formal definition of the theory. Yet no one has found a formalization of QM that does that.

[consistent histories and many worlds] cannot make any predictions without making use of the concept of measurement, so they are useless without that concept (which is not formalized in either).

Consistent histories proponents will present the consistent histories language as universal, applicable to both microscopic and macroscopic systems, with no fundamental distinction. I.e. Both a microscopic system and a macroscopic apparatus that measures the system are encompassed by a Hilbert space, and the properties of the macroscopic system will correspond to much larger subspaces. There is no Heisenberg cut, and we can readily understand macroscopic systems as made up of lots of microscopic systems.

Similarly, measurement in consistent histories is not fundamental. Measurement processes are important insofar as they let us test predictions, but they are no longer a mysterious interaction between a quantum system and an external classical system. Consistent histories language frames measurement similar to the way classical language does: An interaction that establishes a correlation between the variable a physicist is interested in measuring, and a variable the physicist is capable of reading as a datum.

But that's the answer! The shutup-and-calculate interpretation (or a bit more seriously called minimal statistical interpretation) is all that's needed to use QT as a physical theory.

When I get a chance I am going to prove that you are a consistent histories proponent and you just don't know it yet.

 

[PeterDonis]

Consistent histories proponents will present the consistent histories language

"Presenting the language" is not the same as making predictions.

 

[Morbert]

"Presenting the language" is not the same as making predictions.

The point is the language can describe the microscopic system, or the macroscopic system (made up of lots of microscopic systems) or both. Before an experiment is ever even conceptualised, we can use the language to formalise propositions and their likelihoods about the microscopic system we are interested in. We can then use the same quantum language to describe potential macroscopic apparatus, and assess their suitability for testing these propositions.

 

[PeterDonis]

The point is the language can describe the microscopic system, or the macroscopic system (made up of lots of microscopic systems) or both. Before an experiment is ever even conceptualised, we can use the language to formalise propositions and their likelihoods about the microscopic system we are interested in. We can then use the same language to describe potential macroscopic apparatus, and assess their suitability for testing these propositions.

You're making it sound like consistent histories isn't an interpretation of QM, it's a different theory, using a different mathematical framework for making predictions. That's not my understanding of CH--my understanding is that it's an interpretation of QM, meaning it uses the same mathematical machinery as standard QM to make actual predictions, and the "language" you speak of is only for telling stories after the fact about what happened that sound like they make sense, at least to their proponents (which is what any interpretation of QM does, CH is no worse off than other interpretations in that respect, but no better off, either).

 

[Morbert]

You're making it sound like consistent histories isn't an interpretation of QM, it's a different theory, using a different mathematical framework for making predictions. That's not my understanding of CH--my understanding is that it's an interpretation of QM, meaning it uses the same mathematical machinery as standard QM to make actual predictions, and the "language" you speak of is only for telling stories after the fact about what happened that sound like they make sense, at least to their proponents (which is what any interpretation of QM does, CH is no worse off than other interpretations in that respect, but no better off, either).

As an aside, there is some speculation by Gell-Mann et al about whether consistent histories is a generalisation of QM.

But anyway: here are perhaps some relevant passage from Roland Omnes in "Understanding Quantum Mechanics":

"The idea of quantum histories consists in using a similar sequence of quantum properties for giving an account of events in the underworld of atoms and particles. In view of what we saw of the relation between quantum and classical properties, we may expect the procedure to work in both worlds, as a universal language"

"A history will say how a quantum system is prepared, what kind of apparatuses take part in the experiment, how the experimental devices work, what happens at the level of atoms and particles, and which data come out of a measurement. This extraordinary versatility is due to an essential advance over von Neumann's initial language. Whereas he could account only fur the properties of atoms and particles, the recent powerful techniques yielding classical physics can considerably extend the range of the construction. Classically meaningful properties of the preparation device and of the experimental apparatus-what we can see and do, phenomena, and actions-can now be expressed in the language of quantum projectors. This is why this language can now be considered as universal"

The histories to be constructed do, of course, depend on the underlying quantum theory. The interpretation has been used here to discuss histories of particle pairs in an EPR context. Cosmologists might in turn build histories to make predictions about the universe

 

[Demystifier]

But that's the answer! The shutup-and-calculate interpretation (or a bit more seriously called minimal statistical interpretation) is all that's needed to use QT as a physical theory.

If that's the answer, what is the question?

 

[Demystifier]

"Presenting the language" is not the same as making predictions.

Among all interpretations that exist out there, the consistent histories interpretation is the most "philosophical", because this is the only interpretation that proposes that the key lies in the change of language and logic. There is nothing unusual about the physical world, it says, the only unusual thing is a proper way to speak and think about it.

 

[Demystifier]

When I get a chance I am going to prove that you are a consistent histories proponent and you just don't know it yet.

I would really really like to see the proof that @vanhees71 is a proponent of consistent histories.

How would you convince him that unobserved frameworks make physical sense?

 

[vanhees71]

If that's the answer, what is the question?

That's another question I can't answer ;-).

 

[gentzen]

"Presenting the language" is not the same as making predictions.

Making predictions is not the task of "a language", but of the user of a language. If the user prefers to use the language for fairy tales instead, then the language may complain about grammatical errors, or inconsistent use of the language. But giving criteria to distinguish between predictions and fairy tales would be a much more difficult task. Languages are already hard enough to learn without the additional burden of such desirable but incredibly hard tasks.

Among all interpretations that exist out there, the consistent histories interpretation is the most "philosophical", because this is the only interpretation that proposes that the key lies in the change of language and logic.

Do you have a reference for that claim? I would even object to "change of logic" in the first place. Isn't the point rather to continue using normal logic and probabilistic reasoning, without accidentally running into paradoxes?

There is nothing unusual about the physical world, it says, the only unusual thing is a proper way to speak and think about it.

Isn't the claim rather that the unusual thing about quantum mechanics that it allows multiple frameworks that are consistent within themselves, but may become inconsistent when combined?

And the point of view that quantum mechanics can be regarded as a generalized probability theory, and one of the tasks for interpretation is to describe how to use such a generalized probability theory appropriately doesn't seem to be limited to consistent histories proponents either. Even people like Scott Aaronson hold that view, and teach it to their students, without also teaching consistent histories.

Scott Aaronson actually distinguishes between three different quantum like generalized probability theories: those for real numbers, complex numbers, and quaternions. The one with complex numbers is special in that (tensor) products behave much nicer than in the other two. Maybe this even leads to an interesting answer to the original question in this thread:
By failing to discuss "composition of statistically independent quantum systems" and the related (tensor) products, the consistent histories literature doesn't distinguish sufficiently between the real and complex versions of the quantum like generalized probability theories.

 

[PeterDonis]

Making predictions is not the task of "a language", but of the user of a language.

"Presenting a language" is also something that is the task of the user of a language. So I don't see your point here.

 

[gentzen]

"Presenting a language" is also something that is the task of the user of a language.

For example, a computer language like C++ has a specification, which tries to achieve the task of "presenting the language". C++ is implemented by many different compilers, and used by many different programmers. Of course there can be some discussion how much a language like C++ is defined by its specification, and how much by the implementation by different compilers. Still, the ideal is that the "specification is the language".

 

[PeterDonis]

a computer language

We're not talking about computer languages. We're talking about human language that is used in QM interpretations, specifically the consistent histories interpretation. So again I don't see your point here.

 

[gentzen]

We're not talking about computer languages. We're talking about human language that is used in QM interpretations, specifically the consistent histories interpretation. So again I don't see your point here.

My initial point was that I basically agreed with you, but that I didn't see any problem for consistent histories in your statement. However, now I get the impression that we might mean completely different things when we talk about language in the context of consistent histories.

When I talk of consistent histories as a language, what I have in mind is much closer to a computer language than to a human language. I see it as a reasonable quantum logic, more reasonable than the quantum logic of Birkhoff and von Neumann. That logic could be presented a formal language, with propositional variables $A, B, C, \ldots$, connectives $\land$, $\lor$, $\lnot$, and certain axioms. Because of its connection to quantum logic, I still see consistent histories as a formal language. And it is a formal language in the sense that everything you forgot to put in (say for example tensor products) stays missing, and so your language can be incomplete, if you are unlucky.

 

[gentzen]

When I get a chance I am going to prove that you are a consistent histories proponent and you just don't know it yet.

And Simon Saunders "proved" that James Hartle basically agrees with him, except for some minor details. It is not fair when MWI proponents do this to "histories" proponents. So "histories" proponents should not do this to a proponent of the minimal statistical interpretation either. Steven Weinberg was so kind to give a readable introduction to consistent histories in his "Lectures on Quantum Mechanics" (which I just consulted to help me do calculations for my investigations on the tensor products). Here is (an extract of) his critique

Some adherents of the decoherent-histories approach describe the probabilities (3.7.12) as objective properties of the various histories, not necessarily related to anything seen by any observer, and applying even where there are no actual observers, in particular to the early universe. This view seems to me untenable, for reasons like those already described in the case of a single measurement. ... The problem here is not that the choice is not unique, but rather, that it can only be made by people. Of course, the answers to questions depend on what questions we choose to ask, in classical as well as in quantum mechanics, but in classical physics the necessity of choice can be evaded because in principle we can choose to measure everything. It cannot be evaded in this way in quantum mechanics because in general many of these choices are incompatible with each other. ... So the Born rule in the decoherent-histories approach seems to bring people into the laws of nature, as is apparently inevitable for any instrumentalist approach.

 

[PeterDonis]

When I talk of consistent histories as a language, what I have in mind is much closer to a computer language than to a human language.

Can you give any reference that supports this claim?

 

[gentzen]

When I talk of consistent histories as a language, what I have in mind is much closer to a computer language than to a human language. I see it as a reasonable quantum logic, more reasonable than the quantum logic of Birkhoff and von Neumann.

Giving a reference for "what I have in mind" in this case could mean a reference that supports that seeing consistent histories as a reasonable quantum logic is a feeling shared by "histories" proponents. The second and third sentence of the abstract of A Consistent Quantum Ontology by Robert Griffiths reads

First, a logic (system of reasoning) is employed which is compatible with the Hilbert-space structure of quantum mechanics as understood by von Neumann: quantum properties and their negations correspond to subspaces and their orthogonal complements. It employs a special (single framework) syntactical rule to construct meaningful quantum expressions, quite different from the quantum logic of Birkhoff and von Neumann.

 

[Morbert]

@gentzen I think it's ok to interrogate assumed distinctions in interpretations. Lubos Motl once called consistent histories a homework problem for Copenhagen. There's no problem with Saunders arguing that Hartle agrees with him if his argument is interesting (I don't know if it is). And if consistent histories as a project ends up being useful to people doing work on many worlds, great!

Also, Weinberg's objections here seem somewhat subjective. Just as a the freedom of a physicist to choose a coarse-graining is a feature not a bug, perhaps the ability to choose from different fine-grainings is also a feature.

 

[Demystifier]

Isn't the claim rather that the unusual thing about quantum mechanics that it allows multiple frameworks that are consistent within themselves, but may become inconsistent when combined?

Yes, but I see different frameworks as different ways to talk and think about physics. I don't see them as properties of the nature itself. Just like choosing this or that system of coordinates in relativity theory are different ways to talk and think about physics, while nature itself is a Minkowski spacetime which does not have any coordinates at all. My problem with consistent histories interpretation is that I don't see what is the analog of the Minkowski spacetime without coordinates.