Confused by nonlocal models and relativity

[PeterDonis]

But then "beable" is something outside of the natural sciences, referring to someting that cannot be observed and thus not tested by observations.

If that's your opinion, that's fine. And what that means, as I have already pointed out to you in previous discussions, is that you should simply not post in threads like this one, where other people who do not share your opinion want to discuss these things. Continuing to post that you, personally, don't see any point to these discussions does nothing but clutter up the discussion. Please stop doing it.

 

[gentzen]

But then "beable" is something outside of the natural sciences, referring to someting that cannot be observed and thus not tested by observations.

Yes, it is something in between the mathematical theory, and the application of the theory to observations in experiments (or the application to the physical world more general).

 

[vanhees71]

So it's still undefined...

 

[A. Neumaier]

An observable usually doesn't take a determined value. Nevertheless the observable always exists as an objective property

No, it exists only as a label, not as a property. Any two electrons have momentum (the same label), but if you ask how they differ (on the theoretical level) in momentum you cannot tell. Whereas a classical particle has momentum as a property, which depends on the state of the particle.

as far as I understand Bell wanted to express something within quantum theory with his word "beable".

From the reprint collection Speakable and unspeakable in quantum mechanics by Bell, Section 7: The theory of local beables (his italics):

The terminology, be-able as against observabe, [...]

The concept of 'observable' lends itself to very precise mathematics when identified with 'self-adjoint operator'. But physically, it is a rather wooly concept. It is not easy to identify precisely which physical processes are to be given the status of 'observations' and which are to be relegated to the limbo between one observation and another. [...] the beables, which can be described in 'classical terms', because they are there. The beables must include the settings of switches and knobs on experimental equipment, the currents in coilsm and the readings of instruments. 'Observables' must be made, somehow, out of beables.

Thus a beable is something that can be described in classical terms.

Quantum mechanics has therefore in the minimal statistical interpretation no beables except for the measurement results.

More beables are supplied in the thermal interpretation by declaring the N-point functions beables (without change to the quantum formalism), and in Bohmian mechanics by inventing additional particle trajectories.

Our discussion again just demonstrates that this word is not sharply defined at all.

Bell gives a quite clear demarcation from the notion of observable.

 

[vanhees71]

No, it exists only as a label, not as a property. Any two electrons have momentum (the same label), but if you ask how they differ (on the theoretical level) in momentum you cannot tell. Whereas a classical particle has momentum as a property, which depends on the state of the particle.

You can tell, how they differ in momentum. Knowing the state ##\hat{\rho}(t)## (in the Schrödinger picture for definiteness) you can calculate the probability density ##P(t,\vec{p})=\langle \vec{p}|\hat{\rho}|\vec{p} \rangle##. It's well defined, how these distributions differ for differently prepared electrons.

From the reprint collection Speakable and unspeakable in quantum mechanics by Bell, Section 7: The theory of local beables (his italics):

Thus a beable is something that can be described in classical terms.

Quantum mechanics has therefore in the minimal statistical interpretation no beables except for the measurement results.

Then Bell simply has an even more instrumentalist point of view than the statistical interpreter: Only fixed macroscopic measurement results are "beables". I can live easily with this, because that's finally indeed all we can objectively say about an "observed" system ;-).

More beables are supplied in the thermal interpretation by declaring the N-point functions beables (without change to the quantum formalism), and in Bohmian mechanics by inventing additional particle trajectories.

Then it's again a vague notion and it contradicts the above very clear statement you quote from Bell's book: also something that cannot in any way be made concrete as a "pointer reading" in a measurement, i.e., the ##N##-point functions of, e.g., ##\langle \hat{A}_{\mu}(x) \hat{A}_{\nu}(y) \cdots \hat{A}_{\rho}(z) \rangle## in QED, which is a gauge-dependent quantity and as such not observable in any way, i.e., you cannot in any way "depict" it as "pointer readings" of any measurment device.

Bell gives a quite clear demarcation from the notion of observable.

Maybe I should read this again. Perhaps I understand it better now ;-).

 

[A. Neumaier]

You can tell, how they differ in momentum. Knowing the state ρ^(t) (in the Schrödinger picture for definiteness) you can calculate the probability density P(t,p→)=⟨p→|ρ^|p→⟩. It's well defined, how these distributions differ for differently prepared electrons.

OK. Then the probability density of the momentum is a beable in Bell's sense! It exists independent of any measurement.

The probability density of the position is another beable. Whereas the joint probability density of position and momentum is not a beable, because it does not exist!

Then Bell simply has an even more instrumentalist point of view than the statistical interpreter: Only fixed macroscopic measurement results are "beables".

... in the minimal statistical interpretation.

Therefore he asks for better interpretations where more is possible, and therefore has in some papers a bias in favor of Bohmian mechanics.

I can live easily with this, because that's finally indeed all we can objectively say about an "observed" system ;-).

Then it's again a vague notion and it contradicts the above very clear statement you quote from Bell's book:

Not if one adopts a nonminimal interpretation.

which is a gauge-dependent quantity and as such not observable in any way,

That's what Bell in the chapter I cited, explicitly says (p.53):

For example, in Maxwell's theory the beables local to a given region are just the fields E and H, in that region, and all functionals thereof.

Maybe I should read this again. Perhaps I understand it better now ;-).

Yes, its worth getting a clear view of what he meant by beables, since it is, in my opinion, an important concept.

 

[bhobba]

All semantic difficulties are absent if one thinks of particles not as little balls but as excitations of fields.

Yes. I am sure Bell knew it as well, which is rather interesting. Maudlin argues that the term “quantum theory” is a misnomer - he thinks it is just a mathematical formalism. Physically, it is the limiting case of QFT. Fields have energy and momentum, so I have never understood how they can not be real. But perhaps I am missing something.

Thanks
Bill

 

[Lord Jestocost]

I never could figure out, what Bell intended to mean by creating this playful world "beable".

The following might be of help:

"1. The primitive ontology theories of quantum mechanics

Suppose that there is matter distributed in three-dimensional space or four-dimensional spacetime and that the task of physics is to develop an account of matter and its temporal development (plus an account of space and time themselves). If one endorses this supposition in the context of quantum physics, one is committed to what is known as a primitive ontology.¹ The ontology is primitive in the sense that it cannot be inferred from the formalism of textbook quantum mechanics (QM), but has to be put in as the referent of that formalism. The motivation for doing so is to obtain an ontology that can account for the existence of measurement outcomes – and, in general, the existence of the macrophysical objects with which we are familiar before doing science. Hence, what is introduced as the primitive ontology has to be such that it can constitute measurement outcomes and localized macrophysical objects in general. That is why the primitive ontology consists in one actual distribution of matter in space at any time (no superpositions), and the elements of the primitive ontology are localized in space-time, being “local beables” in the sense of Bell (2004, ch. 7), that is, something that has a precise localization in space at a given time.²" [Bold by LJ]

Quoted from section #1 in “The primitive ontology of quantum physics: guidelines for an assessment of the proposals” by Michael Esfeld (Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 47, August 2014, Pages 99-106)

 

[Fra]

the primitive ontology consists in one actual distribution of matter in space at any time (no superpositions), and the elements of the primitive ontology are localized in space-time, being “local beables” in the sense of Bell (2004, ch. 7), that is, something that has a precise localization in space at a given time.²" [Bold by LJ]

With this definition, one presumes the notion of spacetime in the first place, as som background where these beables are. So the question is, how does this choice of primitive ontolgies get along with a relational view of spacetime?

I think it's quite clear that some kind of primitive ontolgy is necessary. But a the usefulness of a primitive ontology that assumes a spacetime index that we today expect to be dynamical and relational is questionable I think.

Can one find anopther "primitve notion" that serves the same purpose, but that does not build on 4D-spacetime as pre-existing?

/Fredrik

 

[Fra]

But then "beable" is something outside of the natural sciences, referring to someting that cannot be observed and thus not tested by observations.

As I see it, I think in a scientific context or a learning perecptive, "primitive ontologies" serve as a kind of initial assumpton, or axiomatic starting point, for a structure of the theory. Without a starting structure one can not even formulate questions or experiments. If this theory then fails to be helpful in exploring nature, or makes bad predictions, then perhaps some of the structure of the theory, and the primitive ontrologies, are not fit to describe nature, then these should be discarded, due to reasons of not useful, rather than "falsified".

For this reasons, I think good primitive ontologies should be somewhat "minimal", and as of 2023, an ontology that builds on existenace of a spacetime, where the beables are located, seems to me very far from minimal. And possibly also not very fit.

/Fredrik

 

[vanhees71]

Then all of (general) relativistic physics is "not very fit"?

 

[gentzen]

With this definition, one presumes the notion of spacetime in the first place, as som background where these beables are. So the question is, how does this choice of primitive ontolgies get along with a relational view of spacetime?

To assume some notion of spacetime is probably one of the motivations for beables in the first place. To physically exist (or "to be") typically means to exist in a certain spacetime region.

 

[A. Neumaier]

as of 2023, an ontology that builds on existenace of a spacetime, where the beables are located, seems to me very far from minimal. And possibly also not very fit.

You shouldn't mistake speculations about the Planck structure of spacetime for solid science. All successful predictive physics of today (as of 2023) assumes that spacetime exists!

 

[vanhees71]

On the other, I think one of the obstacles to find a satisfactory quantum theory of the gravitational interaction that it is so closely related to the general-relativistic dynamical spacetime model, i.e., for a "quantization" of the general-relativistic interaction it is likely that one needs a "quantization" of spacetime itself. On the other hand the concrete realization of the successful quantum theories for matter and their interactions except gravitation hinges on the given (symmetry) structure of the corresponding spacetime models (i.e., the Gailei group for non-relativistic QM and the proper orthochronous Poincare group for relativistic QFT). It seems plausible that these "classical" spacetime models are an effective description in the sense of an emergent phenomenon, if one likes to include the gravitational interaction with its close relation to the spacetime model of GR (or most probably rather some extension like Einstein-Cartan theory to enable the description of particles/fields/matter with spin) into a full quantum description.

 

[Fra]

All successful predictive physics of today (as of 2023) assumes that spacetime exists!

Yes, but none of them have unfied all interactions in a satisfactory way. They are successful and corroborated in their relevant domains. Extrapolating successful structures from microscopic physics to cosmology, or extrapolating successful structure from cosmology down to microphysics is itself a speculation.

But we know that right now it's not an experimental problem, but a conceptaul and theoretical and partly technical one, as alot of the divergences that plauged some theories come from assuming continuum structures all the way down.

I am of course not disputing the existance of large scale spacetime, but the question is still why it's 4D? There is only reason reason for questioning a primitive notion of spacetime in the foundations, and it's not to deny the macroscopic spacetime, it's to maybe seen a better understanding of it's origin. Also the explanation of spacetime (GR) and QM are superficially hard to mix. So I just think we can have an open mind and avoid notions that contains implicit assumptions.

Im not necessarily advocating some specific thing here, but just note that the choices of "primitives" forms what we can build naturally with the theory.

/Fredrik

 

[A. Neumaier]

Yes, but none of them have unfied all interactions in a satisfactory way.

Neither have any of the speculative ideas that change the structure of spacetime;
they work successfully in no domain at all.

In such a case what has worked is much to be preferred.

I am of course not disputing the existance of large scale spacetime, but the question is still why it's 4D?

Large scale spacetime is known to be 4D by thousands of years of observation.

 

[Fra]

Then all of (general) relativistic physics is "not very fit"?

Not sure what you associated to here? If you mean that GR assumes the 4D manifold? But GR explains the large scale phenomena, and there are many important differences that may defend the notion of spacetime in GR, as compare to foundations of QM.

No ONE agent/"observer" can observer the whole manifold! In GR spacetime is just defined by the relations between "hypothetical observers" as Einstiein made us of all the time. Or how their observations are related. To describe this can't be made with statisticla methods like in QM, for obvious reasons. There is only once universe, and we don't prepare the universe etc. Its a different paradigm.

The questioning I had in mind, is rather the motivation of spacetime and its dimenstionallity in the high energy domain, but we need to understand it in a way that allows for the emergence of the large scale 4D spacetime and gives the right gravitational force as per GR, at least to the extent its numerical accuracy so far.

/Fredrik

 

[Fra]

In such a case case what has worked is much to be preferred.

Fully agreed! Convservative ideas should be tried first....

But if the preferred way seems too thard, one may need to try alternative ways. We don't all have to stand under the same heavily visited lamppost.

Large scale spacetime is known to be 4D by thousands of years of observation.

Yes. I do not dispute this.

/Fredrik

 

[vanhees71]

Neither have any of the speculative ideas that change the structure of spacetime;
they work successfully in no domain at all.

True. That's why this is the one big unsolved foundational problem of contemporary physics. It's not the philosophical quibble about some so-called measurement problem or a question of ontology or whatever speculations but this very clear inconsistency in the description of all known physics.

Of course we have very good fundamental theories with the limited applicability to all (known) matter and the electroweak + strong interactions (relativistic local QFT and the Standard Model) on the one hand and the classical description of the gravitational interaction between macroscopic matter (GR). What lacks is a consistent description in one "unified theory". There's no such thing yet, and unfortunately, also no observational hints at how it might look like. That's why there's no success yet, because usually mathematical speculations without any empirical foundation pointing in the right direction are doomed to fail. Philosophical speculations, never lead to new theories. The best one can say is that the philosophical speculations by EPR et al lead to a scientific solution in terms of Bell's theoretical work with subsequent experimental investigations. I must admit in this case the philosophical quibbles even lead to a new branch of engineering with promising new technologies in sight.

In such a case case what has worked is much to be preferred.

True, from a practical point of view yes. However, if physicists never would have wondered about the inconsistency between Maxwell's equations with the Newtonian spacetime model, there'd be no theory of relativity and no GPS. If nobody would have wondered about the inconsistency of the observed atomistic structure of matter (Rutherford's gold-foil experiment) and classical physics (including Bohr's ad hoc "solution" for the hydrogen atom) nobody had discovered QT, and there'd not be semiconductors and all the nice digital equipment we use right now to communicate in this interesting forum :-). To think about the right open scientific (!) questions on a fundamental level often has brought great progress not only for science but also for engineering. Philsophy,... Well you know what I want to say ;-)).

Large scale spacetime is known to be 4D by thousands of years of observation.

It's indeed pretty suggestive. Today there's indeed not the slightest hint for extra dimensions. On the other hand the gravitational interaction is not very well known at small distance scales. Who knows, what happens there?

 

[Fra]

To assume some notion of spacetime is probably one of the motivations for beables in the first place. To physically exist (or "to be") typically means to exist in a certain spacetime region.

That sounds like a reasonable account of historical development...

But "spacetime" has several purposes and properties, first of all, I think it is just a set of "labels" of something - what this something could be "objects" in a classical newtonian space or maybe "observational events" in the "observational perspective" that QM is based on.

So we then first have something "existing", that we "label" by a set of labels. To assume primitive ontologies is "indexable" seems fair, otherwise we can not distinguish them; would could at best COUNT their occurance.

But when we call this set "spacetime", lots of assumptions of cardinality, ordering, dimensionality or metrics is introduced.

This is for me quite a leap with lots of questions omitted! In the "observer perspective", one can wonder, can't the observer decide to do it's "bookkeeping" any way it wants? Ie. by inventing some arbitrary spaces etc? But "choice" of spacetime, obviously influences the dynamics. Questions like, is 4D spacetime, the choice which makes ther interactions look more simple? IF so, that is a very good answer, but to answer that we should be allowedto question the choice of this spacetime? Now with thew purpose of denying it, but with the purpose of a deeper understanding.

Here again come the mysterious argument of mathematical beauty or "simplicity", but can we understand this is a deeper way? In the observational perspective, like QM or QFT, the spacetime "choice" refers to the background observer, right? So then it seems the simplest possible dynamics, seem to translate into some statement about how two observer describe each other? Ie. how they interact? Which they don't in QM, so why can we pick any crazy "background spacetime" we want, as it's just descriptive? This is the problem. So how are about get passed this obstable if we are stuck in thinkging about mechanical spaces. Replacing "particle" with "field" is marginal improvement.

So can we have a "beable" that we just index in any way we want. Then ask, why would one index be preferred over another? This is the kind of question that is leaped over when using the bell defintion.

/Fredrik

 

[A. Neumaier]

But if the preferred way seems too hard, one may need to try alternative ways.

The alternative ways are where there is light, but the way backed by experiment is much more likely to be the place where the key was lost. Except that there is little light....

We don't all have to stand under the same heavily visited lamppost.

In the last 50 years, most researchers on quantum gravity crowded under various different lampposts, and found nothing. Few researchers search in the region backed by experiment.

 

[vanhees71]

The alternative ways are where there is light, but the way backed by experiment is much more likely to be the place where the key was lost. Except that there is little light....

In the last 50 years, most researchers on quantum gravity crowded under various different lampposts, and found nothing. Few researchers search in the region backed by experiment.

The problem is which region? Is there any empirical evidence of a quantum-gravitational effect?

 

[A. Neumaier]

True. That's why this is the one big unsolved foundational problem of contemporary physics. It's not the philosophical quibble about some so-called measurement problem or a question of ontology or whatever speculations but this very clear inconsistency in the description of all known physics.

What you state is not a fact but your personal opinion.

Quantum gravity and the measurement problem might very well be related and have a common solution!

There's no such thing yet, and unfortunately, also no observational hints at how it might look like.

Except for the measurement problem, where the unique outcome is a very well demonstrated fact without a microscopic explanation!

However, if physicists never would have wondered about the inconsistency between [...]

So we have to wonder about the inconsistency and find and explanation that encompasses the mutually inconsistent theories.

To think about the right open scientific (!) questions on a fundamental level often has brought great progress not only for science but also for engineering. Philosophy,... Well you know what I want to say ;-)).

I spend quite some time on the philosophical issues, because they shed light on conceptual issues that one cannot see when simply accepting the known framework, and these conceptual issues point the ways to possible solutions.

 

[A. Neumaier]

The problem is which region?

The right region is that closest to both canonical relativistic quantum field theory and general relativity, because the solution must recover the two as limiting cases.

I don't claim this is easy. But instead people work for many years on fancy ideas where even recovering one of the two is very hard.

Is there any empirical evidence of a quantum-gravitational effect?

No. Except that the measurement problem hints at certain things to be addressed.

 

[vanhees71]

What has the apparent "measurement problem" to do with finding a viable quantum theory of the gravitational interaction? QT is, as any physical theory, a mathematical description of empirical experience. That a measurement has a unique outcome is simply a primitive empirical experience. It's also empirical evidence that these outcomes of measurements are random, if the system is not prepared such that the measured observable takes a determined value before the measurement (within the accuracy of the measurement device, if you have continuous observables).

 

[A. Neumaier]

What has the apparent "measurement problem" to do with finding a viable quantum theory of the gravitational interaction?

Both are unsolved problems whose solution must lie in the unexplored submicroscopic structure of the universe.

 

[vanhees71]

The problem with the measurement problem is that there is no problem to be solved. It's all described correctly by QT. The problem of finding a viable quantum (field?) theory of the gravitational interaction obviously is that there are no empirical facts one can build on and not a fictitious problem with measurements.

 

[A. Neumaier]

The problem with the measurement problem is that there is no problem to be solved. It's all described correctly by QT.

Correctly but not completely. It is not shown why the unitary quantum dynamics gives rise to unique macroscopic outcomes. This is an open problem that you simply ''solve'' by making the metaphysical assumption of intrinsic quantum randomness. But this is hiding the problem under the carpet, not solving it.

 

[Morbert]

While contributions to quantum gravity by quantum foundations can't be ruled out a priori, I don't see it in recent literature. Is there some recent review that explores potential connections?

You have to bump up against the nomological character of a physical theory at some point. A theory that completely determines future outcome from an initial state + dynamics would not explain why those dynamics are correct, as opposed to some alternative scheme.

 

[gentzen]

While contributions to quantum gravity by quantum foundations can't be ruled out a priori, I don't see it in recent literature. Is there some recent review that explores potential connections?

I guess you are aware of Freeman Dyson's opinion on attempts to quantize gravity.

So the idea that you may not need to quantize gravity got some proponents, for example Sean Carroll
https://www.quantamagazine.org/where-do-space-time-and-gravity-come-from-20220504/

And the answer is, you know, under many assumptions that are not entirely solid yet, but seem completely plausible, the geometry of that emergent space obeys Einstein’s equation of general relativity. Not completely as surprising and dramatic as it sounds, because there’s not a lot of equations it could have obeyed. But the point is that if we follow our nose, if we say we start not with space, but with entanglement, how should it behave? How should it interact? We get to a place where it’s not at all surprising that it has dynamics, that it changes, that it responds to what you and I would notice as energy, and the kind of response is the kind that Einstein had there in general relativity.

and Jonathan Oppenheimer
https://www.quantamagazine.org/the-physicist-who-bets-that-gravity-cant-be-quantized-20230710/

and if you search around, you will probably find many more proponents. You are asking for a survey, so that you don't have to search around yourself, and get a better picture of the reactions to those "don't quantize gravity" bets?

 

[A. Neumaier]

While contributions to quantum gravity by quantum foundations can't be ruled out a priori, I don't see it in recent literature. Is there some recent review that explores potential connections?

For example,

• Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics, 35, 1637-1678.

The paper is not very recent, but has 269 citations in Google Scholar since 2022.

I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the measurement problem) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of observer-independent state of a system, or observer-independent values of physical quantities.

Two recent papers are

• Carroll, S. M. (2022). Addressing the quantum measurement problem. Physics Today, 75(7), 62-63.
• Cavalcanti, E. G., Chaves, R., Giacomini, F., & Liang, Y. C. (2023). Fresh perspectives on the foundations of quantum physics. Nature Reviews Physics, 1-3.

See also my comments from 2017 here (Point 12).

You have to bump up against the nomological character of a physical theory at some point. A theory that completely determines future outcome from an initial state + dynamics would not explain why those dynamics are correct, as opposed to some alternative scheme.

The unification of relativistic QFT and general relativity is already so constrained that any successful unification would count as the most correct one, since it explains the most experiments! The question of assessing alternatives arises only if there are several competing successful unifications.

 

[vanhees71]

Correctly but not completely. It is not shown why the unitary quantum dynamics gives rise to unique macroscopic outcomes. This is an open problem that you simply ''solve'' by making the metaphysical assumption of intrinsic quantum randomness. But this is hiding the problem under the carpet, not solving it.

But there's not the slightest hint that this assumption is not correct. You can speculate a lot, but without empirical guidance unlikely to find more comprehensive theories. It's even not clear, whether there should be such a more comprehensive theory. All the Bell tests speak against it.

 

[Fra]

Few researchers search in the region backed by experiment.

Which specific region would you suggest this is?

I ask because there extrapolation from experimentally accessible domain to the hypothetical domain is rarely unique, it is often dependent on interpretation or in what form you seek the answers.

/Fredrik

 

[A. Neumaier]

But there's not the slightest hint that this assumption is not correct.

Neither is there the slightest hint that your assumption is correct. Both are metaphysical assumptions until someone finds a positive solution.

 

[A. Neumaier]

Which specific region would you suggest this is?

https://www.physicsforums.com/threads/confused-by-nonlocal-models-and-relativity.973876/post-6968312

I answered this already. See also the last paragraph here.