Criteria for a good quantum interpretation

[WernerQH]

But that does not mean particle physics is a condensed matter theory. Such should be pretty obvious anyway - how can you use condensed matter (which is made of particles) to explain those particles? It makes no sense. Or rather you would need more details on exactly what the condensed matter in such a theory is or all you have is analogies.

Analogies aren't bad per se. We should only stay away from misleading analogies and obsolete metaphysical baggage. Condensed matter theorists have good reasons to think of their theories as describing really existing structures in liquid helium-3. Pursuing the analogy in the opposite direction, it is likewise more useful to think of QFT as describing really existing correlations in the fabric of spacetime, rather than "particles" moving about and having undefined properties until they are "measured".

QFT is a self-contained theory ("closed" in the sense of Heisenberg): a machinery for calculating correlation functions. It is not mere semantics -- putting the emphasis on "particles" distracts from the essence of the theory.

 

[Sunil]

Claims that there would be only "one (true) logic" or "one (true) probability theory" feel too simplistic to me. For example, mathematical logicians agree that both syntax and semantics are important aspects of logic. Of course, minor differences in syntax or semantics don't give rise to (true) different logics, but major differences do: Propositional logic, predicate logic, quantified propositional logic,

Their difference is essentially only that some other parts of the language have been formalized. Of course, as an object of mathematics something which has only "and" "or" "not" as operations is different from what has also $\exists$ and $\forall$. And one can as well add many other sufficiently general words and formalize their properties and add them to the "rules of logic". But the rules for "and" "or" "not" hold in exactly the same way in all such extensions. So, these are no different logics.

intuitionistic propositional logic, quantified intuitionistic propositional logic, or intuitionistic propositional logic with Hindley-Milner restricted quantification are all different logics.

Intuitionism is also not really different. Classical logic is part of it, with the classical $\exists$ translated as $\lnot\forall\lnot$, so we have simply some additional formalized notion of "constructive existence", which otherwise follows classical logic too.

And they don't just exist, but they do play important roles in their respective application domains.

Maybe, I don't care. For me, these are all part of classical logic.

Weasel words like "generalized" are indeed problematic.

"Generalized" is not a weasel word, it has a quite well-defined meaning in mathematics - some properties of the non-generalized variant no longer holds, the non-generalized thing fulfills the axioms of the generalized thing too, but there are other, generalized things which are not non-generalized things. And this makes "generalized logic" nonsensical - the rules of logic hold, always, everywhere. One may criticize the words, and it is quite justified that the classical "exists" is slightly misleading, and $\lnot\forall\lnot$ more accurate. Similarly, "from A follows B" suggests some causal connection which "A or not B" does not have. Such objections against logic are possible and reasonable. But such possible improvements of verbal expressions does not change the logic.

A "quantum logic" which claims that some parts of classical logic are no longer valid is nonsense. The consideration of the mathematical formalism of things which follow axioms which are somehow similar but weaker than those of classical logic is fine, if that mathematical object is named in a non-misleading way, lattice or so. Just to name it "logic" makes no sense.

A respectable framework for "quantum logic" and "quantum probability theory" like Griffiths' consistent histories approach doesn't need them. It can explain directly why it satisfies the requirements of a logic that enables to base a probability theory on it.

I have no objection against Griffiths' [in]consistent histories approach as far as it is not in conflict with classical logic and probability theory. If it would be in conflict with classical logic, it would have to been thrown away immediately. But I see no base for such a claim.

 

[Sunil]

Reasonable view. But can't you see it is just semantics. And one of the silliest things there is to argue about is semantics.

I see that it is just semantics. And from the point of view of a mathematician, there would be no point to argue about this. Mathematicians, if they want to study something different, give it a different name and everything is fine.
In physics, it should be in principle similar. Usually it works, nobody is confused by "color" in QCD or so. But there are some places in physics where we have misleading names, and where this leads to real confusion. "quantum logic" is one such place. There are really people out there who think that the rules of logic or probability theory are no longer valid in the quantum domain. Really. Or who think that "nonlocal" is something horrible and don't recognize that a theory which is a local in any meaningful sense of the word but allows a maximal speed greater than c is named today "nonlocal".

 

[gentzen]

A "quantum logic" which claims that some parts of classical logic are no longer valid is nonsense. The consideration of the mathematical formalism of things which follow axioms which are somehow similar but weaker than those of classical logic is fine, if that mathematical object is named in a non-misleading way, lattice or so. Just to name it "logic" makes no sense.

My point (or claim) is that the problem of "quantum logic" is that its semantics is not sufficiently interesting or useful, and that it therefore fails to be a logic. (It has models, because it is an algebraic structure, but those models are not sufficiently interesting. Probably Birkhoff and von Neumann also defined a more interesting semantics, but I am not familiar with it, and I guess this is also true for you.) Whether all axioms of classical logic are still true is less important, as demonstrated by intuitionistic logic.

More general, my claim is that your position that there is essentially only one logic and only one probability theory is closely related to the fact that the role of a semantics for a logic remains a bit obscure for you. This is no surprise, because the syntax of a logic is much more visible and also its role is easier to appreciate.

 

[Fra]

My reason is a model building answer.
...
This is very similar to Dirac. He played around with equations until he understood them inside out then tried extending them. Sometimes it worked, sometimes it did not. Feynman and Landau were also masters at it. They were not concerned with why nature was like that - it was enough for them. There is a psychological issue here - some like me are satisfied with this approach - others are not. While having an excellent command of the technical apparatus of physics, like Dirac and Feynman, Einstein actually used his physical insight rather than just playing around with equations. Feynman did so as well. Landau, I do not know enough about to comment.

Thanks this post explained more than the other one, yes it seems the psychology here is settings us apart.

As I am driven by how I think an intrinsic inference process works, by an imagined inside physical agent, and is bothered by the fact that QM as i stands is NOT cast in this form, and hence appears incomprehensible. I am one of those that is not satisfied with the Dirac approach as you describe it. I am convinced there is a deeper graspable reason for why the laws of physics, at some level looks like some pretty rational rules of inference, that may unify the laws of physics and the rules of scientific inference, at a deep level? This for example begs to compare questions: what is the inferential status of a "state"? What is the inferential status of "law"(ie hamiltonian)? If both are the result of an inference (generalized measurement/inference) then why are they treated assymmetrically in current theory?

This is why I "understand" QM as i stands, as almost an theory inference relative to classical observers, looking at atomic scale systems. In this domain QM is fine! But what about the rest? How about cosmological perspectives? or what about big bang, where the classical observers was not around? And what about explanation of hamiltonjians of standard model? If the laws of physics ARE rules of inference, then shouldn't the hamiltonians of standard model correspond to some optimally stable code?

/Fredrik

 

[RUTA]

We have discovered something strange about nature - it uses the generalised probability model suggested by our simple Markov chain model extension. People may ask the question - why is nature like that? It is all very reasonable - we have mathematically extended probability theory to see what happens. But why does it need extending? That I can't answer - future research may shed light on it - but we are forced to accept every model is based on assumptions.

Thanks
Bill

Our answer to that question, i.e., “Why the qubit instead of the classical or generalized bit?” is the relativity principle, as we explain in our publications. It’s quite simple, but you have to accept a principle explanation without any constructive counterpart (like with special relativity).

I agree with you that all theories are constantly being improved, e.g., Hamiltonian and Lagrangian methods for Newtonian mechanics. But, those improvements don’t invalidate what has been improved. Heisenberg’s point is that Newtonian mechanics still holds in its realm of applicability, Hamilton’s methods do not “disprove” Newtonian mechanics. Likewise, QFT improves QM, but QM still holds in its realm of applicability. I think that’s what Heisenberg meant by “closed.” If QM is really ”open,” then it could be refuted in its realm of applicability. I doubt that will happen.

 

[Fra]

Our answer to that question, i.e., “Why the qubit instead of the classical or generalized bit?” is the relativity principle, as we explain in our publications. It’s quite simple, but you have to accept a principle explanation without any constructive counterpart (like with special relativity).

Given RUTAs perspective, I wonder, how many of us here Accept without requiring further explanation of say the concept of the upper bound of signals in space, which is the key postulate beyond observer equivalence leading to SR?

How many of us asks, and seeks an explanation, for WHY there exists and observer invariant upper bound of signal speed?

/Fredrik

 

[Fra]

But there are some places in physics where we have misleading names, and where this leads to real confusion. "quantum logic" is one such place. There are really people out there who think that the rules of logic or probability theory are no longer valid in the quantum domain. Really. Or who think that "nonlocal" is something horrible and don't recognize that a theory which is a local in any meaningful sense of the word but allows a maximal speed greater than c is named today "nonlocal".

I agree there seems to be a mess. Sometimes people try to recast things into "forms" that suit their own personal insight and mental abstractions. I am certainly guilty of that myself. But at the same time, if one can make unambigous progress in the end one can postpone discussing formal classicifactions. The fact that we have different mental abstractions makes communication harder at times.

To me "quantum logic" is really just an extension using the normal logical rules, where one replaces a single event space, with several of them, that are not independent (and hence does not commute in the inference scheme). I also don't like thinking that this is some magic quantum logic. I see nothing magic in this, instead one can understand it using normal logic of course. The question is more, WHY would and agent, hold multiple dependent sets of information? This is where the inference insight suggests its beacuse it's more efficient. Ie. the quantum agent will have an aevolutionary advantage and outcompete the classical agent. This wording, I am thinking probalby makes not sens or adds no insight for those who think in terms of say bohmian ways. I just accept that it's difficult to understand each others logic. I find it interesting still that even different approaches meet at times and find commong junctions.

/Fredrik

 

[vanhees71]

Given RUTAs perspective, I wonder, how many of us here Accept without requiring further explanation of say the concept of the upper bound of signals in space, which is the key postulate beyond observer equivalence leading to SR?

How many of us asks, and seeks an explanation, for WHY there exists and observer invariant upper bound of signal speed?

/Fredrik

As long as general relativity is not disproven by observation, I tend to "believe" in it as a valid description of Nature and thus that there's a limiting velocity for causal effects/signal propagation (though one should be cautioned that as everything this holds within GR only locally!).

 

[RUTA]

Given RUTAs perspective, I wonder, how many of us here Accept without requiring further explanation of say the concept of the upper bound of signals in space, which is the key postulate beyond observer equivalence leading to SR?

How many of us asks, and seeks an explanation, for WHY there exists and observer invariant upper bound of signal speed?

/Fredrik

Note, we're not claiming that there is no constructive counterpart to the principle theory of SR. All we're pointing out is that it's been 116 years since SR was published and the physics textbooks still do not present a constructive counterpart when introducing SR. It seems most physicists have given up on that idea.

Our goal with QM is to show that it can be introduced as a principle theory in analogous fashion. Indeed, you can even use the same relativity principle (just applied to a different constant of Nature, h). We believe this offers an additional means of introducing QM to first-year students, so as to resolve the mystery of entanglement just as the mysteries of time dilation and length contraction are resolved in SR. In SR, the relativity principle + c means that Alice says Bob's clocks run slow and his meter sticks are short, while Bob says the same about Alice's clocks and meter sticks. In QM, the relativity principle + h means that Alice says Bob's measurements of X are only correct on average, while Bob says the same about Alice's measurements of X.

It's been 86 years since the EPR paper with neither a (consensus) constructive nor principle account of entanglement. At least now we have a principle account as robust as that for SR. We believe that constitutes some progress.

The QM question analogous to your SR question would be, "Why does there exist an invariant minimum size h to the action in an emission or absorption of energy/momentum?" The principle account does not answer that question nor the one you asked regarding c.

 

[bhobba]

Note, we're not claiming that there is no constructive counterpart to the principle theory of SR. All we're pointing out is that it's been 116 years since SR was published and the physics textbooks still do not present a constructive counterpart when introducing SR. It seems most physicists have given up on that idea.
one you asked regarding c.

I rather like the following I have posted many times before:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Some books line Rindler and Morin have similar arguments. I rather like Morin because the classical mechanics part has difficult problems and solutions that are very instructive to go through - it also introduces advanced ideas like Noether's Theorem.

Your 'question' would be, why is the c from that derivation finite. There are many experimental and theoretical reasons why it is the speed of light, but it does not answer why nature chose that. I have no idea, except, of course, what future research may turn up. Even more basic is why is an inertial frame, which strictly speaking is an abstraction that does not exist, so useful? It is thought that deep in interstellar space, inertial frames to a high accuracy do exist, but that does not explain why the concept is so useful. The POR is a statement about something that is just an abstraction. To me, that is really strange. In part, it goes to the heart of a models relationship to what it is modelling. I did a formal course on mathematical modelling, and the lecturer mentioned it but just said it's part of why is the world actually comprehensible.

The QM question analogous to your SR question would be, "Why does there exist an invariant minimum size h to the action in an emission or absorption of energy/momentum?" The principle account does not answer that question nor the one you asked regarding c.

Well, we have similar derivations to c, such as found on page 82 of Ballentine, and even what Dirac wrote all those years ago in Principles of QM Chapter 4 based on analogies with Poisson Brackets. Again, that explains why such a number exists, not its value - specifically why it is non zero. Again its value is determined from experiments.

To me, it is part of a wider issue; namely, our theories often demand a value exists, but why it has the value it has; blank-out. I think that is an issue several physicists are grappling with. Possible explanations like the anthropological principle have been proposed.

If history is any guide, the answer often turns out to be completely unexpected. Then afterwards, people say - why did we not see that before. It was like that with QM. Here is a 'modern' introduction:
https://www.scottaaronson.com/democritus/lec9.html

Nothing like that would have occurred to the early pioneers.

Thanks
Bill

 

[Fra]

Note, we're not claiming that there is no constructive counterpart to the principle theory of SR. All we're pointing out is that it's been 116 years since SR was published and the physics textbooks still do not present a constructive counterpart when introducing SR. It seems most physicists have given up on that idea.

I absolutely got that point, and that should make your claims in general more interesting.

/Fredrik

 

[AnssiH]

It's well known that Lorentz ether theory is only philosophically different from Special Relativity - Special Relativity did not push any specific interpretation forward strongly. But Minkowski did, and it is harmful that there are so many people professionals alike, who are not clear on the difference between Minkowski and Special Relativity.

No, what might be "harful" is not really understanding what you are objecting to. If you assume some ether theory, you have implicitly chosen a spacetime geometry that gives you Newtonian physics, i.e., a central extention to the Galilean group, which actually is more complex than choosing the Poincare group for the spacetime of special relativity. So, not only did you choose a spacetime geometry without realizing it, you are trying to introduce a fictional ether that makes it even more complicated as well as makes unphysical predictions to turn it into the spacetime you did not choose for some weird reason known only to ether advocates. As for unphysical predictions, if there is an ether, there should be pressure waves associated with it, yet none have been observed. Choose the right spacetime from the beginning and avoid all of the problems associated with choosing the wrong one and trying to compensate for choosing incorrectly.

Hi Bobob,

I'm afraid your response is a great example of just the kind of slight confusion that I referred to as "harmful". SR is taught today from Minkowski's spacetime perspective in so much that most people assume they are the intractably married. Just because most people are used to think in terms of some paradigm, doesn't mean that is the only paradigm. Lorentz' ether theory is the theory where Lorentz transformation came from, SR is a paper pointing out that the convention of relativistic simultaneity yields the same transformation as symmetrical between reference frames. That equality does not tell us what form ontological reality takes, of course.

To be a scientific mind, it's imperative to differentiate between what can be known, and what can't.

So the way I'd prefer to view this topic is that the only relevant (philosophical) difference is whether or not relativistic simultaneity is to be taken as representing an observational limit (because systems only synchronize using fastest information speed available), or ontological limit. (real existence).

If you are familiar with Einstein's paper, you probably know he very much emphasized the observational limit factor, but did not explicitly claim this way or another in ontological sense. That is why it could be argued it is more philosophically neutral.

In Minkowski's view relativistic simultaneity represents ontological limit, which requires static reality. Unlike Special Relativity.

In my opinion it is little bit silly to claim that static reality is philosophically more elegant idea than a dynamic one, and it is harmful that so many people believe this is the only option we have, because they believe Minkowski = Special Relativity. When they do, they close their eyes from possibilities that exist well within Special Relativity, but not within Minkowski (Exactly what @Sunil was pointing out) -Anssi

 

[AnssiH]

The only difference for Lorentz version is that there is a specific state to reality - we just can't probe what it is.

If by "state" you mean "preferred frame" or "preferred set of surfaces of simultaneity", this is correct.

Basically yes, but want to comment still that I'd greatly prefer if people think of this from the perspective of "what does relativistic simultaneity represent". That's why I am drawing attention to the question; "is there some real state to reality before we can see it".

If one assumes there is - we just can't probe what it is because we can't know C - then they are assuming the core philosophy of Lorentz.

If one assumes there is not - actually the state of reality around us is a static spacetime block and our conscious experience is an illusion concocted by how mind works - then they are assuming the core philosophy of Minkowski.

It just blows my mind that so many people tacitly believe the latter is the only option we logically have

-Anssi

 

[Fra]

Your 'question' would be, why is the c from that derivation finite. There are many experimental and theoretical reasons why it is the speed of light, but it does not answer why nature chose that. I have no idea, except, of course, what future research may turn up.

I have convinced myself of some intuitive abstractions sufficient to guide me forward, but from there to work out the explicits is a big step. But my hunch is that the reasons for the upper bound of "change", is related to the lower bound of action even in a constructive approach. Constructing "inside measures" it seems natural than any agent, has upper and lower bounds. Because the agents information and processing capacity is limited. This is why distinguishing arbitrary high rates of change, would violate the "capacity" of the agent.

Think about it, intuitively, to confidently infer and big change, is the same thing as the confidently infer something a priori improbable. This implies a tension. Because "big change" means a high information divergence, and in terms of spacetime, space is ORDERED as per som locality principle. Anything that distorts this, would likely also eventualyl distort spacetime. It's not hard to imagine, that for an angent here has to be a kind of uncertainty relation between the confidence in an improbable observation, and the a confidence in the prior. Ie, there is an inertia at play here, that means that a finite agent, can not my arbitrary confidence inferences and still survive. So then considering the asymptotic limit where agents are supposed to be stable, one gets the observer equivalence.

To me the problem is to find the right mathematical or algorithmic abstractions needed to turn this into a proper model, and then figure out how to solve it. Right now I am leaning towards Agent based models as the most natural ones for modelling "interacting theories".

So I feel associating the two constants as principal level as RUTA does makes sense, as i think they are related even in the constructive approach (if anyone would suceed)

/Fredrik

 

[AnssiH]

It is on-topic in a historical context. I always thought it assumed Galilean relativity and the Lorentz Transformations are a mere appearance due to the shortening of objects as they move through the aether. However, that will be way off-topic in this thread, and I think it would best be taken up on the Relativity subforum. All predictions are equivalent to SR - but the reason is completely different. This may be due to confusion between the existence of a preferred frame and LET, where the aether is assumed to have certain properties. From a historical perspective, that would be interesting to get to the bottom of.

Yeah that's an astute observation - I think the topic is possibly muddied up by various ideas of assigning properties to ether that may not have anything to do with the core issue of "nature of simultaneity". Indeed the only difference logically is than in LET you just assume some universal frame and stick with it.

Now this could be half a step off-topic as well, but I think philosophically interesting point to think about. People usually view Big Bang theory from General Relativistic perspective where the idea is that reality started from a spacetime singularity, and when things cooled down enough, the universe became transparent. The remnant of this event being of course cosmic microwave background radiation.

The idea implies that at some point of time all of universe was plasma sitting roughly in single reference frame, and starting from the singularity would have roughly cooled down to transparent state simultaneously everywhere. Which is the explanation why CMBR is still today emanating - roughly - from single magical frame (all the images of CMBR you see are actually synthetically corrected to remove the doppler shift contribution of the motion of Earth and our galaxy).

So within that theory I would say that it would be perfectly reasonable to assign "universal simultaneity" to our ability to measure the simultaneity of the cooling of "all of reality" (in that popular interpretation). I mean the basis of this philosophy was "if we can't measure it, it doesn't exist". Well, if all we can measure sat in a single frame, then "no other frames exist" is the stripped down philosophy you'd get.

Cheers,
-Anssi