I The thermal interpretation of quantum physics

[ftr]

So does TI says anything about which slit or slits. Or silent on the issue.

 

[A. Neumaier]

So does TI says anything about which slit or slits. Or silent on the issue.

The C60 field goes through both slits, analogous to a classical electromagnetic field, and materializes at the screen in the form of individual C60 molecules.

 

[vanhees71]

So it says the same as the (minimal) standard interpretation...

 

[Demystifier]

The C60 field goes through both slits, analogous to a classical electromagnetic field, and materializes at the screen in the form of individual C60 molecules.

So it says the same as the (minimal) standard interpretation...

For the sake of comparison, let me tell what what standard Bohmian mechanics (BM) and instrumental Bohmian mechanics (IBM) say.
In BM, C60 goes through one slit only. In IBM, C60 goes through both slits, but the macroscopic pointer on the screen moves to one position only.

 

[EPR]

If the wavefunction goes through both slits what happens to the unactualized possibilities in the TI?

 

[A. Neumaier]

If the wavefunction goes through both slits

The field goes through both slits. This has nothing to do with wave functions (in general there is no wave function but only a density operator).

what happens to the unactualized possibilities in the TI?

They are not actualized, that's all.

 

[EPR]

So it's another description - nice to have but not an interpretation per se. Maybe one day we'll have a complete interpretation. We don't have one. There isn't an interpretation of quantum mechanics

 

[A. Neumaier]

So it's another description - nice to have but not an interpretation per se.

It was always enough to consider what is the case rather than what is just a possibility but then does not happen.

 

[timmdeeg]

I might have misconceptions with the following, so please clarify.

The C60 field goes through both slits, analogous to a classical electromagnetic field, and materializes at the screen in the form of individual C60 molecules.

If the C60 field can be thought as being spread out over a larger area (how large?) and during measurement contracts instantaneously to form a C60 molecule then this notion seems to replace the collapse of the wave function by the collapse of a field. Thereby this field is presumably a real thing, not just a mathematical construct. But if correct so far isn't this an unphysical notion?

Because 4 points are needed to fix a definite frame in space. Thus fixing the mean positions of 4 nuclei produces an approximate rest frame of the C60 molecule. Because such a molecule is quite rigid, it determines the position of all nuclei up to a tiny uncertainty.

Has the TI two views, one where a complex molecule is a field and another one where a complex molecule is rigid?

 

[A. Neumaier]

If the C60 field can be thought as being spread out over a larger area (how large?) and during measurement contracts instantaneously to form a C60 molecule then this notion seems to replace the collapse of the wave function by the collapse of a field. Thereby this field is presumably a real thing, not just a mathematical construct. But if correct so far isn't this an unphysical notion?

In the TI, both fields and collapse are physical. But in general, collapse is described not by jumping into an eigenstate but by the output of an appropriate quantum instrument.

Has the TI two views, one where a complex molecule is a field and another one where a complex molecule is rigid?

No. the TI is a single interpretation. But C60 can be modeled by standard quantum mechanics in different details and in different situations, leading to different descriptions.

The description of C60 as a field is appropriate for C60 beams (as prepared in double slit experiments); these are described by a current (constructible for arbitrary bound states according to a method due to Sandhas). The description of C60 as a reasonable rigid molecule is appropriate for a C60 molecule at the surface of a screen (as measured in double slit experiments). Both descriptions are therefore needed to analyze double slit experiments.

 

[timmdeeg]

In the TI, both fields and collapse are physical. But in general, collapse is described not by jumping into an eigenstate but by the output of an appropriate quantum instrument.

But doesn't the instantaneous collapse of a physical field (to form a molecule on the screen) violate Special Relativity?

The description of C60 as a reasonable rigid molecule is appropriate for a C60 molecule at the surface of a screen (as measured in double slit experiments). Both descriptions are therefore needed to analyze double slit experiments.

My question in #734 was related to your statement "It moves along a fuzzy world tube centered around the path given by the q-expectations of the position, with a width given approximately by the square root of the sum of the q-variances." Which I understood such that the rigid C60 "moves along a fuzzy world tube ..." before it is materialized at the screen. Thanks for clarifying that now.

 

[A. Neumaier]

My question in #734 was related to your statement "It moves along a fuzzy world tube centered around the path given by the q-expectations of the position, with a width given approximately by the square root of the sum of the q-variances." Which I understood such that the rigid C60 "moves along a fuzzy world tube ..." before it is materialized at the screen. Thanks for clarifying that now.

Well, behind a double slit, it changes its shape due to diffraction to a union of two fuzzy spheres centered on the two slits. Moreover this affects only the wholesale shape, not the internal shape. Local and nonlocal qualities coexist.

I have never seen a relativistic discussion of the double slit experiment, so cannot answer your other question.

 

[EPR]

There is no coherent explanation of the double slit experiment. If assumptions of how the world is and how it works is true, the double slit shouldn't produce the patterns it does. This is the weakest point in quantum physics and the topic of many many thousands of unresolved debates. It is where literally all interpretations fail and possibly the biggest mistery of nature at this time.

 

[Mentz114]

There is no coherent explanation of the double slit experiment. If assumptions of how the world is and how it works is true, the double slit shouldn't produce the patterns it does. This is the weakest point in quantum physics and the topic of many many thousands of unresolved debates. It is where literally all interpretations fail and possibly the biggest mistery of nature at this time.

I must say I do not agree. If QFT predicts that a 'collision' between succesive molecules and the slits produces an interference pattern - what is incoherent about that ?

 

[EPR]

I must say I do not agree. If QFT predicts that a 'collision' between succesive molecules and the slits produces an interference pattern - what is incoherent about that ?

QFT is the best and the only coherent 'interpretation' of reality to date. By FAR. No question about it. Though it contains in itself the only mistery - the measurement problem.

The so called world is a collection of fields that produce, 'create'(okay i will back off slightly here) and substitute that term with the more acceptable term - 'emerge' a classical world at the classical limit.

QFT was the best and most coherent description of the world when i started researching this topic 15 years ago. It is still by far the best scientific attempt to explain the world without noise and nonsense. Backed up by thousands successful experiments and established facts. Hardcore science at its best. Can't ask for more.

 

[PeterDonis]

There is no coherent explanation of the double slit experiment. If assumptions of how the world is and how it works is true, the double slit shouldn't produce the patterns it does. This is the weakest point in quantum physics and the topic of many many thousands of unresolved debates.

QFT was the best and most coherent description of the world when i started researching this topic 15 years ago. It is still by far the best scientific attempt to explain the world without noise and nonsense. Backed up by thousands successful experiments and established facts. Hardcore science at its best. Can't ask for more.

These two statements of yours appear inconsistent. Which of them do you really mean to say?

 

[EPR]

These two statements of yours appear inconsistent. Which of them do you really mean to say?

One of them says 'the most coherent description of reality', while the other says 'there is no coherent explanation of the double slit experiment'.

Though obviously related, one of them is an almost complete worldview(sans GR and gravity), the other is the final(though still far away) obstacle to understanding the relationship between the classical and quantum world(the MP). Exemplified in my quote "Though it(QFT) still contains in itself the only mistery - the measurement problem. "

 

[PeterDonis]

One of them says 'the most coherent description of reality', while the other says 'there is no coherent explanation of the double slit experiment'.

Unless you are claiming that double slit experiments are not real, having a coherent explanation of reality should include having a coherent explanation of the double slit experiment.

one of them is an almost complete worldview(sans GR and gravity), the other is the final(though still far away) obstacle to understanding the relationship between the classical and quantum world

Either QFT solves this problem or it doesn't. If it does, then the obstacle you describe has been overcome. If it doesn't, then you don't have a coherent description of reality, since gravity is part of reality.

So, again, which is it?

 

[EPR]

Unless you are claiming that double slit experiments are not real, having a coherent explanation of reality should include having a coherent explanation of the double slit experiment.

You misquote me
I said "QFT is the best and the only coherent 'interpretation' of reality to date. "

When the MP is solved(if it's ever solved), i would remove the inverted commas. The most precisely tested theory in history, agreeing with observations at the level of one part 10 to the power of 9, already provides a vision of what the world is like. The united world of quantum and classical scale. A world of fields.

Either QFT solves this problem or it doesn't. If it does, then the obstacle you describe has been overcome. If it doesn't, then you don't have a coherent description of reality, since gravity is part of reality.

So, again, which is it?

No, QFT does not solve the MP. However it already provides a picture of reality.

 

[PeterDonis]

No, QFT does not solve the MP.

Ok.

However it already provides a picture of reality.

But not of all of reality, since that would require solving the MP.

 

[EPR]

Not all of reality. The appearance of definite macroscopic reality is not understood. Hence my statement

The so called world is a collection of fields that produce, 'create'(okay i will back off slightly here) and substitute that term with the more acceptable term - 'emerge' a classical world at the classical limit.

 

[PeterDonis]

Not all of reality.

Ok, that clarifies it.

 

[ftr]

The description of C60 as a field is appropriate for C60 beams (as prepared in double slit experiments); these are described by a current (constructible for arbitrary bound states according to a method due to Sandhas).

I have googled for W. Sandhas but not sure which paper describes the method. Can you point to a specific paper, thanks.

 

[A. Neumaier]

I have googled for W. Sandhas but not sure which paper describes the method. Can you point to a specific paper, thanks.

• W. Sandhas, Definition and existence of multichannel scattering states, Comm. Math. Phys. 3 (1966), 358-374.

Section 5 constructs for any bound state asymptotic creation and annihilation operators. Section 6 proves that they satisfy standard commutation relations, providing a bosonic field description. As in any bosonic field theory, this gives associated densities and currents.

 

[Demystifier]

@A. Neumaier I have one question for you. The thermal interpretation is an ontological interpretation, so it must be described by a nonlocal theory, as the Bell theorem implies. Is this fundamental nonlocality consistent with fundamental Lorentz covariance? Or does it mean that Lorentz covariance of QFT is emergent, rather than fundamental?

 

[A. Neumaier]

@A. Neumaier I have one question for you. The thermal interpretation is an ontological interpretation, so it must be described by a nonlocal theory, as the Bell theorem implies. Is this fundamental nonlocality consistent with fundamental Lorentz covariance? Or does it mean that Lorentz covariance of QFT is emergent, rather than fundamental?

The nonlocality of the thermal interpretation is a direct consequence of quantum field theory, hence as consistent with fundamental Lorentz covariance as quantum field theory itself. Thus provably in space-time dimensions 2 (quantum wires) and 3 (quantum surfaces), and empirically in space-time dimension 4.

In the thermal interpretation, there are local distribution-valued beables, the q-expectations of fields, and nonlocal distribution-valued beables, the n-point correlation functions, q-expectations of products of fields at different points and their derivatives. These q-expectations are manifestly Lorentz covariant. In a first order formulation (involving with each field also the canonically conjugate field), the time derivative of the local field expectations is given by some (infinite) linear combination of q-expectations of products of fields and their spatial derivatives, hence depends on nonlocal properties. (In the hydrodynamic approximation, these are approximated by products of local terms, giving rise to the equations of fluid mechanics and their relativistic and quantum generalizations. This approximation suffices for the description of the macroscopic regime.)

More precisely, the dynamics is given by the quantum field theory version of the Ehrenfest equations, which express the second time derivative of q-expectations of products of fields with respect to the most time-advanced arguments as a renormalized limit of sums of q-expectations of other products of fields (in the interacting case, some of them have more factors) and their spatial derivatives. However, the conventional treatment is in a Lorentz covariant 4D view, where it is more convenient to express products of fields in terms of products of fewer fields and their spatial, temporal and mixed derivatives. This is encoded in the operator product expansion, which are the modern form of the equation of motion of quantum fields.

 

[vanhees71]

I'm a bit puzzled by what you define as "local" vs. "nonlocal". Why do you consider the (non-observable) n-point functions as "non-local"? They are given by something like (for a scalar self-adjoint field as the most simple example)
$$G^{(n)}(x_1,\ldots,x_2)=\langle \mathcal{T} \hat{\phi}(x_1) \hat{\phi}(x_2) \cdots \hat{\phi}(x_n) \rangle,$$
where $\mathcal{T}$ is some "time-ordering prescription" (like time-ordering for vacuum QFT, contour-ordering for the most general case of real-time many-body QFT), and the expecation is meant as the trace with the stat. op.

The field operators are "local" in the sense that they obey the local transformation laws under Poincare transformations as their classical analogues, and also the interactions are usually taken as local, i.e., the Hamiltonian is a functional of field-operator products at one space-time point and the local observable-operators obey the microcausality constraint. So what's non-local in the thermal interpretation what is considered local in the standard interpretation? The mathematical functions are obviously the same (and also in (1+3)d there are the usual mathematical troubles with the formalism, but this is not under debate here, I guess).

Of course, relativistic QFT is "non-local" in the sense of any type of QT that it admits states where parts of a quantum system that are observable at large spatial distances have correlations described by entanglement, but imho to call this "non-locality" is misleading, because it's rather long-ranged correlations that are stronger than any classical correlation witin a local classical theory can be (which is the content of the violation of Bell's inequality).

It's this subtle balance between "locality of the dynamics" (microcausality condition fulfilled) and "non-locality of correlations" which makes relativistic local QFT consistent with the causality structure of special-relativistic spacetime. In how far this is the case for the more complicated case of QFTs in non-flat "background spacetimes" or even for a possible future quantum-gravity theory, I can't say of course.

 

[A. Neumaier]

I'm a bit puzzled by what you define as "local" vs. "nonlocal". Why do you consider the (non-observable) n-point functions as "non-local"?

Nonlocal = dependent on more than one space-time position (which can be arbitrarily far apart in space).
This is the same notion of nonlocality that is used to decide whether a Lagrangian density is local or nonlocal. It is also the notion of nonlocality that is excluded in assumptions proving Bell inequalities, and is the kind of nonlocality established experimentally in long distance entanglement experiments.

In this sense, quantum fields, their dynamics, and their q-expectations are local, but correlation functions are nonlocal.

They are given by something like (for a scalar self-adjoint field as the most simple example)
$$G^{(n)}(x_1,\ldots,x_2)=\langle \mathcal{T} \hat{\phi}(x_1) \hat{\phi}(x_2) \cdots \hat{\phi}(x_n) \rangle,$$
where $\mathcal{T}$ is some "time-ordering prescription" (like time-ordering for vacuum QFT, contour-ordering for the most general case of real-time many-body QFT), and the expectation is meant as the trace with the stat. op.

Yes, and there are also the unordered correlations corresponding to Wightman n-point functions.

In general, the trace with the statistical operator is a formal q-expectation only, not an expectation in the statistical sense. For a complex scalar field, $\Phi(x)$ and its smeared versions are not selfadjoint operators, hence $\langle\Phi(x)\rangle=Tr\rho\phi(x)$ and their smeared versions have no Born interpretation as statistical expectation values. Let alone the correlation functions.

But the 2-point correlations are in principle observable through linear response theory.

 

[Demystifier]

In the thermal interpretation, there are local distribution-valued beables, the q-expectations of fields, and nonlocal distribution-valued beables, the n-point correlation functions, q-expectations of products of fields at different points and their derivatives. These q-expectations are manifestly Lorentz covariant.

I think I get it. You avoid Bell theorem by something I would call multi-ontology in a single world (as opposed to many-world interpretation, which could be called single-ontology in many worlds). For instance, let $s_A$ and $s_B$ be the ontological spins of two entangled particles, and let their ontological product be $s_A\circ s_B$. In theories covered by the Bell theorem one has
$$s_A\circ s_B=s_As_B$$
while in the thermal interpretation
$$s_A\circ s_B \neq s_As_B$$
The ontology with the inequality above does not make much sense to me, but that's essentially what the thermal interpretation, as far as I understood it, claims to be the case.

 

[PeterDonis]

let their ontological product be

What is an "ontological product"?

 

[Demystifier]

What is an "ontological product"?

An ontological quantity that in the classical limit is given by an ordinary product of two ontological quantities.

 

[PeterDonis]

An ontological quantity that in the classical limit is given by an ordinary product of two ontological quantities.

What is "an ordinary product of two ontological quantities"? I only know how to multiply numbers and other mathematical objects; I don't know how to multiply "ontological quantities".

 

[A. Neumaier]

I think I get it. You avoid Bell theorem by something I would call multi-ontology in a single world (as opposed to many-world interpretation, which could be called single-ontology in many worlds). For instance, let $s_A$ and $s_B$ be the ontological spins of two entangled particles, and let their ontological product be $s_A\circ s_B$. In theories covered by the Bell theorem one has
$$s_A\circ s_B=s_As_B$$
while in the thermal interpretation
$$s_A\circ s_B \neq s_As_B$$
The ontology with the inequality above does not make much sense to me, but that's essentially what the thermal interpretation, as far as I understood it, claims to be the case.

Informally, in the thermal interpretation, the whole is more than its parts, which makes perfect sense to me. Whereas Bell assumed that, as in classical n-particle mechanics, the complete description of the parts furnishes a complete description of the whole.

I don't understand your reformulation in terms of an ontological product which neither figures in Bell's work nor in mine.

 

[vanhees71]

Nonlocal = dependent on more than one space-time position (which can be arbitrarily far apart in space).
This is the same notion of nonlocality that is used to decide whether a Lagrangian density is local or nonlocal. It is also the notion of nonlocality that is excluded in assumptions proving Bell inequalities, and is the kind of nonlocality established experimentally in long distance entanglement experiments.

In this sense, quantum fields and their q-expectations are local, but correlation functions are nonlocal.

Then it's simply "non-local" because I make an experiment with two or more detectors at distant points in space, but that's trivial and has nothing to do with the complicated implications of what's usually meant by "non-locality" in the sense of "spooky actions at a distance", and then it's of course consistent with the standard interpretation of relativistic local QFT.

Of course, the $N$-point functions of various kinds (including the fixed-ordered field-operator products, or Wightman functions) do not correspond directly to expectation values of observables but they are used to calculate them.

E.g., my beloved dilepton and photon production rates as measured in heavy-ion collisions are indeed derivable from the (thermal) retarded two-point correlation function. It's basically the imaginary part or spectral function of the electromagnetic current-current correlation function with some kinematical factors.

It's of course related to the mentioned connection with the linear-response theory, where the retareded two-point correlation functions of appropriate (composite-)field operators are the corresponding response functions. In equilibrium one can use them to evaluate transport coefficients using the famous Kubo formula.

 

[Demystifier]

What is "an ordinary product of two ontological quantities"? I only know how to multiply numbers and other mathematical objects; I don't know how to multiply "ontological quantities".

An ordinary product of two ontological quantities is just an ordinary multiplication of numbers, as in classical physics. The thermal interpretation replaces this with something very non-classical (and in my opinion too weird to make sense ), which, in effect, can be expressed as a weird way of multiplication. It has its roots in the well-known multiplication of operators in QM, which also looks weird if one attempts to interpret operators as ontological. For that reason operators are not interpreted as ontological in any quantum interpretation I am aware of. But the thermal interpretation takes the expectation value of operator products as ontological, which can be expressed as a strange multiplication. This multiplication is mathematically well defined (because the product of operators is mathemicaly well defined), but it is very strange when interpreted ontologically, on which the thermal interpretation insists.

 

[Demystifier]

I don't understand your reformulation in terms of an ontological product which neither figures in Bell's work nor in mine.

I reformulated it in this way to better understand the thermal interpretation in my own terms.

 

[Demystifier]

Informally, in the thermal interpretation, the whole is more than its parts. Whereas Bell assumed that the complete description of the parts furnishes a complete description of the whole.

OK, that's another way to express the fact that the Bell theorem does not apply to the thermal interpretation.

 

[A. Neumaier]

Then it's simply "non-local" because I make an experiment with two or more detectors at distant points in space, but that's trivial and has nothing to do with the complicated implications of what's usually meant by "non-locality" in the sense of "spooky actions at a distance", and then it's of course consistent with the standard interpretation of relativistic local QFT.

"spooky actions at a distance" is not a physical phenomenon but the result of a poor interpretation.

 

[A. Neumaier]

But the thermal interpretation takes the expectation value of operator products as ontological, which can be expressed as a strange multiplication.

No, the expectation value of operator products cannot be expressed as a product of q-expectations, which are the beables of the parts! It gives truly additional beables - whence the whole has more properties than the parts.

OK, that's another way to express the fact that the Bell theorem does not apply to the thermal interpretation.

Yes, and a very intuitive one!

 

[PeterDonis]

An ordinary product of two ontological quantities is just an ordinary multiplication of numbers, as in classical physics.

I think you are confusing the model with reality. Numbers are not "ontological quantities"; they are things in our mathematical model.

 

[ftr]

I think you are confusing the model with reality. Numbers are not "quantities"; they are things in our mathematical model.

I think maybe Demystifier can do a write up on what is meant by "ontological" for various interpretations. He has been always good at summarizing contentious issues. Does "ontology" have a universal agreed upon meaning? or maybe I should open a thread.

 

[A. Neumaier]

Does "ontology" have a universal agreed upon meaning? or maybe I should open a thread.

A discussion of this question surely does not belong to this thread.

 

[ftr]

A discussion of this question surely does not belong to this thread.

yes. This is what I was suggesting.

 

[PeterDonis]

Does "ontology" have a universal agreed upon meaning? or maybe I should open a thread.

You should open a separate thread for this topic. But before doing so, I would advise looking at the literature, since there are already plenty of published papers on the term "ontology" as it pertains to quantum mechanics.

 

[Demystifier]

No, the expectation value of operator products cannot be expressed as a product of q-expectations, which are the beables of the parts! It gives truly additional beables - whence the whole has more properties than the parts.

In ontological theories such as Bohmian mechanics of many worlds, if $A$ and $B$ are beables, then so is $AB$. In thermal interpretation, it is not so. I find it too weird for my taste.

Yes, and a very intuitive one!

Would you say that the thermal interpretation denies reductionism?

 

[Demystifier]

I think maybe Demystifier can do a write up on what is meant by "ontological" for various interpretations. He has been always good at summarizing contentious issues. Does "ontology" have a universal agreed upon meaning? or maybe I should open a thread.

I would categorize all the interpretations into 3 categories:
1) Interpretations without ontology (most variants of Copenhagenish interpretations)
2) Interpretations with ontology but without primitive ontology (consistent histories, thermal interpretation)
3) Interpretations with primitive ontology (Bohmian, many worlds, objective collapse)

Primitive ontology is the fundamental ontological quantity to which all other ontological quantities can be reduced. In Bohmian mechanics it is particle positions of all particles in the Universe. In many worlds it is the wave function of the multiverse.

 

[A. Neumaier]

In ontological theories such as Bohmian mechanics of many worlds, if $A$ and $B$ are beables, then so is $AB$. In thermal interpretation, it is not so. I find it too weird for my taste.Would you say that the thermal interpretation denies reductionism?

In the TI, the product of the q-expectations of A and B is a different beable than the q-expectation of the product AB. Nothing weird is involved.

I don't care about reductionism. What counts is what is explained.

 

[Demystifier]

In the TI, the product of the q-expectations of A and B is a different beable than the q-expectation of the product AB. Nothing weird is involved.

In TI, the q-expectation does not have a statistical interpretation. It is a property of a single system, not of an ensemble of systems. From that perspective, I understand how a q-expectation of the product AB is calculated, but I can't understand what a q-expectation of the product AB is. Is there perhaps some analogy?

 

[ftr]

I would categorize all the interpretations into 3 categories:
1) Interpretations without ontology (most variants of Copenhagenish interpretations)
2) Interpretations with ontology but without primitive ontology (consistent histories, thermal interpretation)
3) Interpretations with primitive ontology (Bohmian, many worlds, objective collapse)

Primitive ontology is the fundamental ontological quantity to which all other ontological quantities can be reduced. In Bohmian mechanics it is particle positions of all particles in the Universe. In many worlds it is the wave function of the multiverse.

Thanks. I hope to open a thread soon.

 

[PeterDonis]

In ontological theories such as Bohmian mechanics of many worlds, if $A$ and $B$ are beables, then so is $AB$.

I still don't understand how you multiply beables. Beables aren't numbers. Maybe a specific example would help me to understand what you are saying here.