I Incompleteness of Griffiths' consistent histories interpretation

[gentzen]

Robert Griffiths version of consistent histories can be presented as a quantum logic, which is "intentionally" incomplete as an interpretation of QM. The advantage is that one can just require the exact decoherence condition $D(\alpha,\beta)=0$ for all $\alpha\neq \beta$ (with the decoherence functional $D(\alpha,\beta)=Tr[K^\dagger(Y^\alpha)K(Y^\beta)]$). Then one doesn't need to worry about appropriate approximate forms of it. And of course, one doesn't need to invoke decoherence for the existence of approximately consistent quasi-classical frameworks, and instead just invokes the principle of Liberty:

This is the principle of Liberty: the physicist can use whatever framework he chooses when describing a system

However, this raises the question whether it would not be more straightforward to require only $\operatorname{Re}D(\alpha,\beta)=0$ for all $\alpha\neq \beta$, which would be enough to ensure that applicability of classical logic and probability theory within a single framework. This is not done, because of the observation by Lajos Diós that the (canonical) composition of two statistically independent quantum systems $A$ and $B$ would not necessarily satisfy that condition (for given frameworks for $A$ and $B$ satisfying that condition). But the composition of such statistically independent quantum systems is not otherwise discussed in any substantial way in typical presentations of consistent histories.

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.

 

[Demystifier]

Robert Griffiths version of consistent histories can be presented as a quantum logic, which is "intentionally" incomplete as an interpretation of QM.

In what sense is it "intentionally" incomplete?

 

[gentzen]

In what sense is it "intentionally" incomplete?

With respect to Robert Griffiths, the incompleteness is "intentional" in the way that he responds to criticism and misunderstandings:

As is often the case with new ideas, the histories approach was subject to serious criticisms by (among others) d’Espagnat [20, 21], Dowker and Kent [22], Kent [23–25], and Bassi and Ghirardi [26, 27], during the decade and a half that followed the original publications. Responses were published in [28–31]; in some cases a further reply to the response will be found immediately after the response. While these criticisms were (in the author’s opinion) largely based upon misunderstandings of the histories program, they had the good effect of leading to a better and clearer formulation of its basic concepts. Vigorous scientific debate is often beneficial in this way, though it becomes ineffective if criticisms are cited while responses thereto are ignored.

Those misunderstandings start much earlier than stuff where he himself admits: "the task is still incomplete". Therefore it makes sense for him to focus on the basics (and give up on wishful thinking of how one day the histories program might get completed):

A lack of clarity on the part of the advocates of the histories approach during its first ten or fifteen years contributed to the misunderstanding, but by now these earlier problems have been cleared up. It is hoped that the present paper, supplementing the detailed exposition found in CQT, may serve to further understanding of an approach to quantum foundations that deserves careful attention.

 

[Demystifier]

Is your answer to my question "intentionally" incomplete?

 

[gentzen]

Is your answer to my question "intentionally" incomplete?

Of course, you are joking a bit. I don't want to put too many words into Griffiths mouth. Not sure what I should write. The misunderstandings and "misuses" to which Griffiths had to react are "breathtaking" in a certain sense. As a typical example, Simon Saunders writes

The goal was once again a one-world interpretation of quantum mechanics. But for that, fairly obviously, the history space had to be fixed once and for all. It was clear from the beginning that there were many consistent history spaces for a fixed initial state and Hamiltonian—which one should we choose? But it was thought that ...
But this difficulty does not apply to the marriage of decoherence theory in the more general sense with the consistent histories formalism, as carried through by Gell-Mann and Hartle and J.J. Halliwell ... histories in the latter sense are robustly defined. But decoherence (and the consistency condition) obtained in this way is never exact. ...
It is otherwise if decoherent histories theory is in service of the Everett interpretation - defining, among other things, the preferred basis. In that case it hardly matters if, for some states and regimes, decohering histories are simply absent altogether: ...

It is a complete misunderstanding that the "histories space would have to be fixed once and for all", or that anybody ever "though that ..." this could be achieved in some ridiculously misguided way. The trouble how to handle the tension between "not exactly satisfied consistency conditions" and becoming a fully fledged interpretation was certainly well known to the proponents. But the solution to simply put the histories program "in service of the Everett interpretation" is as far from any goals Griffiths had than you possibly could imagine.

Maybe this is another sense in which consistent histories is "intentionally" incomplete. The Everett interpretation claims to be able to derive the Born rule, and claims to derive some ontology of many quasi-classical worlds. The status of both claims is controversial, to say the least. If one of them fails, then the Everett interpretation becomes "unintentionally" incomplete. So "intentionally" being incomplete might also be a way to avoid being "misused" too badly "in the service of some competing interpretation".

 

[vanhees71]

Why is everybody so obsessed to "derive Born's rule" and not simply take it as one of the postulates? As any system of postulates quantum theory is justified by its success to describe the phenomena. Also what is gained assuming "many worlds", of which only one is observed or "consistent histories" which seemingly is not even a clearly defined interpretation?

 

[PeterDonis]

Why is everybody so obsessed to "derive Born's rule"

Because the Born rule is unsatisfactory as a postulate since it involves the concept of "measurement", which is only informally defined. A postulate in a scientific theory should have a clear formal definition.

 

[vanhees71]

In which sense are the other postulates, as written in our Insight article by @A. Neumaier ,

https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

more formally defined than Born's rule?

Of course, it's the rule (and in my opinion the only rule really needed) which links the purely mathematical axioms to observations and as such makes it a physical rather than a purely mathematical theory, but what's "not formal enough" for being a postulate of a physical theory?

It's also clear that the postulates have to be somewhat modified to make them really accurate (e.g., it's not $|\psi \rangle$ which represents a pure state but the corresponding statistical operator $|\psi \rangle \langle \psi|$ (or, equivalently the corresponding unit ray) and the operators representing observables must be self-adjoint and not only hermitean. Also for a complete description of quantum mechanics you need more general, i.e., "mixed" states, but all these are subtle mathematical details. I don't see, why all the other postulates are "more formally defined" than Born's rule. I'm talking about "physical postulates" not a mathematically strict axiomatic formulation of QT (which we have for non-relativistic QM only, anyway).

 

[PeterDonis]

In which sense are the other postulates, as written in our Insight article by @A. Neumaier ,

https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

more formally defined than Born's rule?

Of the 7 basic rules as we gave them in that Insights article, the last three, 5, 6, and 7, all use the term "measurement" and are therefore only informally defined. So 5 and 7 as we gave them are open to the same objection as Born's rule (6).

 

[Demystifier]

Because the Born rule is unsatisfactory as a postulate since it involves the concept of "measurement", which is only informally defined. A postulate in a scientific theory should have a clear formal definition.

Of course, there is nothing wrong with taking the Born rule in a measurement context as a practical rule. But in this case it should be clear that the Born rule is the "map", not the "territory". The problem arises when some practical users of the map become so successful in the use of the map that they start to believe that the map is the territory. Furthermore, the problem turns into an irony and self-contradiction when those practical users, who insist that only practical use matters and all philosophy is meaningless, promote this dictum into philosophy.

 

[vanhees71]

Of the 7 basic rules as we gave them in that Insights article, the last three, 5, 6, and 7, all use the term "measurement" and are therefore only informally defined. So 5 and 7 as we gave them are open to the same objection as Born's rule (6).

Hm, but what makes this "only informally defined". It's a physical theory not a set of meaningless mathematical axioms. Of course math is always more rigorous, because it's just a "game of rules" without any observational meaning. That's the difference between a structural and a natural science.

 

[vanhees71]

Of course, there is nothing wrong with taking the Born rule in a measurement context as a practical rule. But in this case it should be clear that the Born rule is the "map", not the "territory". The problem arises when some practical users of the map become so successful in the use of the map that they start to believe that the map is the territory. Furthermore, the problem turns into an irony and self-contradiction when those practical users, who insist that only practical use matters and all philosophy is meaningless, promote this dictum into philosophy.

Of course it's a map, as all the mathematical items in any physical theory. You are right, physics is an empirical science and the theories/models are just describing ("mapping" if you wish) what's observed.

The philosophy is beyond the natural sciences. It's not founded in observations, i.e., different interpretations of the same theory cannot be empirically tested. Whether you consider philosophy as "meaningless" is also just a personal matter of taste.

 

[PeterDonis]

what makes this "only informally defined"

Because it doesn't tell you what a "measurement" is or how to determine when a "measurement" has happened. That is left up to the informal judgment of each individual person making use of the formalism. Whereas other terms, such as "quantum system" and "observable", are given exact formal definitions; it's not left up to the individual judgment of each person to say what those things are.

 

[Demystifier]

but what's "not formal enough" for being a postulate of a physical theory?

To support @PeterDonis, it's not formal enough because the formal definition of measurement is missing.

 

[Fra]

It's ironic that one of the keys for upholding the rationality of natural sciences, the empirical component - "observation or measurement" (corroboration involves measurments) - is seen as a deep "problem" by so many? They want to get rid of measurements and get rid of observers because its fuzzy. What would be left? metaphysics?

Sure the interface between theory making and reality is fuzzy, but what else to expect from a learning process? Physics (not even theoretical physics) is not unique axiomatic constructions, and I don't see that it's a sound goal?

I must that admit that I have a hard time to fine a better and natural junction than "observation" and "measurement" for theory and practice to meet, so why do some insist in trying to recast this to hide the junctions? This is why for me the observer and it's measurements are a natural starting point, even if it's a bit fuzzy, but the fuzziness is right where it belongs IMO.

/Fredrik

 

[PeterDonis]

They want to get rid of measurements and get rid of observers

No, they don't. They want to have complicated things like "measurements" and "observers" be built from the fundamental entities of the theory, instead of being unanalyzed postulates. Just as we expect complicated things like "macroscopic objects" to be built from the fundamental entities of the theory.

 

[gentzen]

Why is everybody so obsessed to "derive Born's rule" and not simply take it as one of the postulates?

I might have been a bit unfair by implicitly hinting that all MWI proponents would claim that Born's rule can be derived. As an example of a proponent who doesn't, Lev Vaidman wrote:

Negative publicity for the MWI comes from the controversial claims about advantages of the MWI relative to other interpretations, e.g., that the Born Rule can be derived instead of postulated [30]. The claim is natural, because it is not simple to postulate the Born Rule in the MWI, but I believe it is false. In any case, the difficulties of this program reflect negatively on the MWI.

Also what is gained ... "consistent histories" which seemingly is not even a clearly defined interpretation?

It is clearly defined, it is just not complete. In fact, what is gained by caring less about whether it is complete is that its definition can be made simpler and clearer. You can use it to investigate certain controversial questions, like for example locality. Or analyze certain paradoxes.

 

[vanhees71]

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!

Also I think it's pretty plausible that Born's rule cannot be derived from the other postulates (see, e.g., Weinberg's textbook on quantum mechanics), though it seems not to be proven not to be deriable either.

 

[Fra]

No, they don't. They want to have complicated things like "measurements" and "observers" be built from the fundamental entities of the theory, instead of being unanalyzed postulates. Just as we expect complicated things like "macroscopic objects" to be built from the fundamental entities of the theory.

Ok, I get your point, but I still see that is problematic as from my perspective the "observer" is technically at the center of the inference (and the organism learning and evolving), and probably can't be captured as a "state" in a fixed statespace. The problems are similar to reductionist approach to biology... it usually gets extremely unnatural, evolutionary explanations are usually required to actually get some explanatory value.

/Fredrik

 

[vanhees71]

But the "theory defines", what fundamental entities are. In Newtonian mechanics the "fundamental entity" are "point particles", which of course are fictitious simplifications of "little bodies of final extent". Using the same fictitious simplification in classical electrodynamics ("electron theory" a la Lorentz et al) it becomes a problem making the whole edifice inconsistent, i.e., it's oversimplified.

In QM the "fundamental entities" are "elementary particles", very abstractly defined as described by irreducible (ray) representations of the underlying space-time-symmetry group.

"Macroscopic objects" are then built from the fundamental entities by deriving all kinds of "effective theories". We just celebrated the anniversary Andersons famous article "More is Different"!

https://www.science.org/doi/10.1126/science.177.4047.393
https://www.nature.com/articles/s42254-022-00483-x

 

[PeterDonis]

you cannot formally define, what a measurement is

Which, if true, means that "measurements" should not appear in the formal definition of the theory at all. See below.

the "theory defines", what fundamental entities are

Yes.

"Macroscopic objects" are then built from the fundamental entities

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.

 

[vanhees71]

With this ambition, we don't have any physical theories at all ;-). You cannot even define, what a "point particle" in Newtonian mechanics is at the demand of rigor you want!

 

[PeterDonis]

I still see that is problematic as from my perspective the "observer" is technically at the center of the inference (and the organism learning and evolving), and probably can't be captured as a "state" in a fixed statespace.

An "observer" is a complex object, so one would not expect a single state to capture it, any more than such a thing could capture a macroscopic object in general. You would need to build an observer out of a large number of fundamental entities, and of course an observer would not be a static thing, it would be dynamic, changing with time as it interacts with the world.

 

[Fra]

observer would not be a static thing, it would be dynamic, changing with time as it interacts with the world.

Evolving unitarily, yet learning?

/Fredrik

 

[PeterDonis]

The problems are similar to reductionist approach to biology... it usually gets extremely unnatural, evolutionary explanations are usually required to actually get some explanatory value.

I'm not sure what you mean by the "reductionist approach to biology", but the fact that organisms are made of cells, which in turn are made of proteins, nucleic acids, etc., is essential in understanding how living organisms work. Evolutionary explanations are certainly important as well, but they're not the whole story. For example, understanding how metabolism works is independent of working out how the metabolic systems in current living organisms evolved.

 

[PeterDonis]

Evolving unitarily, yet learning?

Unitary evolution only applies to an entire closed system. Obviously an observer is not an entire closed system. Only the universe as a whole is.

 

[vanhees71]

But we understand the "observer" (or rather measurement devices) at least to enough extent that we can construct them. E.g., a silicon pixel detector at the LHC is based on solid-state (semi-conductor) physics, which describes the corresponding solids with help of effective theories of many-body systems consisting of elementary particles. It's in a sense a more challenging part of theoretical physics to find these effective theories from a given more fundamental theory (in this case the "standard model of elementary particle physics").

 

[Fra]

Unitary evolution only applies to an entire closed system. Obviously an observer is not an entire closed system. Only the universe as a whole is.

So you need to model the whole universe to model the observers from fundamental parts unitarily? Is that a viable method?

/Fredrik

 

[PeterDonis]

So you need to model the whole universe to model the observers from fundamental parts unitarily?

No, you just need to recognize that when dealing with a subsystem, you won't necessarily have unitary dynamics for just that subsystem. You trace over the parts of the universe you're not including in your model. In some cases (if the subsystem's interactions with the rest of the universe are small enough during the time period of interest), the dynamics of the subsystem are close enough to unitary that they can be approximated as unitary to a good enough accuracy. But in general you would not expect a subsystem's dynamics to be unitary since it is interacting with the rest of the universe.

 

[A. Neumaier]

Hm, but what makes this "only informally defined". It's a physical theory not a set of meaningless mathematical axioms. Of course math is always more rigorous, because it's just a "game of rules" without any observational meaning. That's the difference between a structural and a natural science.

Formally means in formal mathematical terms.

With this ambition, we don't have any physical theories at all ;-). You cannot even define, what a "point particle" in Newtonian mechanics is at the demand of rigor you want!

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.

But the "theory defines", what fundamental entities are. In Newtonian mechanics the "fundamental entity" are "point particles", which of course are fictitious simplifications of "little bodies of final extent". Using the same fictitious simplification in classical electrodynamics ("electron theory" a la Lorentz et al) it becomes a problem making the whole edifice inconsistent, i.e., it's oversimplified.

In QM the "fundamental entities" are "elementary particles", very abstractly defined as described by irreducible (ray) representations of the underlying space-time-symmetry group.

"Macroscopic objects" are then built from the fundamental entities by deriving all kinds of "effective theories".

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".

 

[Fra]

Unitary evolution only applies to an entire closed system. Obviously an observer is not an entire closed system. Only the universe as a whole is.

Yes of course, this was my point, but I see I was expressing myself poorly.

My point was though that in order to understand/explain the observers evolution, in that view, you need to know everything and from the unitary evolution of everthing, them average out/reduce the environment. But that idea seems to not help when the observer is an "open system" as you say. I think it's a problem if you by "open system" implicitly assume it's a subset of a "closed system", because that hypothetical close system is out of reach for inference as long as it's unknown and not possible to manage from computational perspective at hand.

/Fredrik

 

[A. Neumaier]

you need to know everything and from the unitary evolution of everthing, them average out/reduce the environment. But that idea seems to not help when the observer is an "open system" as you say. I think it's a problem if you by "open system" implicitly assume it's a subset of a "closed system",

All systems that we can observe are subsystems of the closed system called the universe, and hence are open systems, even when they may be regarded at unitary for sufficiently simple observables.

because that hypothetical close system is out of reach for inference as long as it's unknown and not possible to manage from computational perspective at hand.

The universe is not out of reach. On the contrary, we know quite a lot about the universe. The far away part matters only in terms of incoming light, which we understand quite well. The solar system and smaller scales are also known quite well. For most observations, nuch, much less from the environment must be known.

 

[Fra]

An "observer" is a complex object, so one would not expect a single state to capture it, any more than such a thing could capture a macroscopic object in general. You would need to build an observer out of a large number of fundamental entities, and of course an observer would not be a static thing, it would be dynamic, changing with time as it interacts with the world.

Yes, but the point of the argument which one can differ upon is to what extent an observer can learn a timeless dynamical law, and distinguish it from the state in a statespace in which the law operates, in a timely manner.

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

My original intent in the thread was supportive of Vanhees empirical/instrumental perspective and take on physical postulates, but i have a more abstract take on "emprisim/instrumentalism" which leads ot the abstracted observer centerted view, and here I learned by know Vanhees disagrees as it becomes too philosophical.

/Fredrik

 

[Fra]

The universe is not out of reach. On the contrary, we know quite a lot about the universe. The far away part matters only in terms of incoming light, which we understand quite well. The solar system and smaller scales are also known quite well. For most observations, nuch, much less from the environment must be known.

I didn't mean we can't literally see, we can still see light back to the era of recombination etc, but I meant out of reach as in not beeing deductively inferrable from the perspective of the inside observer, according the reductionist model, imagined as computational simulation, due to limits of information capacity processing. We CAN infer it softly though by abduction, but then I think the mode of thinking as thinking of the universe as a closed fixed system in a timeless statespace of which we see a small parts is not helpful for me at least.

/Fredrik

 

[PeterDonis]

in order to understand/explain the observers evolution, in that view, you need to know everything

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.

 

[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.