Undergrad The thermal interpretation of quantum physics

[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.

 

[A. Neumaier]

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?

If A and B are local properties at different location, it is a nonlocal property of the system, a property that figures in the dynamical law. In general it has no interpretation except as a part of the dynamical law - something needed to determine the evolution of the whole system. Asking what it is is like asking in Bohmian mechanics what the wave function is.

However, some nonlocal properties can be given an interpretation. The 2-point correlations $C(x,y):=\langle \Phi(x)\Phi(y)\rangle$ can be Wigner transformed and then produce a (not necessarily positive) phase space density of the kind that figures in the Boltzmann equation (which can be obtained from the field dynamics in a suitable approximation). In general, many 2-point correlations can be observed through linear response theory, hence are true properties of a system.

 

[A. Neumaier]

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.

Numerical beables are meant here. One can multiply the time traveled (a nonlocal beable) with the speed (another beable) and gets the distance traveled (a third beable).

 

[Demystifier]

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.

Beables are represented by numbers. Consider, for example, a classical harmonic oscillator. The fundamental beable is the particle position represented by the number $X$. Its potential energy can also be considered a beable, but it's not fundamenatal. It is represented by the number $V=kX^2/2$.

 

[A. Neumaier]

Beables are represented by numbers. Consider, for example, a classical harmonic oscillator. The fundamental beable is the particle position represented by the number $X$. Its potential energy can also be considered a beable, but it's not fundamenatal. It is represented by the number $V=kX^2/2$.

With your distinction, the fundamental beables in the thermal interpretation are [represented by] the (distributional) q-expectations of products of fields (generalized Wightman n-point functions) , and the other beables are what is computable from them, such as smeared field expectations, Wigner functions, etc..

 

[Demystifier]

With your distinction, the fundamental beables in the thermal interpretation are [represented by] the (distributional) q-expectations of products of fields (generalized Wightman n-point functions) , and the other beables are what is computable from them, such as smeared field expectations, Wigner functions, etc..

That's helpful for the sake of comparison with other ontological interpretations. Bell introduced the notion of local beables. Those are not beables with local interactions, but beables defined locally at space points. In this sense Bohmian mechanics is a theory of fundamental local beables (particles have well defined positions in space) with nonlocal interactions. Many-world interpretation, on the other hand, is a theory of nonlocal fundamental beables (the state in the Hilbert space is not defined at a space point). Thermal interpretation is somewhere in between, because it contains both local fundamental beables (e.g. $\langle\phi(x)\rangle$) and nonlocal fundamental beables (e.g. $\langle\phi(x)\phi(y)\rangle$).

 

[A. Neumaier]

Bell introduced the notion of local beables. Those are not beables with local interactions, but beables defined locally at space points. In this sense, Bohmian mechanics is a theory of fundamental local beables (particles have well defined positions in space) with nonlocal interactions. The many-world interpretation, on the other hand, is a theory of nonlocal fundamental beables (the state in the Hilbert space is not defined at a space point). The thermal interpretation is somewhere in between, because it contains both local fundamental beables (e.g. $\langle\phi(x)\rangle$) and nonlocal fundamental beables (e.g. $\langle\phi(x)\phi(y)\rangle$).

Yes. the thermal interpretation has both local and nonlocal fundamental beables. Hence it is not affected by Bell's theorem, which assumes fundamental beables to be local.

 

[indefinite_123]

Yes. the thermal interpretation has both local and nonlocal fundamental beables. Hence it is not affected by Bell's theorem, which assumes fundamental beables to be local.

Sorry for the trivial question, but is the presence of nonlocal fundamental beables a nonclassical feature of the thermal interpretation?

Thanks in advance!

 

[A. Neumaier]

Sorry for the trivial question, but is the presence of nonlocal fundamental beables a nonclassical feature of the thermal interpretation?

Thanks in advance!

There are a number of traditional classical nonlocal features such as distances, areas, and volumes, derived from local fundamental features.

But the presence of nonlocal fundamental beables is definitely a nonclassical feature characteristic of the TI.

 

[indefinite_123]

There are a number of traditional classical nonlocal features such as distances, areas, and volumes, derived from local fundamental features.

But the presence of nonlocal fundamental beables is definitely a nonclassical feature characteristic of the TI.

Ok! thank you!

 

[member 673059]

@A. Neumaier How does the reformulation of quantum mechanics and electroweak theory in terms of the Clifford algebra $C(\mathbb{R}^{3,1})$ (cf. https://www.researchgate.net/publication/305483161_Geometric_Algebra_as_a_Unifying_Language_for_Physics_and_Engineering_and_Its_Use_in_the_Study_of_Gravity, https://www.researchgate.net/publication/252922221_Mysteries_and_Insights_of_Dirac_Theory, https://www.researchgate.net/publication/1739641_Gauge_Gravity_and_Electroweak_Theory) mathematically fit into your coherent foundations for quantum physics?