I Incompleteness of Griffiths' consistent histories interpretation

[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.

 

[Demystifier]

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.

I don't have problems with thinking about QM as a generalized probability theory. But probability theory, at least in classical (statistical) physics, tells us what we can know about the physical system, not what its objective properties independent of our knowledge are. The CH interpretation, on the other hand, claims that it tells us something about objective properties of the physical system, which I cannot reconcile with the idea that it is only a generalized probability theory.

 

[Demystifier]

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?

Let me explain my point on an example. I will use an analogy between frames in relativistic physics and frameworks in the CH interpretation. In relativity you can combine statements from different frames. For example, it is meaningful to say

Earth is moving in the Sun's frame, and Earth is not moving in the Earth's frame.

By contrast, in the CH interpretation it is not meaningful to say

Particle has spin $s_x=\frac{1}{2}$ in the $X$-framework, and particle has spin $s_y=\frac{1}{2}$ in the $Y$-framework.

Thus we see that frames in classical physics and frameworks in the CH interpretation of quantum physics obey different rules for combination of statements. But those different rules are logical rules, hence the CH interpretation is based on a different logic.

 

[gentzen]

I don't have problems with thinking about QM as a generalized probability theory. But probability theory, at least in classical (statistical) physics, tells us what we can know about the physical system, not what its objective properties independent of our knowledge are.

But "normal" probability theory is not a theory of "the physical system". Instead, it has an event algebra (at least if presented in Kolmogorov style), and that event algebra has a structure (namely it is a Σ-algebra) that "hints at the existence" of objective atomic properties, especially in the finite case.

So a generalized probability theory should not be forced either to be a theory of "the physical system". Nevertheless, it should still be sufficiently clear what the knowledge or probabilities are about. For consistent histories, those are the histories within a single framework.

The CH interpretation, on the other hand, claims that it tells us something about objective properties of the physical system, which I cannot reconcile with the idea that it is only a generalized probability theory.

Do you have a reference for "CH ... claims that it tells us something about objective properties of the physical system"?

Let me explain my point on an example. I will use an analogy between frames in relativistic physics and frameworks in the CH interpretation. In relativity you can combine statements from different frames.

Nobody ever claimed any analogy between frames in relativistic physics and frameworks in the CH interpretation.

The point of CH is exactly that you should not combine statements from incompatible frameworks.

 

[Demystifier]

Nobody ever claimed any analogy between frames in relativistic physics and frameworks in the CH interpretation.

Griffiths, arXiv:1105.3932, page 9: "Similarly, choosing a framework is something like choosing an inertial reference frame in special relativity. The choice is up to the physicist, and there is no law of nature, at least no law belonging to relativity theory, that singles out one rather than another. Sometimes one choice is more convenient than another when discussing a particular problem; e.g., the reference frame in which the center of mass is at rest. The choice obviously does not have any influence upon the real world. But again there is a disanalogy: any argument worked out using one inertial frame can be worked out in another; the two descriptions can be mapped onto each other. This is not true for quantum frameworks: one must employ a framework (there may be several possibilities) in which the properties of interest can be described; they must lie in the event algebra of the corresponding PD."

 

[Demystifier]

Do you have a reference for that claim? I would even object to "change of logic" in the first place.

Griffiths, arXiv:1105.3932.

page 4: "First, the quantum world must be understood using an appropriate form of
reasoning with features which differ not only from ordinary propositional logic, ..."

page 26: "The new logic, in which conjunctions and other combinations of incompatible quantum propositions, represented by noncommuting projectors, are ruled out of acceptable quantum descriptions by the single framework rule, represents a radical break with classical physics."

page 27: "It is a form of quantum logic in the sense of a scheme for correct reasoning in the quantum domain that differs from the logical scheme of
classical physics."

 

[martinbn]

Let me explain my point on an example. I will use an analogy between frames in relativistic physics and frameworks in the CH interpretation. In relativity you can combine statements from different frames. For example, it is meaningful to say

Earth is moving in the Sun's frame, and Earth is not moving in the Earth's frame.

By contrast, in the CH interpretation it is not meaningful to say

Particle has spin $s_x=\frac{1}{2}$ in the $X$-framework, and particle has spin $s_y=\frac{1}{2}$ in the $Y$-framework.

Thus we see that frames in classical physics and frameworks in the CH interpretation of quantum physics obey different rules for combination of statements. But those different rules are logical rules, hence the CH interpretation is based on a different logic.

But in classical physics you cannot say "The Earth is moving in the Sun's frame with velocity $v=\frac12$ (with a certain choice of units). And the Earth is moving with velocity $v=-\frac12$ in the Earth's frame." So it doesn't seem that different from CH, does it?

 

[gentzen]

Griffiths, arXiv:1105.3932, page 9: "Similarly, choosing a framework is something like choosing an inertial reference frame in special relativity. The choice is up to the physicist, and there is no law of nature, at least no law belonging to relativity theory, that singles out one rather than another.

That phrasing indeed seems "unlucky" to me, because there are laws of nature (in the case of CH) that make most "formally valid choices" at least useless. Of course, that does not single out any specific single framework, but it is still completely different from the situation in special relativity.

... The choice obviously does not have any influence upon the real world. But again there is a disanalogy: any argument worked out using one inertial frame can be worked out in another; the two descriptions can be mapped onto each other. This is not true for quantum frameworks: one must employ a framework (there may be several possibilities) in which the properties of interest can be described; ..."

Here Griffiths tries to rescue it after the damage was done. At least he didn't use the word "analogy" before, and here he explicitly uses the word "disanalogy".

 

[Demystifier]

Do you have a reference for "CH ... claims that it tells us something about objective properties of the physical system"?

Griffiths arXiv:1105.3932.

Sec. 6.3: "Objective properties of isolated individual systems do not change when something is done to another non-interacting system. ... Essential to the argument is, of course, the assumption that any objective properties of A must be represented by projectors on its Hilbert space, and if the family of histories contains a sequence of such properties at three or more times (including the initial time) then the consistency conditions are satisfied. The properties of A are objective in the sense that the whole situation is modeled from the perspective of a
physicist who is outside the system being described."

page 26: "One can speak of an objective quantum reality: different observers can agree because there is something “out there” in the world, external to themselves, about which agreement is possible"

 

[Demystifier]

but it is still completely different from the situation in special relativity.

Yes, that's what I pointed out in #72.

 

[gentzen]

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.

There simply is no such analogy to the Minkowski spacetime without coordinates. (At least CH does not provide such an analogy.)

From "Do we really understand quantum mechanics?" as the conclusion how CH leaves the Schrödinger cat paradox unsolved:

One would much prefer to have a “super-consistency” rule that would eliminate these superpositions; this would really solve the problem, but such a rule does not exist for the moment. At this stage, one can then do two things: either consider that the choice of sensible histories and reasonable points of view is a matter of common sense – a case in which one returns to the usual situation in the traditional interpretation, where the application of the postulate of wave packet is also left to the good taste of the physicist; or invoke decoherence and coupling to the external world in order to eliminate all these unwanted families – a case in which one returns to the usual situation where, conceptually, it is impossible to ascribe reasonable physical properties to a closed system without referring to the external world and interactions with it.

 

[gentzen]

Do you have a reference for "CH ... claims that it tells us something about objective properties of the physical system"?

page 26: "One can speak of an objective quantum reality: different observers can agree because there is something “out there” in the world, external to themselves, about which agreement is possible"

That statement is fine in the context of that paper, because Griffiths had clearly separated such statements from the logic (system of reasoning) part. From the abstract:

The (consistent or decoherent) histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic (system of reasoning) is employed... Second, quantum time development is treated as an inherently stochastic process under all circumstances, not just when measurements take place. The time-dependent Schrödinger equation provides probabilities, not a deterministic time development of the world. The resulting interpretive framework has no measurement problem and can be used to analyze in quantum terms what is going on before, after, and during physical preparation and measurement processes.

It is fine for Griffiths to have an opinion on how QM should be interpreted. He didn't claim that this part of the interpretation would follow from the logic part.

Sec. 6.3: "Objective properties of isolated individual systems do not change when something is done to another non-interacting system. ... Essential to the argument is, of course, the assumption that any objective properties of A must be represented by projectors on its Hilbert space, ...

In CH, there are objective properties within a single framework. So in this sense, talk of objective properties is fine.

Still, that section is difficult for me. My initial question here was about incompleteness issues of CH when it comes to composition of independent systems. This section talks about "isolated individual systems" and "another non-interacting system", i.e. precisely about that stuff were I am unsure whether the logical language of CH doesn't currently have issues. But an analysis of whether that section is fine should be done it terms of CH itself, not based on a misunderstanding of what it tries to achieve, or what it means when it talks about "objective properties".

 

[Demystifier]

From "Do we really understand quantum mechanics?" as the conclusion how CH leaves the Schrödinger cat paradox unsolved:

Would you agree that CH leaves the Schrödinger cat paradox unsolved?

 

[PeterDonis]

in classical physics you cannot say "The Earth is moving in the Sun's frame with velocity $v=\frac12$ (with a certain choice of units). And the Earth is moving with velocity $v=-\frac12$ in the Earth's frame."

Yes, you can say this in classical physics. That is @Demystifier's point. Both of these statements can correspond to the same invariants in classical (relativistic) physics, so they can both be true at the same time. In other words, statements in different frames in classical physics are compatible. But in the quantum CH case there are no "invariants" that stay the same when you change frameworks. Statements in different frameworks are not compatible. So the claimed analogy with classical physics is not valid.

 

[gentzen]

Would you agree that CH leaves the Schrödinger cat paradox unsolved?

Griffiths and Omnès are both clear that the cat is either dead or alive, long before the box is opened. But as Omnès said, they cannot prove it. There are frameworks in which the cat is indeed either dead or alive, so in this sense there is no paradox in CH. But there are no good general rules to exclude those frameworks were it is not.

But my own opinion should not be overly important anyway. In the end, just like "most everybody else", I am unwilling to read the 54 pages of Griffiths original paper from 1884, or the 100 pages of an important report by Gell-Mann & Hartle from 1991. What I do read (completely) is shorter stuff, like Griffiths' SEP article, the section in Weinberg's book, the section in Laloë's book, or the section in Schlosshauer's old survey on decoherence. That stuff seems "well written" to me, and I see no reasons for me to object to them. I quoted them (Weinberg & Laloë), because what they wrote seemed valid to me.

For me, it is a much more difficult decision what to do with stuff like:

what do you think about the consistent histories interpretation?

It gives the probability of sequences of results, but it is based on the Wigner formula which does not depend on interpretation. See e.g. Appendix B in my recent https://arxiv.org/abs/2107.08777.

I cannot see how anything ignoring the consistency condition should be a valid summary of CH.

As long as it does not solve the problem of one measurement as you say, I think that this interpretation does not serve a purpose that an interpretation of QM is supposed to serve.

An honest incomplete interpretation like CH that I can understand "easily" seems much more useful to me than a supposedly complete interpretation like MWI, where I can forever read long articles without ever fully understanding it.

 

[Demystifier]

An honest incomplete interpretation like CH

I think I still haven't seen that the proponents of CH say that it is incomplete.

 

[gentzen]

I think I still haven't seen that the proponents of CH say that it is incomplete.

How exactly would you like them to say it? Perhaps in the way of only presenting the part with the single framework and the consistency condition, and then mentioning the role of decoherence for narrowing down the choice of frameworks? Or being even more explicit about the need for decoherence, and the difficulties of "integrating" it with the exact decoherence condition? Or is it enough that most summaries present certain difficulties of CH, and the proponents don't contradict those summaries?

How about this interview of Gell-Mann (the video has a transcript below)?

Do you think ... that the traditional way of teaching quantum mechanics ... should evolve into teaching it more from the sum over histories viewpoint?

Well the… not only the sum over histories viewpoint, but the decoherent histories viewpoint. Well, when the point of view is perfected, which may be very soon, I think that's true. ...

Or this quote from page 214 of “Quantum Philosophy”?

… have reproached quantum physics for not explaining the existence of a unique state of events. It is true that quantum theory does not offer any mechanism or suggestion in that respect. This is, they say, the indelible sign of a flaw in the theory, … Those critics wish at all costs to see the universe conform to a mathematical law, down to the minutest details, and they certainly have reason to be frustrated.
…
I embrace, almost with prostration, the opposite thesis, the one proclaiming how marvelous, how wonderful it is to see the efforts of human beings to understand reality produce a theory fitting it so closely that they only disagree at the extreme confines. They must eventually diverge, though; otherwise Reality would lose its nature proper and identify itself with the timeless forms of the kingdom of signs, frozen in its own interpretation. No, science’s inability to account for the uniqueness of facts is not a flaw of some provisional theory; it is, on the contrary, the glaring mark of an unprecedented triumph. Never before has humanity gone so far in the conquest of principles reaching into the heart and the essence of things, but that are not the things themselves.

 

[martinbn]

Yes, you can say this in classical physics. That is @Demystifier's point. Both of these statements can correspond to the same invariants in classical (relativistic) physics, so they can both be true at the same time. In other words, statements in different frames in classical physics are compatible. But in the quantum CH case there are no "invariants" that stay the same when you change frameworks. Statements in different frameworks are not compatible. So the claimed analogy with classical physics is not valid.

How can you say that the Earth's velocity in the Earth's frame is not zero?!

 

[PeterDonis]

How can you say that the Earth's velocity in the Earth's frame is not zero?!

Yes, the statement I was responding to should be corrected to say that (or to say that the Sun's velocity in the Earth's frame is $- \frac{1}{2}$). But that doesn't change the main point, which is that the two statements in different frames are compatible; they are both consistent with the same invariants. That is not true for statements in different frameworks in the consistent histories interpretation.

 

[Fra]

Interesting discussion, I was never attracted to consistent histories, and after reading this I guess it is because I also feel that it's "incomplete", but as thinking about this if you are to make it "complete" perhaps it's not longer a pure interpretation but the seed for something more?

The issue of "selection among frameworks" is actually a central point to me, which is perhaps why I am not attracted to consistent histories as it's stated, some random reflections to add to the thread.

Griffiths, arXiv:1105.3932, page 9: "Similarly, choosing a framework is something like choosing an inertial reference frame in special relativity. The choice is up to the physicist, and there is no law of nature, at least no law belonging to relativity theory, that singles out one rather than another.

Sounds like associating the framework to a gedanken "inside-observer" to me, and the "gedanken observer", as opposed to REAL observer, is imagined to be insertable without affecting the rest of the system. This gedanken observer is treated mathematically and thus is up to the freedom of the physicists. But if one instead considers the idea to associate this "observer" with physical agents (ie matter). Then there will be a selection principle, namely any framework is allowed that is "represented" in the population. Environmental decoherence may be said to partly do the same, buy I think the explanatory logic of decoherence is exstrinsic and therefore not satisfactory, but the effect likely similar.

This is what I would like to "add" when reading this, but that is a more radical claim than CH. But it's what I think is missing.

Sometimes one choice is more convenient than another when discussing a particular problem; e.g., the reference frame in which the center of mass is at rest. The choice obviously does not have any influence upon the real world. But again there is a disanalogy: any argument worked out using one inertial frame can be worked out in another; the two descriptions can be mapped onto each other. This is not true for quantum frameworks: one must employ a framework (there may be several possibilities) in which the properties of interest can be described; they must lie in the event algebra of the corresponding PD."

One needs then to have a communication path in between the frameworks, that explains how views deform as they are communicated. This is manifest be the poincare transformations in classical physics, which is what one can make sense of the conjuction of information from differen observers. In classical physical observers can "share information".

In QM, "inside-observers" can not "share information" is it may break entanglements. My understanding here is the trying to do - what works well in the classical models - in quantum theory, necessariy involves physical interactions. Ie. one can not model observer-observer relations as a gauge, it must be modeled as actual interactions, that have duration in time.

This is how I arrived at my preferred interpretation, I agree with plenty of Griffiths writings, but as to wether Griffiths idea is the ultimate "pure interpratation" (ie disallowing suggesting improviing theory) I have never thought about.

In other words, statements in different frames in classical physics are compatible. But in the quantum CH case there are no "invariants" that stay the same when you change frameworks. Statements in different frameworks are not compatible. So the claimed analogy with classical physics is not valid.

Yes, I agree, this is the core poitn. but if you for some reason you want to PUSH this analogy, what I wrote above is what I see as the natural path, and also what I might say is making the CH "incomplete"? But wether it's incomplete or not, may depend on wether it's admiddetly left incompete in order to NOT become a conjecture, but a pure interpratation? I haven't read up on CH history in detail to tell how the founders reason.

Edit: I corrected the terms, as I sometimes forget to no mix up standard notions with my own understanding. I used the term ""inside-observers" instead of observers so distinguish from the "classical observer" from say copenhagen, to what I interpret the "framework" in CH refers to.

/Fredrik

 

[Fra]

But that doesn't change the main point, which is that the two statements in different frames are compatible; they are both consistent with the same invariants. That is not true for statements in different frameworks in the consistent histories interpretation.

One could ask, is it a problem that statements in different frameworks are inconsistent if they never interact?
I think no.

But if they do interact (whatever it means), new questions form. And I would like to ask these questions, but CH probably not?

/Fredrik