I Nature Physics on quantum foundations

[Demystifier]

I never understood what "beables" should be, if not "observables".

Yes, that's the main obstacle to understand correctly any Bohmian-like theory, even in non-relativistic context.

 

[vanhees71]

It just means violation of Bell type inequalities, since this is the only reason why people say that QM is nonlocal. There is no problem with this meaning.

But then one could simply declare the case closed, i.e., their is no realistic theory at all, because the Bell-type inequalities are violated in precisely the way QT describes (it must be QT, because as a non-relativistic heory QM of course violates relativistic causality).

 

[Demystifier]

their is no realistic theory at all

Now, what do you mean by "realistic"? I hope you don't mean the opposite of probabilistic.

 

[Demystifier]

I said convincing! I never understood what "beables" should be, if not "observables". I want of course a physical argument and theory and not some philosophical gibberish.

By that definition of "convincing", even Bohmian mechanics for non-relativistic QM should be unconvincing for you. Since you don't understand what "beable" is, you don't understand Bohmian mechanics for non-relativistic QM. To paraphrase Bohr, if you think that Bohmian mechanics for non-relativistic QM is convincing, you misunderstood it.

 

[A. Neumaier]

But then one could simply declare the case closed, i.e., their is no realistic theory at all, because the Bell-type inequalities are violated in precisely the way QT describes (it must be QT, because as a non-relativistic heory QM of course violates relativistic causality).

No. There are realistic foundations - such as my thermal interpretation - that respect Bell-type inequalities exactly, but violate other assumptions in Bell's reasoning.

 

[vanhees71]

By that definition of "convincing", even Bohmian mechanics for non-relativistic QM should be unconvincing for you. Since you don't understand what "beable" is, you don't understand Bohmian mechanics for non-relativistic QM. To paraphrase Bohr, if you think that Bohmian mechanics for non-relativistic QM is convincing, you misunderstood it.

No, Bohmian mechanics within non-relativistic QM makes sense as a non-local deterministic theory. Maybe I misunderstood it, but I also never understood anything what Bohr wrote ;-)).

 

[Demystifier]

No, Bohmian mechanics within non-relativistic QM makes sense as a non-local deterministic theory.

But in that theory, Bohmian particle positions are beables and not observables. How does it make sense to you?

 

[vanhees71]

What are beables? I indeed think that Bohmian mechanics doesn't add anything in understanding Nature from the point of view of a natural science. It's only an example for a deterministic non-local theory, which is in agreement with non-relativistic quantum mechanics.

 

[ohwilleke]

There is empirical evidence for randomness, but not for its irreducibility. The latter cannot be empirical since it is an intrisically theoretical question!

Of course, it is virtually impossible to distinguish a deterministic system that is chaotic in the mathematical sense (i.e. with evolution of the system being highly sensitive to tiny changes in initial conditions such as Planck scale differences in locational in space-time) from a genuinely random one.

 

[martinbn]

In what sense would such hypothetical theory be "non-local", if there are no causal connections between space-like separated events?

Something I still cannot make sense of is "causally connected events, which are spacelike seperated". What does it mean!?

 

[ohwilleke]

Something I still cannot make sense of is "causally connected events, which are spacelike seperated". What does it mean!?

The converse is easier to express. In a local theory ever event that causes another event is connected by interactions that take place at the same place in space.

For example, in quantum electrodynamics, a charged particle emits a photon at a particular place, then the photon travels to someplace where it is absorbed by another charged particle at a particular place. The photon interactions with the charged particles are "contact interactions" at the same place. If something doesn't touch any other particle then nothing happens and it continues on its merry way without anything happening.

Something in point X can't instantly affect something at point Y.

Of course, something can randomly happen at point X at the same time that something randomly happens at point Y, but what is happening at point X can't cause what is happening at point Y at the same time, in a local theory.

A non-local theory is a theory that does not satisfy this definition of "local".

"Space-like separated" is a turn of phrase that reflects the notion that two events happening "at the same time" in common sense language, is actually observer dependent in special relativity, that seeks to solve the fact that the common sense language of "at different places at the same time" isn't quite accurate by using a phase defined in a way that overcomes that technical difficulty in the common sense way of thinking about it. The notion that two thing are "in the same place at the same time", however, is well-defined in special relativity. So, the term "space-like separated", which means "not in the same place at the same time", solves this problem.

 

[Fra]

What are beables?

I think the the more interesting explanations from a Bohmist is from then Demysitifer probably had a "bad day" and wrote this...

Solipsistic hidden variables​

It actually gives a sensible take on "hidden variables" / beables.

I indeed think that Bohmian mechanics doesn't add anything in understanding Nature from the point of view of a natural science.

I said convincing! I never understood what "beables" should be, if not "observables".

There exists a conceptual problem also with "observables", namely that it is corresponds to something an interacting population of "agents" (we can call this the domain of classical reality) can agree upon, by means of a symmetry operation relating their perspectives (in case of SR for example). This may seem good and not a problem, but the problem is that it presumes the unique existence of such symmetries and set of elements.

Here the "beable" potentially corresponds to facts known to the single agent only (ie solipsist HV), but for various reasons they can not be shared, copied etc without beeing compromised. These facts can be argue are not less "real", and can be the result of "measurements" by the specific agent, they are however not "objective", and they can not be represented by "observables".

Beables here, serves a purpose observables do not, even from the point of view of inference and scientific development, because even if the consencus and the negotiated facts in science are a goal, their emergence needs to be "explained" but the interacting pieces of evidence. In such abstractions, observables are a blunt tool. Objective yes, but blunt.

/Fredrik

 

[vanhees71]

Something I still cannot make sense of is "causally connected events, which are spacelike seperated". What does it mean!?

That's a contradiction to the causality structure of relativistic spacetime models and thus must not occur. That's the very point here. For me at the current status of knowledge the correct quantum description of everything except the gravitational interaction is local (i.e., microcausal) relativistic QFT, and given that conjecture what's ruled out of Bell's assumptions about a realistic local HV theory is realism since as any QT also QFT implies that there's no discpersion free state, i.e., in any state a quantum system can be prepared in some observables don't take determined values, but at the same time it's "local" in the sense of microcausality.

So what's left as an alternative to QT are non-local HV theory, i.e., one would have to either construct a Poincare covariant non-local theory that obeys the causality principle (which obviously is very difficult since nobody has come up yet with such a model) or the proof of a no-go theorem, i.e., that such a construction cannot exist.

 

[vanhees71]

I think the the more interesting explanations from a Bohmist is from then Demysitifer probably had a "bad day" and wrote this...

Solipsistic hidden variables​

It actually gives a sensible take on "hidden variables" / beables.
There exists a conceptual problem also with "observables", namely that it is corresponds to something an interacting population of "agents" (we can call this the domain of classical reality) can agree upon, by means of a symmetry operation relating their perspectives (in case of SR for example). This may seem good and not a problem, but the problem is that it presumes the unique existence of such symmetries and set of elements.

Here the "beable" potentially corresponds to facts known to the single agent only (ie solipsist HV), but for various reasons they can not be shared, copied etc without beeing compromised. These facts can be argue are not less "real", and can be the result of "measurements" by the specific agent, they are however not "objective", and they can not be represented by "observables".

Beables here, serves a purpose observables do not, even from the point of view of inference and scientific development, because even if the consencus and the negotiated facts in science are a goal, their emergence needs to be "explained" but the interacting pieces of evidence. In such abstractions, observables are a blunt tool. Objective yes, but blunt.

/Fredrik

I read about "beables" in Bell's papers as well as on scholarpedia about Bell's theorem:

http://www.scholarpedia.org/article/Bell's_theorem

I don't understand, what the difference between observables in the usual sense of the word and "beables" should be. From Bell's example from classical electrodynamics that the electromagnetic field is a "beable" within this theory but the electromagnetic potential is not, I can only conclude that "beables" are synonymous to "observables", i.e., a quantity within the theory which represents observables in the sense that this quantity is uniquely determined by the physical situation that is described. Gauge-dependent quantities in a gauge theory, i.e., a theory where some elements (here the electromagnetic four-potential) are not uniquely determined by the physical situation described, cannot represent observables.

What I'm also not clear about is, what Bell considers a "beable" in QT. Are all self-adjoint operators representing observables in QT "beables"? I'd not say so, because these operators are not uniquely determined since you can always make an arbitrary (even time-dependent) unitary transformation of states (represented by the statistical operator of the system) and these operators that represent observables. In my understanding what should be "beables" (or "observable quantities") within QT are the probabilities/probability distributions for the measurement of sets of compatible observables since this is the meaning of the formalism and this is what can be observed on the system (or rather ensembles of equally prepared systems) and thus represents an objective description of the corresponding properties of the system.

 

[Demystifier]

Are all self-adjoint operators representing observables in QT "beables"?

No. An operator cannot be a beable. In non-relativistic Bohmian mechanics, for instance, the actual particle position is not an operator. Hence it is not an observable, but is a beable.

In standard QM you can associate a number by an operator, for example as an eigenvalue or a mean value of that operator in a given state. A beable can also be thought of as a way to associate a number with an operator, but in general this number may differ from both eigenvalue and mean value. However, not all observables need to have an associated beable. In non-relativistic Bohmian mechanics only positions have associated beables. Other observables such as momentum, Hamiltonian and spin do not have associated beables.

 

[vanhees71]

That doesn't help me. My question is, what does "some abstract construct of the theory is a beable" mean within QT. That Bohmian trajectories are not observable on a single particle is clear, but what then does it mean physics-wise that they are "beables"? For me it's just a superfluous philosophical gibberish to confuse the subject even more than it has been confused by other philosophy-inclined physicists (most notably Heisenberg and Bohr ;-)).

 

[Demystifier]

My question is, what does "some abstract construct of the theory is a beable" mean within QT.

By abstract you probably mean mathematical. There is no mathematical definition of the general notion of "beable". In that sense it's a philosophical concept that sounds like gibberish to you. But in every sentence you (or anybody else) write in English there are many words which are not defined mathematically, and yet you don't complain that they are philosophical gibberish. For example, from your last post the words "help", "me", "my", "question", "abstract", "construct", ... are all notions without a precise mathematical definition. Are they gibberish? Not for you. Likewise, the word "beable" is not gibberish for many people, despite the fact that it's not defined mathematically. If you want to understand that word, try to understand it non-mathematically, just like you understand "help", "me", "my", "question", "abstract", "construct", etc. non-mathematically.

 

[vanhees71]

I keep Einstein's advice about theorists: "Don't listen to their words. Look at their deeds." An empty phrase like "beable" doesn't help to understand what Bell wants to say. Looking at his math, defining what a "local realistic theory" is, is sufficient to understand the "hard content" of his work on EPR.

 

[Demystifier]

I keep Einstein's advice about theorists: "Don't listen to their words. Look at their deeds."

But this advice itself is words, not deeds. Hence this advice can only be followed by not following it.

 

[Demystifier]

Looking at his math, defining what a "local realistic theory" is, is sufficient to understand the "hard content" of his work on EPR.

But understanding the "hard content" of the Bell's work without its "soft content" is very incomplete.

 

[Peter Morgan]

I keep Einstein's advice about theorists: "Don't listen to their words. Look at their deeds." An empty phrase like "beable" doesn't help to understand what Bell wants to say. Looking at his math, defining what a "local realistic theory" is, is sufficient to understand the "hard content" of his work on EPR.

I have an appendix about beables in my paper in JPhysA 2006, "Bell inequalities for random fields", https://arxiv.org/abs/cond-mat/0403692 (DOI there).

I don't want to claim this is definitive, particularly because I was parenthetically facetious at the end of the second paragraph, but I think it's still pretty close to how I feel about the question. As far as I've ever seen, Bell's use of beables is in practice always associated with probabilities. I'd be glad of pointers to other stuff.

 

[vanhees71]

So I'm not alone in my question, what beables actually are meant to be. Bell's examples don't tell me, what he means this word to mean, particularly not in the obviously intended use in the connection with QT. You express my question very precisely at the end of the quoted appendix:

It is not quite clear what we should take the common feature
of these examples to be, except perhaps the odd behaviour (the electromagnetic potential is
guilty only of ‘funny behaviour’), which is the signal for mathematics to be taken to be only
a convenience instead of real.

 

[vanhees71]

Another thought: As you also mention in your appendix, Bell also says "the wave function" were not a beable. Is this because only its modulus squared is one (or in the abstract Dirac formalism, it's not the "state ket" that represents a pure state but only the corresponding statistical operator, i.e., the projector $|\psi \rangle \langle \psi|$ or equivalently the "unit ray") or is it, because it doesn't describe anything referring to a single actual quantum system but only a probability (distribution), which refers only to an ensemble of (equally prepared) systems? On the other hand Bell seems to be a Bohmian, and @dextercioby mentioned above that the Bohmian trajectories are beables though they are not observables, and as far as I understand the Bohmian standpoint the Bohmian trajectories refer to a single system. In this sense it may be a beable, but if it isn't observable, what's then the status of a "beable" as a physical property of a system? I can claim a lot of things to be a "beable", but if I can't observe it, it's not subject to the scientific method of testing it's meaning by observation.

 

[Fra]

I don't understand, what the difference between observables in the usual sense of the word and "beables" should be.

If we take Bells ideas as the definition of beable, then it becomes hard to guess of course. When interpreting them in the light of today perhaps he turns in his grave, who knows. I hope he is forgiving.

But I have within my own understanding always entertained the a notion of what relates to the agents state; which in turn can be understood as a result of it's own interactions/measurements on it's environment. I have then realized that this is strongly related to the notion of beable, but I have a very different context. Demystifiers solipsist HV, resonates fine with this.

From Bell's example from classical electrodynamics that the electromagnetic field is a "beable" within this theory but the electromagnetic potential is not, I can only conclude that "beables" are synonymous to "observables", i.e., a quantity within the theory which represents observables in the sense that this quantity is uniquely determined by the physical situation that is described. Gauge-dependent quantities in a gauge theory, i.e., a theory where some elements (here the electromagnetic four-potential) are not uniquely determined by the physical situation described, cannot represent observables.

In my view, the definition of what are beables is observer dependent. So I don't think Alices beables are not beables of Bob. Yet one can entertain the idea that the beables are their respective "locally encoded facts", they "just are" as I think Bell puts it. But that does not (I think) necessarily mean they are inexplicable! I consider them to be a result of a series of "local", agent-perspective measurements, that does NOT necessarily store their results in classical (public to the agent community) pointer variables. They are stored only in the agents state. (thus solipsist HV). One can think of they as definitely REAL (ontological), but this ontology is not inferrable to other agents, in the way can one copy classical information. This is my take on this. So since a few years, I found this "similarly" between my thinking which is at the almost opposite camp of hidden variable theories, to actually be compatible with this.

Observables OTOH, are defined by measurements attached in the classical domain, where agents can agree and share information, but this information (ie the whole equivalence class and it's structure and symmetries) are I think invisble to the agent itself.

Beable could then related to "intrinsic" measurements (by an agent), and observables can be related to "extrinsic" measurments (say by the classical collective of agents). I think that value of the beable, is that the interaction of beables has the potential to explain the emergence of observables.

/Fredrik

 

[Peter Morgan]

Another thought: As you also mention in your appendix, Bell also says "the wave function" were not a beable. Is this because only its modulus squared is one (or in the abstract Dirac formalism, it's not the "state ket" that represents a pure state but only the corresponding statistical operator, i.e., the projector $|\psi \rangle \langle \psi|$ or equivalently the "unit ray") or is it, because it doesn't describe anything referring to a single actual quantum system but only a probability (distribution), which refers only to an ensemble of (equally prepared) systems? On the other hand Bell seems to be a Bohmian, and @dextercioby mentioned above that the Bohmian trajectories are beables though they are not observables, and as far as I understand the Bohmian standpoint the Bohmian trajectories refer to a single system. In this sense it may be a beable, but if it isn't observable, what's then the status of a "beable" as a physical property of a system? I can claim a lot of things to be a "beable", but if I can't observe it, it's not subject to the scientific method of testing it's meaning by observation.

I'm pretty prejudiced about this, I'm afraid. I'm completely focused on how Bell uses beables in the argument in his article "The theory of local beables", using probabilities, and in the various articles where he rediscusses that argument in the light of Shimony's and others' introduction of what we would today call superdeterminism. As he used beables in those arguments, there is always a probability measure, which makes his usage effectively a classical equivalent of a quantum field, which we might call random-variable-valued distributions, or, as I do, using a pre-existing name in the mathematics literature, a random field.
Although Bell discusses Bohmian trajectories in many places because it's clearly a mathematically reasonable approach, my understanding is that he was enough of a field theorist in his CERN-influenced heart of hearts that he wanted a field theoretic approach and was dissatisfied with what could be done with Bohm's approach applied to quantum fields? For Bohmian trajectories, the particle positions in configuration space seem to me to be perfectly good beables, but they seem never to have been entirely palatable to Bell? Anyway, I have always been somewhat dissatisfied with configuration space as a theater for beables even though it is mathematically reasonable.

 

[Demystifier]

I can claim a lot of things to be a "beable", but if I can't observe it, it's not subject to the scientific method of testing it's meaning by observation.

You are right, it's meaning cannot directly be tested by observation. Beable is a tool for thinking. It is natural for a human mind to think that physical "things" exist even when we don't observe them, and "beable" is a concept referring to exactly such things. It is nevertheless "scientific", in the sense that at least some scientists find it useful in thinking about science. For example, I like to think that the Moon has a round shape even when it isn't observed, so for me the shape of the Moon is a beable. Perhaps you, on the other hand, prefer to think that the Moon has no shape when it's not observed (the shape is not a conserved Noether charge), so for you the shape of the Moon is not a beable.

 

[Demystifier]

I have always been somewhat dissatisfied with configuration space as a theater for beables

Why?

 

[vanhees71]

In my view, the definition of what are beables is observer dependent. So I don't think Alices beables are not beables of Bob. Yet one can entertain the idea that the beables are their respective "locally encoded facts", they "just are" as I think Bell puts it. But that does not (I think) necessarily mean they are inexplicable! I consider them to be a result of a series of "local", agent-perspective measurements, that does NOT necessarily store their results in classical (public to the agent community) pointer variables. They are stored only in the agents state. (thus solipsist HV). One can think of they as definitely REAL (ontological), but this ontology is not inferrable to other agents, in the way can one copy classical information. This is my take on this. So since a few years, I found this "similarly" between my thinking which is at the almost opposite camp of hidden variable theories, to actually be compatible with this.

But isn't this the perfectly opposite interpretation of "beable" to what Bell intended when introducing this word? He insisted on defining the theory without reference to "observers" and "measurements". Of course, I agree with you that this doesn't make sense within minimally interpreted QT, because there is hinges on the state (i.e., the applied preparation procedure in an experiment) whether an observable takes a defined value or not, and the question is, whether a "beable" must be some quantity which takes determined values. Then this would indeed imply that a "beable" can only be an observable which takes a determined value, and thus this would be state dependent, i.e., dependent on the preparation procedure for the system to be measured.

On the other hand it could also be that a "beable" is simply synomymous with "observable". Then it refers to the measurement procedure, and of course one can measure any observable, independent of the state the measured system is prepared in. But then the "beable" is a quantity which does not necessarily take a determined value, i.e., it makes only sense to talk about the probability for the outcome of a measurement of this "beable", but this again contradicts Bell's declared aim that "beables" should be defined as something independent of measurements.

That's the dilemma I'm in in my inability to understand what Bell means with his nice word play, introducing the notion of "beables".

Observables OTOH, are defined by measurements attached in the classical domain, where agents can agree and share information, but this information (ie the whole equivalence class and it's structure and symmetries) are I think invisble to the agent itself.

For me there's no distinction between "classical" and "quantum" domains. The classical behavior of macroscopic objects is due to an effective coarse-grained description of collective observables. E.g., a "classical point particle" never is an elementary particle like an electron but a "macrocopic body", and the position and momentum is something like the center-of-mass position and momentum.

Beable could then related to "intrinsic" measurements (by an agent), and observables can be related to "extrinsic" measurments (say by the classical collective of agents). I think that value of the beable, is that the interaction of beables has the potential to explain the emergence of observables.

/Fredrik

What is an "intrinsic" vs. an "extrinsic" measurement?

 

[Peter Morgan]

Why?

— have I "always been somewhat dissatisfied with configuration space as a theater for beables"?
It's just "somewhat". It's not a deal-breaker for deBB, which, given QM, is perfectly good mathematics, but it's enough that I feel motivated to look for alternatives.
I'm unhappy with nonrelativistic QM in its common axiomatic or textbook constructions because from modern experiments I think we have records of where and when events happened, not of particles and their positions and momenta (with the latter perhaps requiring continuous trajectories for us to construct them), and that reason also applies to deBB. The possibility of transforming the wave function into deBB's configuration space formalism derives from QM's insufficiently considered leap from the properties of events to the properties of particles.
Axiomatic QFT, algebraic QM, and Bell's account of classical physics in "The theory of local beables" associate measurements/beables with regions of space-time, not with specific particles, which I think better aligns with what we might call the raw signal and event data out of experimental apparatus. If we can with certainty derive the existence of particles from the events we record, then fine, but otherwise we should hesitate to put particles (though I won't be telling anyone here something they don't know if I say that usually the word used is "system") into the axioms. For FAAPP* work, however, I'm entirely happy to put tables and chairs and bulk components of an experimental apparatus into the axioms of whatever mathematics we're using.
*That's "For Almost All Practical Purposes", because there are always special cases.

 

[Peter Morgan]

For me there's no distinction between "classical" and "quantum" domains. The classical behavior of macroscopic objects is due to an effective coarse-grained description of collective observables. E.g., a "classical point particle" never is an elementary particle like an electron but a "macrocopic body", and the position and momentum is something like the center-of-mass position and momentum.

Unless I've misunderstood your meaning here, saying that 'there's no distinction between "classical" and "quantum" domains' has you needing, I think, something like my work to justify it. I suppose that for most physicists your lack of distinction must ring false. The traditional no-go theorems —Gleason, Kochen-Specker, and Bell— tell us fairly decisively, I think, that ordinary definitions of classical physics are not able to model experimental apparatus and analysis that can be modeled by quantum physics.
That turns EPR's 1935 question, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" on its head: the answer to "Can Classical-Mechanical Description of Physical Reality Be Considered Complete?" is "No".
I say explicitly that we have to "model experimental apparatus, results, and analysis" because Copenhagen, I think rightly, insists that that the experimental apparatus and results must be communicated classically, which in modern times requires Megabytes or Terabytes of interpersonally and institutionally sharable information, but the analysis of the results often requires us to consider results that are contextual or incompatible (or insert your preferred word here), which ordinary classical mechanics is not able to do in a systematic way. QM models that analysis by using noncommutativity, which ordinary definitions of classical physics are not allowed to use. Here I'll leave it to my recent published papers to fill in how I see how the story develops from there. If you don't like my papers —which you might not because most people say they find them a difficult read— then please publish something better (which, to be clear, I very much want someone to do but if that has to be me in a few years time, so be it), so everyone will nod along when you say 'there's no distinction between "classical" and "quantum" domains'.