A How does the thermal interpretation explain Stern-Gerlach?

[charters]

I don't see the problem

Ok, let me try a different route. Consider a basic SG experiment with an N=1 beam. You claim the TI is deterministic. Accordingly, to encode this hidden determinism we should be able to write the state of the experiment *prior* to the detector click as

(|UP>| + |DOWN> ) ⊗ {up}

where the Dirac notation is the normal quantum state and {n} is the state of the hidden variable which deterministically predicts the click. In the TI, I believe {up} and {down} would represent different fine grained distinctions in the configuration of the detector itself (as opposed to BM, where it represents different configurations of the beam).

Do you agree with this description being faithful to the TI so far?

 

[A. Neumaier]

Ok, let me try a different route. Consider a basic SG experiment with an N=1 beam. You claim the TI is deterministic. Accordingly, to encode this hidden determinism we should be able to write the state of the experiment *prior* to the detector click as

(|UP>| + |DOWN> ) ⊗ {up}

where the Dirac notation is the normal quantum state and {n} is the state of the hidden variable. In the TI, I believe {up} and {down} would represent different fine grained distinctions in the configuration of the detector itself (as opposed to BM, where it represents different configurations of the beam).

Do you agree with this description being faithful to the TI so far?

No. The beables (hidden variables) are the collection of all q-expectations of the universe. Given a single spin prepared in a pure state $\psi$ we know at preparation time that for any 3-vector $p$ that the quantity $S(p):=p\cdot\sigma$ of the spin satisfies $\langle S(p)\otimes 1\rangle= \psi^*S(p)\psi$. In your case, this is the sum of the four entries of $S(p)$. Your curly up and down correspond to pointer readings, i.e., functions of q-expectations (beables, hidden variables) of the detector, not to a state of the detector. Many states of the detector lead to identical pointer readings.

This is completely independent of the deterministic dynamics, which is the Ehrenfest dynamics of the universe.

In the most general case we know nothing more, unless we make assumptions a similar kind about the environment, i.e., the state and the dynamics of the remainder of the universe and its interactions with the spin. These assumptions define a model for what it means that this environment contains a detector with a pointer or screen, that responds to the prepared spin in the way required to count as a measurement.

Thus you need to specify a complete model for the measurement process (including a Hamiltonian for the dynamics of th model universe) to conclude something definite. This is the reason why the arguments for analyzing meaurement are either very lengthy (as in the AB&N paper) or only qualitative (as in my Part III).

 

[A. Neumaier]

As I said in my previous post, being deterministic does not imply being superdeterministic. Classical mechanics is not superdeterministic.

In essence a deterministic world where the initial conditions never evolve into states corresponding to observers obtaining an accurate determination of the physical laws.

Do you have different notions of the meaning of superdeterminisitc?

 

[charters]

Your curly up and down correspond to pointer readings, i.e., functions of q-expectations (beables, hidden variables) of the detector, not to a state of the detector. Many states of the detector lead to identical pointer readings

Ok it is possible I just don't get it or you are talking about hidden variables in a way very different from what I am used to. But this may all be semantics around the use of the word "state" so I want to rephrase:

All I am trying to pin down is whether or not the hidden variable descriptions are such that, just before the measurement, all HV descriptions of the detector that will lead to an observable "up" reading (for a particular choice of axis) are completely disjoint/distinct from all the HV descriptions that will lead to an observable "down" reading?

In essence, would knowledge of the hidden variable description of the detector at t<1 allow me to perfectly predict the observed click at t=1?

 

[DarMM]

Do you have different notions of the meaning of superdeterminisitc?

I'm saying:
A superdeterministic world is a deterministic world where the initial conditions never evolve into states corresponding to observers obtaining an accurate determination of the physical laws.

A world can be deterministic without being superdeterministic if the initial conditions permit the development of observers who obtain accurate enough measurements to determine the laws of the world.

So for example in 't Hooft's model Quantum Mechanics is literally completely wrong. Not approximately right but inaccurate in some remote regimes like the Early Universe, but literally completely wrong even in its predictions of say the Stern Gerlach experiment. However the initial conditions of the world are such that experimental errors occur that make it look correct.

 

[A. Neumaier]

would knowledge of the hidden variable description of the detector at t<1 allow me to perfectly predict the observed click at t=1?

I don' think so, because in reading a discrete pointer there is a fuzzy decision boundary. This is like race conditions in computer science which may delay decisions indefinitely. Thus there is a partition into 3 sets, one deciding for spin up, one deciding for spin down, and one for indecision; the third one having positive measure that goes to zero only as the duration of the measurement goes to infinity.

In experimental practice, this accounts for the limited efficiency of detectors.

 

[A. Neumaier]

As I said in my previous post, being deterministic does not imply being superdeterministic. Classical mechanics is not superdeterministic.

A world can be deterministic without being superdeterministic if the initial conditions permit the development of observers who obtain accurate enough measurements to determine the laws of the world.

In a classical Laplacian universe, a Laplacian detector of finite size perfectly knowing its own state can never get an arbitrarily accurate estimate of a single particle state external to it. Thus a classical Laplacian universe would be superdeterministic. Do you mean that, @DarMM, contradicting @stevendaryl?

If so, the thermal interpretation is also superdeterministic, for essentially the same reason.

 

[charters]

I don' think so, because in reading a discrete pointer there is a fuzzy decision boundary. This is like race conditions in computer science which may delay decisions indefinitely. Thus there is a partition into 3 sets, one deciding for spin up, one deciding for spin down, and one for indecision; the third one having positive measure that goes to zero only as the duration of the measurement goes to infinity.

In experimental practice, this accounts for the limited efficiency of detectors.

I don't understand how this answer is consistent with what you wrote in III.4.2, specifically:

"These other variables therefore become hidden variables that would determine the stochastic elements in the reduced stochastic description, or the prediction errors in the reduced deterministic description. The hidden variables describe the unmodeled environment associated with the reduced description.6 Note that the same situation in the reduced description corresponds to a multitude of situations of the detailed description, hence each of its realizations belongs to different values of the hidden variables (the q-expectations in the environment), slightly causing the realizations to differ."

Would your answer be different had I phrased my question as?:

would knowledge of the hidden variable description of the detector plus its local environment (eg, the detector casing or surrounding air in the lab) at t<1 allow me to perfectly predict the observed click at t=1?

 

[A. Neumaier]

I don't understand how this answer is consistent with what you wrote in III.4.2, specifically:

"These other variables therefore become hidden variables that would determine the stochastic elements in the reduced stochastic description, or the prediction errors in the reduced deterministic description. The hidden variables describe the unmodeled environment associated with the reduced description. Note that the same situation in the reduced description corresponds to a multitude of situations of the detailed description, hence each of its realizations belongs to different values of the hidden variables (the q-expectations in the environment), slightly causing the realizations to differ."

Would your answer be different had I phrased my question as?:

would knowledge of the hidden variable description of the detector plus its local environment (eg, the detector casing or surrounding air in the lab) at t<1 allow me to perfectly predict the observed click at t=1?

No. You can take the detector to be the whole orthogonal complement of the measured system, and my answer is still the same. You can also take it to be just the pointer variable; all other beables of the universe are effectively hidden variables, no matter whether they are actually hidden. My first response was less focussed and ignored the race conditions since your question was less clear.

This is because of the nature of a real detection process (which is what is modeled in the thermal interpretation). There is a continuous pointer variable $x$ (a function of the beables = hidden variables = q-expectations, all of them continuous) of the detector that is initially at zero. Suppose that the pointer readings for a decision up are close to $1$, that for down are close to $-1$, and a reading counts as definite only if the sign and one bit of accuracy have persisted for more than a minimal duration $\Delta t$. This defines the three response classes up, down, and undecided. At short times after the preparation, the detector didn't have sufficient time to respond, and the third (undecided) set of conditions has measure essentially 1; the up and down measures are essentially zero. These measures are a continuous function of the observation time and gradually move to $0,p,1-p$, but achieve these values only in the limit of infinite time.

 

[charters]

Ok I appreciate the details, but I don't think this is necessary for the heart of my question. Some finite time after the N=1 beam has become incident on the detector, the pointer is going to visibly have pointed towards 1 or -1. I am not concerned with how quickly this happens.

All I want to know is: would a full hidden variable/beable description of the detector/environment at some time before the beam is incident be sufficient to predict whether the detector eventually reads 1 or -1 (for any given beam).

I take this to be the minimal definition of hidden variable determinism in quantum foundations, so if you say no to this, I don't understand how you claim the TI is deterministic (except in the classical limit where all interpretations are effectively deterministic) or has meaningful hidden variables. Hidden variables that don't make this sort of prediction are not really fulfilling their defined purpose.

 

[A. Neumaier]

the pointer is going to visibly have pointed towards 1 or -1. I am not concerned with how quickly this happens.

or continues to oscillate, or is stuck near zero, due to race conditions. If you ignore this, you ignore a loophole that makes a practical difference - real efficiency is never 100%, and a good model of a deterministic universe must predict this reduced efficiency!

would a full hidden variable/beable description of the detector/environment at some time before the beam is incident be sufficient to predict whether the detector eventually reads 1 or -1 (for any given beam).

It would, in all cases where a definite decision is reached, and it would predict when this is the case.

 

[charters]

It would, in all cases where a definite decision is reached, and it would predict when this is the case.

Ok perfect. So then something you need to explain is how, in an EPR experiment, the hidden variables describing the configuration of detector 1, and (when applicable) predicting the outcome of its measurement, are able to coordinate with the hidden variables doing the same for detector 2, such that Bell violations become possible.

The only known hidden variable solutions to this problem are

A) add a non-local pilot wave that can surgically adjust the local HVs as needed to create Bell violations, while using an absolute definition of simultaneity

B) superdeterminism, where the Bell violations are ultimately just the result of dumb luck in the initial conditions, and entanglement itself is just an illusion of this coincidence.

C) Retrocausality is an option too, but that's not quite a hidden variable approach per se.

But I also get the sense from earlier in the discussion you think its okay to stop short of making this choice and therefore don't need to engage with their perceived downsides in the existing foundations literature. I don't agree, and I expect you'll have a hard time getting folks to adopt (or even know if they'd want to adopt) the TI while not clearly biting one of these bullets. So that's my main point.

(One extra thing I hope for clarity: the idea that Bohmian mechanics has non-local hidden variables is not really accurate. What it has are local hidden variables that receive the benefit of non-local corrections via the pilot wave in order to permit Bell violations. And I don't see how a "non-local" hidden variables interpretation could be anything other than this.)

 

[A. Neumaier]

The only known hidden variable solutions to this problem are

Nothing in your arguments forbids that the thermal interpretation provides an additional, previously
unknown way to achieve that. @DarMM gave in post #268 of the main thread on the thermal interpretation a nice summary of the thermal interpretation, where he addresses this in his point 4.

 

[charters]

Nothing in your arguments forbids that the thermal interpretation provides an additional, previously
unknown way to achieve that. DarMM gave in post #268 of the main thread on the thermal interpretation a nice summary of the thermal interpretation, where he addresses this in his point 4.

I don't agree that what he calls correlator properties in that post can be consistent hidden variable determinism.

A correlator is a conditional of the form: "when subsystem A takes value x, B takes y; when A takes y, B is x". By construction, it requires that there is some uncertainty in the local description of each subsystem.

If such a correlator description is complete, the hidden variable descriptions of each local detector will not be definite and so will not satisfy the determinism/predictability condition we just established.

In hidden variable determinism, a non-local HV description is only of the form: "detector A will measure UP and B will measure DOWN" which is of course consistent with the truth of "detector A will measure UP" on its own. There are no conditionals. And just like local HVs, these trivial non-local HVs will not violate Bell ineqs without adopting one of the previously discussed options.

 

[DarMM]

In a classical Laplacian universe, a Laplacian detector of finite size perfectly knowing its own state can never get an arbitrarily accurate estimate of a single particle state external to it. Thus a classical Laplacian universe would be superdeterministic. Do you mean that, @DarMM, contradicting @stevendaryl?

If so, the thermal interpretation is also superdeterministic, for essentially the same reason.

No it's not just about not being able to obtain total precision. Its more that the initial state is conspiratorial. Let me take a real world example.

There was a recent test of CHSH violations that used light from distant quasars to select the spin orientations.

In a superdeterministic world quantum mechanics is actually false, but the light from the quasars happens to always select the correct orientation to incorrectly give the impression the CHSH inequalities are violated.

So it's not just a lack of arbitrary accuracy it's that the observers are determined to come to false conclusions about the physical laws that apply to their world.

 

[A. Neumaier]

will not violate Bell ineqs without adopting one of the previously discussed options.

Where is the theorem you refer to? I don't know of any theorem that has as one of its necessary alternatives a pilot wave statement as your post #62 states. There is a big difference between

known hidden variable solutions to this problem

and necessary properties.

In any case, all interpretation have open research questions, and the thermal interpretation has these, too; some of these are discussed in post #293 of the main thread. No interpretation must indicate how it falls into a particular classification, though those interested in classifying interpretations may want to investigate these issues. Those interested in understanding quantum mechnaics only need one plausible interpretation they can make sense of.

 

[A. Neumaier]

No it's not just about not being able to obtain total precision. Its more that the initial state is conspiratorial. Let me take a real world example.

There was a recent test of CHSH violations that used light from distant quasars to select the spin orientations.

In a superdeterministic world quantum mechanics is actually false, but the light from the quasars happens to always select the correct orientation to incorrectly give the impression the CHSH inequalities are violated.

So it's not just a lack of arbitrary accuracy it's that the observers are determined to come to false conclusions about the physical laws that apply to their world.

In this sense, the thermal interpretation is definitely not superdeterministic. Very coarse knowledge of the state of the universe at preparation time, together with some more details about the detector and how it works, are sufficient to predict with the traditional approximations everything known.

 

[charters]

Where is the theorem you refer to?

I don't think I need a theorem. I'm only listing the solutions I am aware of and agree are viable, but I don't mean to be closed off to alternatives I've never contemplated.

However, I would say the burden of proof is on the proponent of a new interpretation to convince readers they've indeed found such a viable alternative to the accepted approaches to HVs that works in light of Bell's theorem. It is not enough just to say you have non-local, determinist HVs and be done with it. You need to elaborate on what exactly this means, especially when you claim its emphatically not a pilot wave or superdeterministic.

In any case, all interpretation have open research questions, and the thermal interpretation has these, too; some of these are discussed in post #293 of the main thread. No interpretation must indicate how it falls into a particular classification

Sure, and I would expect this will be one of the particular open questions that folks who think a lot about foundations will want to see tackled in the TI context. This is more than just a sociological classification exercise. It speaks to what the ontology of the TI is, what it claims the universe is like.

 

[DarMM]

In this sense, the thermal interpretation is definitely not superdeterministic

Yes, I would have said the thermal interpretation is deterministic, but not superdeterministic.

A correlator is a conditional of the form: "when subsystem A takes value x, B takes y; when A takes y, B is x". By construction, it requires that there is some uncertainty in the local description of each subsystem.

If such a correlator description is complete, the hidden variable descriptions of each local detector will not be definite and so will not satisfy the determinism/predictability condition we just established

Remember one of the main differences between the thermal interpretation and other views is really that probability theory itself is given a different interpretation.

In the Thermal Interpretation a correlator does not have the meaning you give. Rather it is a bilocal property, that is a nonlocal property that requires measurements at two locations to ascertain. It has a fixed deterministic value.

However it is the metastability of the slow modes of the devices at each location that cause them to develop discrete inaccurate readings of this quantity. This inaccuracy requires one to use several measurements to determine the correlator.

So in this view it's not fundamentally a conditional and it doesn't require that there is (fundamental) uncertainty in each local device. That just arises as it normal does in the Thermal Interpretation.

 

[A. Neumaier]

. It is not enough just to say you have non-local, determinist HVs and be done with it. You need to elaborate on what exactly this means

It is enough to explain how this is compatible with long-distance entanglement experiments, and I did this in Part II of my series of papers.

 

[charters]

Rather it is a bilocal property, that is a nonlocal property that requires measurements at two locations to ascertain. It has a fixed deterministic value.

If there is a fixed deterministic value, it does not mean anything to say it is bilocal, and it would be trivial to describe it this way. A fixed, deterministic bilocal value is of the form "particle A is spin up and particle B is spin down". All you really have here are two separate, local claims, namely: "particle A is spin up"; "particle B is spin down." Assigning bilocal HVs like this is isomorphic to assigning local HVs and cannot by themselves violate Bell ineqs.

 

[A. Neumaier]

A fixed, deterministic bilocal value is of the form "particle A is spin up and particle B is spin down".

There are more general deterministic bilocal properties, those of the kind ''The bilocal variable $C(x,y)$ has a given value at a pair of spacetime positions $x,y$''.

 

[stevendaryl]

In a classical Laplacian universe, a Laplacian detector of finite size perfectly knowing its own state can never get an arbitrarily accurate estimate of a single particle state external to it. Thus a classical Laplacian universe would be superdeterministic.

Why does that make it superdeterministic? The reason superdeterminism is relevant to interpretations of quantum mechanics, as I said, is because superdeterminism is a loophole in Bell's argument against local hidden variables theories. In an attempt to reproduce the statistics of spin-1/2 EPR, you would have five "players":

1. Alice, who chooses a detector orientation $\overrightarrow{\alpha}$
2. Bob, who chooses a detector orientation $\overrightarrow{\beta}$
3. Charlie, who chooses a value for $\lambda$ according to some probability distribution $P(\lambda)$
4. Alice's detector, that computes a result $A(\overrightarrow{\alpha}, \lambda) = \pm 1$ based on $\overrightarrow{\alpha}$ and $\lambda$
5. Bob's detector, that picks a result $B(\overrightarrow{\beta}, \lambda) = \pm 1$ based on $\overrightarrow{\beta}$ and $\lambda$

Bell shows that there is no probability distribution $P(\lambda)$ that can reproduce the correlations predicted by quantum mechanics. However, there are a number of loopholes in the argument:

1. if Bob's detector is allowed to depend on $\overrightarrow{\alpha}$, or if Alice's detector is allowed to depend on $\overrightarrow{\beta}$ (nonlocality) then there is no problem in reproducing the predictions of quantum mechanics.
2. If Charlie's choice of $\lambda$ is allowed to depend on $\overrightarrow{\alpha}$ and $\overrightarrow{\beta}$ (superdeterminism), then there is no problem in reproducing the predictions of quantum mechanics.

Alice being a deterministic machine doesn't make her choice predictable, because as I argued earlier, Alice can consult the whole rest of the universe in order to make her choice. Simple determinism would allow us to predict Alice's choice based on her state plus the inputs she receives from the rest of the universe. Superdeterminism would require that not only Alice but the whole rest of the universe be known and predictable.

 

[A. Neumaier]

Why does that make it superdeterministic?

It was, in my tentative understanding of DarMM's definition of superdeterminism. In the mean time, he clarified his definition, and in my resulting understanding, my old comment makes no longer sense.

superdeterminism is a loophole in Bell's argument against local hidden variables theories.

Since the thermal interpretation has multilocal hidden variables, Bell's argument doesn't apply anyway.

 

[stevendaryl]

Since the thermal interpretation has multilocal hidden variables, Bell's argument doesn't apply anyway.

How does "multilocal hidden variables" explain the EPR results?

 

[A. Neumaier]

How do "multilocal hidden variables" explain the EPR results?

They don't explain them by itself, they are just outside the scope of Bell's arguments since his assumptions are incompatible with multilocal hidden variables.

The explanation of the nonclassical long-distance correlations is the standard quantum dynamics, which is assumed exact in the thermal interpretation and predicts the standard correlations. These are bilocal beables, approximately measurable (by the weak law of large numbers as any q-expectation; see Section 3 of Part II of my series of papers) through averaging over many independent realizations of discrete tests. The discrete response is explained by environment-induced randomness and environment-induced dissipation, as discussed in Subsections 4.3 and 5.1 of Part III.

The thermal interpretation does not give an explanation, though, of how Nature is able to figure out how to behave according to the quantum laws. It just follows them.

 

[DarMM]

If there is a fixed deterministic value, it does not mean anything to say it is bilocal

I think a deterministic variable can be bilocal is a well defined concept, I don't understand how it is meaningless. It might be wrong, but to have no meaning seems unlikely to me.

A fixed, deterministic bilocal value is of the form "particle A is spin up and particle B is spin down". All you really have here are two separate, local claims, namely: "particle A is spin up"; "particle B is spin down." Assigning bilocal HVs like this is isomorphic to assigning local HVs and cannot by themselves violate Bell ineqs.

That's not what is happening in the Thermal Interpretation, the fixed deterministic value is not "A is up and B is down" or anything like that. First before I explain further, have you read @A. Neumaier 's papers in detail? In order to know what level of detail to go into.

 

[Demystifier]

That's not what is happening in the Thermal Interpretation, the fixed deterministic value is not "A is up and B is down" or anything like that.

Then what is it? Perhaps something like $(A,B)=(up,down)$?

 

[A. Neumaier]

Then what is it? Perhaps something like $(A,B)=(up,down)$?

see my post #72.

 

[DarMM]

Then what is it? Perhaps something like $(A,B)=(up,down)$?

One has the quantity $\langle AB\rangle$, not understood in the typical probabilistic manner as a correlation between $A$ and $B$ but as a quantity in and of itself. This can take a continuous range of values.

There are then the local variables $\langle A\rangle$ and $\langle B\rangle$. The quantum mechanical state does imply that there is a constraint between their values, but fundamentally they are separate quantities.

Local observations of $\langle A\rangle$ and $\langle B\rangle$ appear discrete due to how the device's slow modes evolve.

However repeated observation of $\langle A\rangle$ and $\langle B\rangle$ allows one to obtain statistical estimates on their values.

Then by comparing the joint statistics of $\langle A\rangle$ and $\langle B\rangle$ you can also obtain an estimate of the value of $\langle AB\rangle$.

 

[A. Neumaier]

Then by comparing the statistics of $\langle A\rangle$ and $\langle B\rangle$ you can also obtain an estimate of the value of $\langle AB\rangle$.

by comparing their joint statistics

 

[charters]

That's not what is happening in the Thermal Interpretation, the fixed deterministic value is not "A is up and B is down" or anything like that. First before I explain further, have you read @A. Neumaier 's papers in detail? In order to know what level of detail to go into.

I have read the papers, but I think what will be more helpful is for you to simply state a fixed, deterministic HV that is a counterexample. This disagreement is not really about the TI, it is a much more general question of what it means for anything to be a hidden variable.

My argument is very simple: in a deterministic hidden variables interpretation, you must assign hidden variable which uniquely predicts the outcome of each local measurement. Otherwise, local measurements cannot be deterministic. If local measurements are not deterministic, the interpretation is not deterministic. The Bell's theorem non-locality only enters as a means of correcting the HVs when necessary, reacting to other local measurements performed elsewhere. This will be a de facto pilot wave.

If, as you say, "the fixed deterministic value is not "A is up and B is down" or anything like that" then I do not see what it can even mean to call these values fixed or deterministic.

Arnold has suggested:

There are more general deterministic bilocal properties, those of the kind ''The bilocal variable $C(x,y)$ has a given value at a pair of spacetime positions $x,y$''.

But I can just turn this around into: "the value at spacetime point x is C(x)" and "the value at spacetime point y is C(y)". As long as C(x,y) maps to a pair of unique values (not a statistical mixture at each local site), this is clearly isomorphic to the above. If C(x,y) maps to statistical mixtures at each local site, this bilocal variable is not a deterministic HV for local measurements.

Dar, you said:

However repeated observation of ⟨A⟩⟨A⟩\langle A\rangle and ⟨B⟩⟨B⟩\langle B\rangle allows one to obtain statistical estimates on their values.

Then by comparing the joint statistics of ⟨A⟩⟨A⟩\langle A\rangle and ⟨B⟩⟨B⟩\langle B\rangle you can also obtain an estimate of the value of ⟨AB⟩⟨AB⟩\langle AB\rangle.

If each individual observation of ⟨A⟩ and ⟨B⟩ reveals a preexisting hidden variable of ⟨A⟩ or ⟨B⟩, the joint stats will not violate Bell ineqs without assuming something more (pilot wave, superdeterminism).

If there are no preexisting hidden variables for ⟨A⟩ and ⟨B⟩ individually, local measurements are not deterministic, and this is not a deterministic HV interpretation at all.

 

[PeterDonis]

As long as C(x,y) maps to a pair of unique values

Which it might not; that's exactly the point. Not every function of two variables can be decomposed into two functions, each of one variable.

 

[charters]

Which it might not; that's exactly the point. Not every function of two variables can be decomposed into two functions, each of one variable.

I agree. But if it doesn't do this, it is not going to make deterministic predictions for local measurements of an individual subsystem.

 

[ftr]

I think a deterministic variable can be bilocal is a well defined concept, I don't understand how it is meaningless. It might be wrong, but to have no meaning seems unlikely to me.

I have already given such example in a post two years ago, which is nothing but a generalization of the concept I gave in this post, the lines connecting two points can represent energy(or momentum times speed of light).

 

[A. Neumaier]

I have read the papers, but I think what will be more helpful is for you to simply state a fixed, deterministic HV that is a counterexample. This disagreement is not really about the TI, it is a much more general question of what it means for anything to be a hidden variable.

My argument is very simple: in a deterministic hidden variables interpretation, you must assign hidden variable which uniquely predicts the outcome of each local measurement. Otherwise, local measurements cannot be deterministic. If local measurements are not deterministic, the interpretation is not deterministic. The Bell's theorem non-locality only enters as a means of correcting the HVs when necessary, reacting to other local measurements performed elsewhere. This will be a de facto pilot wave.

If, as you say, "the fixed deterministic value is not "A is up and B is down" or anything like that" then I do not see what it can even mean to call these values fixed or deterministic.

Arnold has suggested:
But I can just turn this around into: "the value at spacetime point x is C(x)" and "the value at spacetime point y is C(y)". As long as C(x,y) maps to a pair of unique values (not a statistical mixture at each local site), this is clearly isomorphic to the above. If C(x,y) maps to statistical mixtures at each local site, this bilocal variable is not a deterministic HV for local measurements.

Dar, you said:
If each individual observation of ⟨A⟩ and ⟨B⟩ reveals a preexisting hidden variable of ⟨A⟩ or ⟨B⟩, the joint stats will not violate Bell ineqs without assuming something more (pilot wave, superdeterminism).

If there are no preexisting hidden variables for ⟨A⟩ and ⟨B⟩ individually, local measurements are not deterministic, and this is not a deterministic HV interpretation at all.

There are local pointer variables a(x) and b(y) but their deterministic dynamics depends on bilocal and mulilocal variables.

 

[charters]

There are local pointer variables a(x) and b(y) but their deterministic dynamics depends on bilocal and mulilocal variables.

Ok this I can agree is a workable and well understood solution to Bell's theorem. Basically, instead of saying a "pilot wave" is steering the deterministic time evolution of the local pointer variables, the TI says it is "multilocal variables" doing so.

 

[A. Neumaier]

Ok this I can agree is a workable and well understood solution to Bell's theorem. Basically, instead of saying a "pilot wave" is steering the deterministic time evolution of the local pointer variables, the TI says it is "multilocal variables" doing so.

The nonlocal dynamics is the Ehrenfest dynamics introduced in Section 2 of my Part II paper.

 

[Demystifier]

There are local pointer variables a(x) and b(y) but their deterministic dynamics depends on bilocal and mulilocal variables.

I don't think that their dynamics depends on bilocal and multilocal variables. Their dynamics is given by equations of the form
$$\langle a(x,t)\rangle={\rm Tr}\rho(t)a(x)$$
which depends only on the state of the Universe $\rho(t)$.

 

[A. Neumaier]

$$\def\<{\langle} \def\>{\rangle}$$

I don't think that their dynamics depends on bilocal and multilocal variables. Their dynamics is given by equations of the form
$$\langle a(x,t)\rangle={\rm Tr}~\rho(t)a(x)$$
which depends only on the state of the Universe $\rho(t)$.

Only in the noncovariant Schrödinger picture, where the essence of the thermal interpretation is hidden: Your $a(x)$ is a space-dependent operator depending on spatial coordinates $x$. On the other hand,

The nonlocal dynamics is the Ehrenfest dynamics introduced in Section 2 of my Part II paper.

I was using covariant beables $a(x) =\langle A(x)\rangle={\rm Tr}~\rho A(x)$ in the covariant Heisenberg picture dependent on a vector of spacetime coordinates $x$, with a fixed state of the universe. Their dynamics is given by the covariant Ehrenfest equation (Section 4.2 of Part II)
$\frac{d}{dx_\nu} \<A\>_x=\<p_\nu~\angle~ A(x)\>$, specialized to $t=x_0/c$, giving
$$\frac{d}{dt} \<A\>_x=\<H~\angle~ A(x)\>,$$
where $H=cp_0$ is the (frame-dependent) Hamiltonian of the quantum field theory of the universe and $A ~\angle~ B:=\frac{i}{\hbar}[A,B]$; see Section 2 of Part II.

Since $H$ is a sum of integrals over multilocal operators, the right hand side is a sum of integrals over multilocal q-expectations.

 

[Demystifier]

$H$ is a sum of integrals over multilocal operators

Can you better explain what do you mean by that? (Pinpoiting to the right part of your paper would be OK.)

 

[A. Neumaier]

Can you better explain what do you mean by that? (Pinpointing to the right part of your paper would be OK.)

In my paper I didn't discuss the detailed form of the Hamiltonian of the universe. It depends on stuff yet to be discovered about how to represent quantum gravity. But the general form of the Hamiltonian is already visible from simpler quantum field theories such as QED, where it is derived as usual from the action, and later modified through renormalization.

Already a free Hamiltonian contains a term with a spatial integral over quadratic expressions, and interactions plus renormalization at all orders add terms of all higher degrees, which become multilocal when inserted into the Ehrenfest dynamics. (Search for Hamiltonian in this Wikipedia article to find the explicit unrenormalized expression for scalar field theory; the integration variable runs over points distinct from the $x$ in the Ehrenfest equation.)

 

[indefinite_123]

Hi all,

sorry if I post in a relatively old thread.

Ok this I can agree is a workable and well understood solution to Bell's theorem. Basically, instead of saying a "pilot wave" is steering the deterministic time evolution of the local pointer variables, the TI says it is "multilocal variables" doing so.

Personally, I do not understand how can one avoid a 'non-locality' of the kind of the pilot-wave theory if multi-local properties dependent on more than one space-like separated space-time regions are accepted. Are there any references on this?
Also, is the thermal interpretation the only one that uses this possible solution to Bell's theorem?

 

[A. Neumaier]

I do not understand how can one avoid a 'non-locality' of the kind of the pilot-wave theory if multi-local properties dependent on more than one space-like separated space-time regions are accepted. Are there any references on this?

I discuss nonlocality in Part II of my preprints, Section 4.5, mentioned in post #1 of the main thread on the TI (linked to in post #2 of the present thread) .

For a more polished account of bilocal quantities and nonlocality see my recent book also mentioned there.

 

[indefinite_123]

I discuss nonlocality in Part II of my preprints, Section 4.5, mentioned in post #1 of the main thread on the TI (linked to in post #2 of the present thread) .

For a more polished account of bilocal quantities and nonlocality see my recent book also mentioned there.

Thank you very much!