Nature Physics on quantum foundations

[A. Neumaier]

there's only emprical evidence for this irreducible randomness, and none against it.

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

 

[vanhees71]

Well, yes, if you believe in a non-local deterministic HV, you are right, and of course one cannot exclude it by the simple fact that nobody has been able to provide a convincing one (in the relativistic case; for non-relativistic QM you can take de Broglie-Bohm as an example).

 

[bhobba]

Well, yes, if you believe in a non-local deterministic HV,

It sort of reminds one of the differences between LET and SR. There is no way to tell the difference experimentally. Still, virtually everyone recognises SR as more elegant, more straightforward and more penetrating to the essence of what is going on - namely, the symmetries of the POR implying up to a constant to be determined by experiment (it turns out to be the speed of light), the transformation between inertial frames. It is like some wit remarked. If I push some antique pen, an educated person would say it was the force I applied that moved it. But if I said no - when I pushed, it was not the force that moved it but the shade of Newton I annoyed by pushing on his favourite pen. You can't prove me wrong - but it is obvious it is a superfluous, unnecessary, even silly assumption and reject it. A deeper analysis boils down to a philosophical discussion of 'simplicity' which we do not do here. It is just noted virtually everyone recognises the force explanation is more straightforward.

Thanks
Bill

 

[Demystifier]

nobody has been able to provide a convincing one

Define "convincing"!

 

[vanhees71]

It sort of reminds one of the differences between LET and SR. There is no way to tell the difference experimentally. Still, virtually everyone recognises SR as more elegant, more straightforward and more penetrating to the essence of what is going on - namely, the symmetries of the POR implying up to a constant to be determined by experiment (it turns out to be the speed of light), the transformation between inertial frames. It is like some wit remarked. If I push some antique pen, an educated person would say it was the force I applied that moved it. But if I said no - when I pushed, it was not the force that moved it but the shade of Newton I annoyed by pushing on his favourite pen. You can't prove me wrong - but it is obvious it is a superfluous, unnecessary, even silly assumption and reject it. A deeper analysis boils down to a philosophical discussion of 'simplicity' which we do not do here. It is just noted virtually everyone recognises the force explanation is more straightforward.

Thanks
Bill

LET is just another interpretation of standard SR. In contradistinction to that there's not even a convincing non-local deterministic reinterpretation of relativistic QT to be discussed about. With convincing I mean a non-local theory that obeys the causality structure of relativistic spacetime, i.e., that there cannot be causal connections between space-like separated events.

 

[bhobba]

Define "convincing"!

That's like 'simplicity' in my post - a philosophical question. There is no right or wrong answer - just what most seem to find simple or convincing.

Thanks
Bill

 

[vanhees71]

For me convincing means to find a non-local (field?) theory that is Poincare covariant and obeying the causality constraint, i.e., that there are no causal connections between space-like separated events.

 

[Demystifier]

For me convincing means to find a non-local (field?) theory that is Poincare covariant and obeying the causality constraint, i.e., that there are no causal connections between space-like separated events.

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

 

[vanhees71]

That's the question! If you want a realistic HV theory in accordance with the measured facts (violation of Bell's inequality) it must be non-local, and the question is whether there is a non-local realistic theory that is Poincare covariant and causal. I think, it's very difficult to find such a theory, but of course I'm not aware of any "no-go theorem" proving that such a theory is impossible.

 

[Demystifier]

That's the question! If you want a realistic HV theory in accordance with the measured facts (violation of Bell's inequality) it must be non-local, and the question is whether there is a non-local realistic theory that is Poincare covariant and causal. I think, it's very difficult to find such a theory, but of course I'm not aware of any "no-go theorem" proving that such a theory is impossible.

The problem is not that it is difficult to find such a theory. The problem is that it is not clear what it even means that the theory is "non-local", if the causal connections between space-like separated events are forbidden. In my view, the kind of theory you would find "convincing" is self-contradictory by definition, because "non-local" in the Bell theorem means existence of causal connections between space-like separated events. I'm sure you would not find convincing something which is self-contradictory, so for you "non-local" must mean something else, but I don't know what.

 

[vanhees71]

Then you say that there is no realistic HV theory at all, and the case is closed. I tend to agree with that since I also don't know, how to construct a non-local theory that obeys the causality constraint. I also don't see any necessity to look for such a model since local relativistic QFT describes all known matter with high accuracy correctly. Of course this Standard Model is incomplete, because it doesn't describe the gravitational interaction.

In field theory it would perhaps be described by a Lagrangian that is not a polynomial of the fields and their derivatives at one spacetime argument and which is not a gauge theory, where you can have such constructions without violating the locality/microcausality of observables (e.g., QED in Coulomb gauge).

As I said, I don't have an idea, whether such a model exists but also don't know whether there's a no-go theorem, which definitely excludes such a possibility.

 

[Demystifier]

Then you say that there is no realistic HV theory at all,

No I don't.

In field theory it would perhaps ... not a gauge theory, where you can have such constructions without violating the locality/microcausality of observables (e.g., QED in Coulomb gauge).

A Bohmian theory of that kind has been constructed, see e.g. my https://arxiv.org/abs/2205.05986
and references therein. The locality/microcausality is not violated for observables, but is violated for beables.

As I said, I don't have an idea, whether such a model exists but also don't know whether there's a no-go theorem, which definitely excludes such a possibility.

As I just said, a model exists.

 

[A. Neumaier]

The problem is that it is not clear what it even means that the theory is "non-local", if the causal connections between space-like separated events are forbidden.

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.

 

[vanhees71]

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. Also in your abstract you already say that it violates Lorentz (and thus also Poincare) covariance. So that's not convincing for me either on a technical level.

 

[A. Neumaier]

"non-local" in the Bell theorem means existence of causal connections between space-like separated events.

Not in general, only assuming hidden variables with certain properties...

 

[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.