This paper treats the core of the thermal interpretation. It is the second in a series of three papers presenting a fully worked out version of Neumaier's thermal interpretation. A fourth paper that "summarizes the main features and adds intuitive explanations and new technical developments" was added later to the series. A fifth paper added later also claims to be part of the series, but is only indirectly related to the thermal interpretation. The book "Coherent Quantum Physics – A Reinterpretation of the Tradition" presents the material from these and more papers in a restructured form together with additional material. The most recent official description of the thermal interpretation of quantum physics is given in Section 9.2 of that book.

## Presentation of material

The presentation is easy to read, and contains many remarks and observations that are spot on both practically and philosophically. They are so much spot on that I started to read Neumaier's old material just to learn whether he was so spot on right from the beginning. Especially I browsed a preliminary German version from 2007 (http://arnold-neumaier.at/physfaq/therm/ThermDeutsch.txt) and a paper which contains the beginnings

A. Neumaier,

Ensembles and experiments in classical and quantum physics,

Int. J. Mod. Phys. B 17 (2003), 2937-2980.

quant-ph/0303047

http://arnold-neumaier.at/papers/physpapers.html#ensembles

http://arnold-neumaier.at/ms/ensembles.pdf

The old material also seems spot on, but not as smooth to read. Instead of chaining "convenient" truth together, it asks difficult questions and gives "inconvenient" answers. For example

--------------------------------------------

S33. Was wird aus dem Superpositionsprinzip?

--------------------------------------------

In der traditionellen Analyse des Messsprozesses nach von Neumann wird radikal vereinfacht (wodurch die Probleme entstehen), indem man Messungen als Reduktion auf Eigenwerte auffasst, und allgemeinere Situationen dann mit Hilfe des Superpositionprinzips analysiert.

In der Thermischen Interpretation ist das ein klein bisschen komplizierter. Wenn man nämlich ein Experiment wiederholt, hat sich der Zustand des Rests der Welt schon verändert, und man hat daher nicht mehr exakt dieselbe Situation.

Sondern nur noch im Mittel dieselbe. Das macht den ganzen Unterschied, Man kann nämlich nicht ganze Universen superponieren. Jedenfalls wüsste ich nicht, wie das präpariert werden soll. Es gibt in der Thermischen Interpretation nur _einen_ Zustand, den des gesamten Universums. Alles andere sind Derivate.

Das Superpositionsprinzip gilt nur für Systeme, die so klein sind, dass man sie innerhalb dieses Universums in praktisch beliebiger Anzahl herstellen und manipulieren kann. Makroskopische Systeme gehören definitiv nicht mehr dazu!

Diese Einschränkung bringt Wigners klassisches Argument

J.A. Wheeler and W. H. Zurek (eds.),

Quantum theory and measurement.

Princeton Univ. Press, Princeton 1983,

Kapitel II.2, insbes. pp. 285-288.

(siehe dazu den Beitrag ''Does decoherence solve the

measurement problem?'' in meinem theoretical physics FAQ

auf http://arnold-neumaier.at/physics-faq.txt)

zu Fall, das die Unvereinbarkeit von uneingeschränkter Unitarität, dem uneingeschränkten Superpositionsprinzip und dem Kollaps des Zustands bei einer Messung beweist.

Wir betrachten das detailliert im nächsten Beitrag anhand der Messung eines einzelnen Spins.

After browsing the old material, I am no longer sure whether the easy readability of the current presentation is really a virtue. However, there is also the fact that I was able to work completely through the new presentation. I noticed that I could just read page after page, and the subsections and sections would be finished before it got difficult. However, there are the many references to the literature, and trying to read those (or lookup some of the used concepts on wikipedia) is slow and tiring. (At least I did work through the relevant concepts on wikipedia after having read about 2/3 of the new presentation (i.e. the book/the entire series), and it was hard for me.) But I never managed to work through the old material (I first tried in 2014), and even now I only managed to browse it.

(Section "1 Introduction" ends with the following remark: "The bulk of this paper is intended to be nontechnical and understandable for a wide audience being familiar with some traditional quantum mechanics. [...] However, quite a number of remarks are addressed to experts and then refer to technical aspects explained in the references given." My impressions above confirm that this remark contains some truth.)

Because I quoted one difficult question and Neumaier's "inconvenient" answer above, I will give my (also "inconvenient") opinion later. The question also came up in discussions of Neumaier's papers, and I will give links demonstrating this (and also that my "inconvenient" opinion already occurred in those discussions). But let me now return to the paper itself, and some of its topics.

## Probability via expectation (non-ensemble interpretation)

This paper contains the non-ensemble interpretation of q-expectations which also applies to single systems, not just to ensembles. This was what initially interested me, and why I knew I had to schedule the time to read Neumaier's paper(s). This part is discussed in subsection "2.3 Uncertainty" (~2 pages), subsection "3.3 Deterministic and stochastic aspects" (~3 pages) and subsection "3.6 The stochastic description of a deterministic system" (~2 pages). Is is well written. I especially liked the eight "important examples of statistical models for deterministic situations with increasingly random appearance," with an explicit reference for each example to a paper or book where it is discussed in more detail. However, since section "3 Thermal interpretation of statistics and probability" (~14 pages) is part of a paper on the interpretation of quantum mechanics (~40 pages), the question arises how this non-ensemble interpretation can contribute to good foundations.

There is a bullet point in the section "5 Conclusion" that the thermal interpretation "applies both to single quantum objects (like a quantum dot, a neutron star, or the universe) and to statistical populations". The non-ensemble interpretation also allows to use the same concept/interpretation in both classical and quantum mechanics. (Can't find it explicitly mentioned in the paper, but this answer would fit well. In the next paper, it is conjectured that randomness too is the same concept (and has the same origin) in both classical and quantum mechanics.) And section "2.5 Formal definition of the thermal interpretation" adds the answer "The thermal interpretation avoids both the philosophically problematic notion of probability, and the anthropomorphic notions of knowledge and measurement."

However, an important answer is missing: His non-ensemble interpretation does not run into problems with "counterfactual definiteness". This is where previous attempts to base interpretation on the objective reality of q-expectations remained incomplete. David Mermin in What is quantum mechanics trying to tell us? explains (in section "IX. Absence of Correlata") why his "Ithaca interpretation of quantum mechanics" (IIQM) that insists that "only correlations between subsystems have objective reality" is forced to be a theory of "correlations without correlata":

"The correlata cannot all have physical reality because in spite of the existence of all subsystem joint distributions and of unique marginal distributions for individual subsystems, it is impossible to construct, in the standard way, a full and mutually consistent set of *conditional *distributions from the joint and individual subsystem distributions."

Mermin explicitly acknowledges that this forces his interpretation to remain incomplete:

This problem — how to make sense of correlations without correlata — brings us up against two major puzzles:

(1) How is probability to be understood as an intrinsic objective feature of the physical world, rather than merely as a tactical device for coping with our ignorance? How is one to make sense of fundamental, irreducible correlation?

(2) [...]

I propose to set aside both of these puzzles.

The old initial version of the "consistent histories interpretation" also explicitly acknowledges that it remains incomplete. However, it addressed the problems with "counterfactual definiteness" in a completely different way, a very formal and "calculational" one. In section "XI. Comments on other approaches," Mermin explains this as follows:

"The consistent histories interpretation of quantum mechanics applies to time-dependent as well as equal-time correlations. In contrast to the IIQM, consistent historians are not at all shy about dealing with the correlata that underly a given set of correlations. They gain this interpretive flexibility by insisting that any talk about either correlations or correlata must be restricted to sets of observables singled out by certain quite stringent consistency conditions."

## Core of the thermal interpretation

Subsection "2.2 Properties" discusses the ontological status of the thermal interpretation, making precise the concept of properties of a quantum system. Those are:

(S1) The state of a system (at a given time) encodes everything that can be said about the system, and nothing else.

(S2) Every property of a subsystem is also a property of the whole system.

(S3) The state of a system determines the state of all its subsystems.

(CC) Callen’s criterion: Operationally, a system is in a given state if its properties are consistently described by the theory for this state.

This is based on discussions from part I. It was shown that "If the state of every composite quantum system contains all information that can be known about this system, it cannot be a pure state in general." The density operator was defended as more fundamental than pure states, for example "... the deficiency always has the same root – the treatment of the density operator as representing a state of incomplete knowledge, a statistical mixture of pure states – ..." Even the state of the "one single world" is not assumed to be pure.

The states of a system in the thermal interpretation are *encoded* by density operators. However, a state itself is rather the collection of all q-expectations for that state. Section "4.1 Beables and observability in quantum field theory" states this as follows:

"According to the thermal interpretation, there is nothing in quantum field theory apart from q-expectations of the fields and q-correlations. The quantities accessible to an observer are those q-expectations and q-correlations whose arguments are restricted to the observer’s world tube. More precisely, what we can observe is contained in the least oscillating contributions to these q-expectations and q-correlations. The spatial and temporal high frequency part is unobservable due to the limited resolution of our instruments."

This quote is relevant for a number of reasons. The q-expectations have a spatial and temporal dependence (as parameters). The q-correlations even depend on more than one different spatial and temporal parameter. (This is how I interpret the difference between q-expectations and q-correlations in this quote.) We are given an explicit reason why some q-expectations are not observable (because their high frequency dependence of the spatial and temporal parameters exceed the resolution limits of our instruments). And this quote shows that the thermal interpretation applies to quantum field theory just as it applies to quantum mechanics, and also to classical statistic mechanics. This is also written explicitly in section "5 Conclusion":

"The thermal interpretation of quantum physics (including quantum mechanics, statistical mechanics and quantum field theory) is an interpretation of everything. It allows a consistent quantum description of the universe from the smallest to the largest levels of modeling, including its classical aspects."

## Superdeterminism rescues "Many Worlds minus the Many Worlds"

There are many other nice and interesting things I could (and would want to) write about this paper specifically and the thermal interpretation in general. But this review is already quite long now, and I still need to express my promised "inconvenient" opinion on Neumaier's difficult question together with relevant links. Scott Aaronson described the difficult question as making sense of "Many Worlds minus the Many Worlds" in an old comment (2011):

Tim Maudlin #6: The view that I take Banks to be defending here is actually one I’ve found extremely common among physicists, so maybe it would be worth philosophers trying to understand it sympathetically and seeing how much sense they can make of it. I like to think of this view as “Many Worlds minus the Many Worlds” — i.e., many worlds without *calling* it that, or even acknowledging a need to discuss that apparent implication of what you’re saying.

My "inconvenient" opinion is that Neumaier's "inconvenient" answer implicitly invokes (a valid form of emergent) superdeterminism, but still can't prevent Many Worlds completely. His answer only seems to succeed to prevent Many Worlds for our world today, but doesn't seem to exclude the possibility that the world initially splitted many times before our current macroscopic world emerged. Here is the translation of the relevant part of Neumaier's "inconvenient" answer:

You cannot superpose entire universes. In any case, I don't see how that should be prepared. There is only _one_ state in the thermal interpretation, that of the entire universe. Everything else is derivatives.

The superposition principle only applies to systems that are so small that they can be produced in practically any number and manipulated within this universe. Macroscopic systems are definitely no longer one of them!

This limitation brings down Wigner's classic argument, which proves the incompatibility of unrestricted unitarity, the unrestricted superposition principle and the collapse of the state during a measurement.

The implicit superdeterminism in this argument is that whenever we prepare a small system and measure it, the state of the measurement device together with the rest of the universe will be such that the measurement device ends up in a valid (i.e. non-superposed, neither coherent nor incoherent) macroscopic state. It is a valid form of emergent superdeterminism, because the macroscopic observables emerged such that they will never encounter superpositions from the evolution of the _one_ state of the universe.

This is less troublesome than to invoke superdeterminism to get *locally realistic determinstic results emulating the results from* weird quantum superpositions, which is how the superdeterminism loophole of the Bell test experiments is normally understood. In discussions of Neumaier's papers, this comment by charters (Apr 22, 2019) was not the first to mention superdeterminism, but it explained well why it is relevant. When charters wrote later (May 15, 2019) "I think we eventually clarified that the TI is not superdeterministic", it only meant that the meaning of superdeterminism how it is normally understood as a loophole of the Bell tests didn't apply.

This answer by Neumaier (May 8, 2019) in another thread shows how the debate with charters evolved. I didn't find the comment where they resolved their dispute, but when eloheim later tried to restart the dispute, Neumaier wrote (May 14, 2019): "**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." And Subsection 5.1 of Part III says: "In the thermal interpretation, the traditional difficulty to show that there is always a unique outcome is trivially solved since by definition, the outcome of reading a macroscopic quantity is its expectation value, with negligible uncertainty."

I think this quote from Subsection 5.1 of Part III nicely illustrates how Neumaier has polished away his old difficult questions and "inconvenient" answers. But if he wants to convince people like Tim Maudlin or Scott Aaronson that his thermal interpretation must be taken seriously, I guess acknowleding the implication of what he once wrote would have a better chance to succeed. (Just like S. Hossenfelder and T.N. Palmer in Rethinking Superdeterminism directly address objections raised by Tim Maudlin and Mateus Araújo in section "4.4 The Tobacco Company Syndrome".)