# I The thermal interpretation of quantum physics

#### akhmeteli

In the wave function, there is no actual motion of particles, just a motion of probability amplitude.
Moreover, everything happens in a fixed frame in which the spatial Fourier transform is performed; one cannot argue with time dilation or length contraction.

From the Schrödinger equation, the support of $\psi$ is ,after sufficiently short but positive time, definitely the union of the initial support and that of $H\psi$. But there is no reason to suppose that the fairly arbitrary $H$ allowed by the construction in K/P leads to an $H\psi$ with bounded support; note that $M$ can be quite arbitrary. To preserve the relativistic probability interpretation in concrete cases, one would have to construct very special $M$ that preserve a bounded support - but this seems quite a nontrivial mathematical task.
Again, the Green function for the Dirac equation is causal. So I don't see how your Section 3.3 contains the argumentation.

And what is K/P? I guess I missed something.

#### A. Neumaier

Again, the Green function for the Dirac equation is causal. So I don't see how your Section 3.3 contains the argumentation.

And what is K/P? I guess I missed something.
K/P is Keister & Polyzou. I am not discussing the Dirac equation, which has acausal solutions!

#### akhmeteli

I am not discussing the Dirac equation, which has acausal solutions!
What acausal solutions of the Dirac equation do you have in mind? And again, if the Dirac equation has problems, why is this the Born's rule's problem? Again, I fail to find the argumentation in your Section 3.3.

#### A. Neumaier

What acausal solutions of the Dirac equation do you have in mind? And again, if the Dirac equation has problems, why is this the Born's rule's problem? Again, I fail to find the argumentation in your Section 3.3.
The revised version of Part I no longer mentions the Dirac equation, hence there is no point bringing it up again.

My argument is solely about the consistent relativistic multiparticle dynamics in K/P.

#### akhmeteli

I am not discussing the Dirac equation, which has acausal solutions!
What acausal solutions of the Dirac equation do you have in mind?
The revised version of Part I no longer mentions the Dirac equation, hence there is no point bringing it up again.

My argument is solely about the consistent relativistic multiparticle dynamics in K/P.
Again, I have yet to understand your arguments in post 646, but you also stated there:
A. Neumaier said:
The argumentation is completely contained in point 4 of Subsection 3.3 of my Part I.

I explained that there is no valid argumentation in point 4 of Subsection 3.3, as the argumentation in footnote 16 is not valid for the Dirac equation, and that is how the Dirac equation is relevant. Note that point 4 does not mention K/P, and footnote 16 has nothing to do with multiple particles. The reference to K/P in point 5 is just that, a reference to a huge article, so there is no valid argumentation in your arxiv article. Again, maybe the reasoning in your post 646 is correct, and I will try to understand it, but there is no argumentation in the article for your statement about relativistic particles in point 5.

#### PeterDonis

Mentor
If momentum is large, the speed still cannot exceed the velocity of light in the relativistic case.
Not if the momentum is timelike, no. But in quantum field theory, there is a nonzero amplitude for the momentum to be spacelike (at least, that's one way of describing what the math says).

#### A. Neumaier

Not if the momentum is timelike, no. But in quantum field theory, there is a nonzero amplitude for the momentum to be spacelike (at least, that's one way of describing what the math says).
I referred to spatial momentum, in a fixed frame, in a covariant multiparticle setting defined in the papers cited. It lacks the cluster decomposition property and is not easily related to quantum field theory.

#### akhmeteli

Not if the momentum is timelike, no. But in quantum field theory, there is a nonzero amplitude for the momentum to be spacelike (at least, that's one way of describing what the math says).
While we were not discussing QFT, could you please specify what situation or result you have in mind?

#### PeterDonis

Mentor
could you please specify what situation or result you have in mind?
It's a fairly general statement about QFT. Another way of stating it is that if you look at the Feynman propagators for various quantum fields, they won't vanish for a pair of events that are spacelike separated. The key property that preserves causality is that field operators at spacelike separated events commute. See, for example, the discussion in sections 2.6.1 and 2.7 of these lectures:

#### akhmeteli

It's a fairly general statement about QFT. Another way of stating it is that if you look at the Feynman propagators for various quantum fields, they won't vanish for a pair of events that are spacelike separated. The key property that preserves causality is that field operators at spacelike separated events commute. See, for example, the discussion in sections 2.6.1 and 2.7 of these lectures:

Well, this is indeed a specific property of QFT. In this case one cannot be sure that the particle detected outside the light cone is the same particle that was created initially. So I am not sure this is quite relevant in the context of A. Neumaier's critique of the Born's rule (see also his post 657).

#### A. Neumaier

if the Dirac equation has problems, why is this the Born's rule's problem?
The only problem is that you apply a faulty equation to the reasoning in my paper. The K/P Hamiltonians have no such problems.

#### akhmeteli

The argumentation is completely contained in point 4 of Subsection 3.3 of my Part I. The Keister-Polyzou paper just contains dynamical relativistic examples. If you want a definite example, you may take the example of spinless quarks in Section 2.3 (p.26 in the copy cited in post #642). But the details do not matter.

The only relevant points for my argument are that, although the setting is Poincare-covariant,
1. the wave function at fixed time is a function of several spatial momenta, which after Fourier transform to the position representation becomes wave function that is a function of spatial positions,
2. Born's rule makes claims about the probabilities of measuring,
3. the Hamiltonian and the position operators have a nonlocal commutator.
As a result, the dynamics introduces (as claimed in Part I) after arbitrarily short times nonzero probabilities of finding an initially locally prepared particle (initial wave function with compact support), at almost any other point in the universe.

Thus the position probability interpretation itself contradicts the principles of relativity!
I failed to understand how the example in K/P is relevant. Could you please explain?

I understand items 1 and 2 in your quoted post. I don't understand item 3 as I don't know what Hamiltonian you have in mind. (Neither do I understand how you get your conclusion "
the dynamics introduces ... after arbitrarily short times nonzero probabilities of finding an initially locally prepared particle", but maybe this will be clearer after you explain item 3)
Could you please explain? Thank you.

#### atyy

Do you write "Many-Worlds Interpretation" or "many-worlds interpretation"?

Why did you choose "thermal interpretation" instead of "Thermal Interpretation"?

#### A. Neumaier

Do you write "Many-Worlds Interpretation" or "many-worlds interpretation"?

Why did you choose "thermal interpretation" instead of "Thermal Interpretation"?
I write all interpretations in lower case, except possibly in copy/paste mode. But MWI, TI. In the 7 basic rules of quantum mechanics, I kept the convention from the earlier draft by tom.stoer....

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#### eloheim

I’ve been following some of the discussion on here about the Thermal Interpretation, and I’ve reviewed the linked papers. I like the idea of positing expectation values, rather than eigenstates, as primary, and taking something like a fluid mechanics approach to quantum physics. In the end though I can’t understand how the TI is supposed to solve the problems of other interpretations, beyond merely decreeing, “It’s resolved. Don’t worry about it.”

Say we’re doing a standard bell-type test on entangled photons, with anticorrelted results for measurements with identical orientations. We will put one of the detectors (Bob’s) millions of miles away in space for clarity. According to the thermal interpretation, the perfectly anticorellated results we get for each entangled pair is NOT due to any property of beams themselves (aka what other interpretations call the individual particles), but instead due to FAPP unknowable details of the macroscopic detectors.

Alice’s detector is near the photon source and is ready to take a measurement immediately. Bob, on the other hand, doesn’t even start building his detector until his photon is well en route. Despite the fact that detector A(lice) was already in existence when the experiment began, and detector B(ob) wasn’t assembled until well after Alice’s particle was measured, each detector happens to be composed in such a way that they “magically” give opposite results for measurements of the beam performed at the same angle. These two detectors have nothing in common; they were produced completely separately, millions of miles apart and at different times, and yet essentially their random micro-details conspire in intimate coordination!

(To add one more layer to further illustrate the point, say Bob built 3 detectors instead of one. At the last minute before detection he directs his photon to one of the three chosen at random (say conditioned on a photon from a distant star in the opposite direction from Alice). At the same time, he also does his own (completely unrelated) Bell experiment, using the other two detectors. We now have a situation where the microscopic details of just one of the detectors is, again for seemingly no reason, aligned in such a way as to produce perfect anticorrelation with Alice, while the other two detectors happen to be composed such that they correlate with one another instead. And yet we can randomly switch which detector is used for what purpose at the last moment with no ramifications. How is this at all plausible?)

Essentially my question is, “how are these coincidences explained by the TI?” Other interpretations point to the entangled particles, or a pilot wave, for example, but the TI doesn’t have that same luxury. If this was a foundations-agnostic interpretation that presented itself as (just) a new tool for calculation, I wouldn’t complain, but the TI is billed as solving the measurement problem and fixing quantum physics’ outstanding contentions. IMHO resolving quantum foundations via fiat doesn’t do the trick.

#### A. Neumaier

I can’t understand how the TI is supposed to solve the problems of other interpretations, beyond merely decreeing, “It’s resolved. Don’t worry about it.”
Essentially my question is, “how are these coincidences explained by the TI?”
No interpretation explains this, except by voicing the mantra ''nonlocality''. How Nature manages to realize these nonlocal coincidences is a secret of its creator. Bell's analysis just shows that one needs explicitly nonlocal beables if one wants to avoid all sorts of other weird assumptions. Nonlocal beables depends on simultaneous values at very far away points, and once one acknowledges that these influence local beables, nonlocal correlations between the latter are explained (in some sense).

The TI is nonlocal enough to be consistent with these findings. Moreover, it explains why there is nothing to worry about, since the usual worry has to do with a seeming incompatibility with special relativity. But there is no such incompatibility, as discussed in Subsection 4.4-4.5 of Part II. Thus Nature can consistently be relativistic and have nonlocal coincidences of Bell type.
Other interpretations point to the entangled particles, or a pilot wave
How does this pointing provide an explanation??? It only says that certain dynamical calculations leads to the result, but does not explain the result, unless calculation is deemed explanation. (But the same calculations then work for the TI.)
the TI is billed as solving the measurement problem
The problem you posed in your post is not the measurement problem but the nonlocality puzzle.

The measurement problem is the problem of why there are unique and discrete outcomes for single quantum systems although the wave function produces only superpositions of (measurement,detector state) pairs. This problem is solved by the TI; see Subsection 5.1 of Part III and Section 3 of Part IV.

#### ftr

How Nature manages to realize these nonlocal coincidences is a secret of its creator.
You are being sarcastic ,right? You don't actually believe what you said as a physicist, do you?

#### A. Neumaier

You are being sarcastic ,right? You don't actually believe what you said as a physicist, do you?
Physicists lifted many secrets of Nature but not (yet?) this one.

#### eloheim

The problem you posed in your post is not the measurement problem but the nonlocality puzzle.

The measurement problem is the problem of why there are unique and discrete outcomes for single quantum systems although the wave function produces only superpositions of (measurement,detector state) pairs. This problem is solved by the TI; see Subsection 5.1 of Part III and Section 3 of Part IV.
You are absolutely right about this; my apologies for a poor choice of words. I was trying to suggest that the TI has the same issues with how it treats (or rather doesn't treat) such foundational problems in general. However, I didn't defend any other criticisms in my post (and I'm not sure that I could) so please disregard my mention of the measurement problem if you will.
How does this pointing provide an explanation??? It only says that certain dynamical calculations leads to the result, but does not explain the result, unless calculation is deemed explanation. (But the same calculations then work for the TI.)
The difference is that, according to most interpretations, the singlet state (i.e. the two entangled particles) is a nonlocal beable, so when you do something to one of the particles (like measure spin) the other is affected accordingly. This, combined with the local detector settings on each end of the experiment, is enough to produce the desired QM statistics. In this case the detectors would be entangled only after interacting with the particles, and no nonlocal correlations at all between the detectors themselves are necessary to explain the phenomenon. Conversely, the TI wants to say that the correlations are in the detectors from the beginning, and are only acting on noise in the particle beam.

#### A. Neumaier

Conversely, the TI wants to say that the correlations are in the detectors from the beginning, and are only acting on noise in the particle beam.
No. The correlations are caused by the interaction - without interaction there is of course no measurement result. The beam produces a bilocal field characterized (among others) by local and bilocal beables, namely the q-expectations of $A(x)$, $B(y)$, $A(x)B(y)$ and $B(y)A(x)$ at spacetime positions $x$ and $y$. When reaching the detectors at $x$ and $y$ (including the prepared controls manipulated by Alice and Bob, respectively), these interact according to the deterministic, covariant dynamics of the system beam+detector and result in correlated local measurement results at $x$ and $y$, depending on these controls.

Thus the explanation is similar to that that you accepted as explanatory in the other interpretations:
according to most interpretations, the singlet state (i.e. the two entangled particles) is a nonlocal beable, so when you do something to one of the particles (like measure spin) the other is affected accordingly. This, combined with the local detector settings on each end of the experiment, is enough to produce the desired QM statistics. In this case the detectors would be entangled only after interacting with the particles, and no nonlocal correlations at all between the detectors themselves are necessary to explain the phenomenon.

#### Auto-Didact

No interpretation explains this, except by voicing the mantra ''nonlocality''. How Nature manages to realize these nonlocal coincidences is a secret of its creator.
The reference to not just QM but Nature itself being nonlocal is an implication that QM is - as the realists claim - an incomplete theory which can be completed by creating the correct mathematization of the concept of nonlocality. This means inventing or identifying the branch of mathematics for this concept, and then applying that branch of mathematics to QM such that QM itself may be reformulated in this new mathematical language which naturally captures and explicitizes the nonlocality in a mathematically useful form, in the hope that this will naturally lead to a completion of QM.

#### A. Neumaier

such that QM itself may be reformulated in this new mathematical language which naturally captures and explicitizes the nonlocality in a mathematically useful form, in the hope that this will naturally lead to a completion of QM.
Well, my claim is that the thermal interpretation does just this!

#### Auto-Didact

Well, my claim is that the thermal interpretation does just this!
I'm aware that you think that and I applaud your effort. I haven't had enough time to chew on the TI yet, haven't read the three papers yet in depth.

Having read a significant portion of this thread though, it feels to me that the TI is a form of superdeterminism, wherein even what seems to be truly random (i.e. measurement outcomes as dictated by the Born rule) is actually completely a deterministic consequence of the initial condition of the universe, in conjunction with a novel 'thermalization' scheme for generating quasiprobabilities.

#### A. Neumaier

Having read a significant portion of this thread though, it feels to me that the TI is a form of superdeterminism, wherein even what seems to be truly random (i.e. measurement outcomes as dictated by the Born rule) is actually completely a deterministic consequence of the initial condition of the universe, in conjunction with a novel 'thermalization' scheme for generating quasiprobabilities.
What you state here makes the TI a form of determinism (which it is). Superdeterminism, I was told, is a more specific label that does not apply to the TI.

#### Auto-Didact

What you state here makes the TI a form of determinism (which it is). Superdeterminism, I was told, is a more specific label that does not apply to the TI.
It isn't clear to me from that post alone that the TI actually is or is not superdeterministic, nor whether it conceptually adheres to any other form of predeterminism which has yet to be mathematicized. So far, the TI still seems to be more deterministic than other physical theories are; that isn't a good thing.

It goes without saying that accepting any form of predeterminism is not merely a death blow to some theory, but one to science itself, since then the very idea of experimental verification and falsification would turn out to be so hopelessly misguided that it would render the entire human scientific enterprise as a completely ridiculous enormous waste of time.

"The thermal interpretation of quantum physics"

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