# Foundations of quantum physics II. The thermal interpretation

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Referee this paper: arXiv:1902.10779 by Arnold Neumaier

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Abstract: This paper presents the thermal interpretation of quantum physics. The insight from Part I of this series that Born's rule has its limitations -- hence cannot be the foundation of quantum physics -- opens the way for an alternative interpretation: the thermal interpretation of quantum physics. It gives new foundations that connect quantum physics (including quantum mechanics, statistical mechanics, quantum field theory and their applications) to experiment. The thermal interpretation resolves the problems of the foundations of  quantum physics revealed in the critique from Part I. It improves the traditional foundations in several respects:

• The thermal interpretation reflects the actual practice of quantum physics, especially regarding its macroscopic implications.
• The thermal interpretation gives a fair account of the interpretational differences between quantum mechanics and quantum field theory.
• The thermal interpretation gives a natural, realistic meaning to the standard formalism of quantum mechanics and quantum field theory in a single world, without introducing additional hidden variables.
• The thermal interpretation is independent of the measurement problem. The latter becomes a precise problem in statistical mechanics rather than a fuzzy and problematic notion in the foundations. Details will be discussed in Part III.
requested Mar 1
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paper authored Feb 27 to quant-ph
edited Mar 1

## 1 Review

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The motivation for a new interpretation of quantum mechanics to have a framework, that includes the applications of quantum mechanics and actual macroscopic measurements, was presented in the previous paper.  Accordingly, the thermal interpretation discussed in this work is intended to bridge the gap between the formal core of quantum mechanics and its applications and macroscopic measurements.  The name for the interpretation is chosen from the fact that real-world measurements are done in a thermal environment at a certain temperature.

To describe quantum mechanics, the thermal interpretation uses as usual a Hilbert space, the field content of the fundamental forces, and a unitary representations of the Heisenberg, Galilei or Poincare group.  The q-expectations follow the deterministic dynamics of the so-called Ehrenfest picture.  The Ehrenfest picture is obtained by introducing a Lie operator that represents the Poisson bracket in the classical case and the commutator in the quantum case, as well as a unified notation for Liouville integration and the quantum trace. The dynamics of the q-expectations of a quantity can then be shown to be given by the Ehrenfest equations. The thermal interpretation considers two kinds of uncertainty; one that can in principle be resolved and a conceptual uncertainty. The quantum uncertainty is assumed to be of the same conceptual kind as the uncertainty of position of macroscopic objects. It can be shown, the thermal interpretation fullfills the requirements for good foundations as outlined in the previous paper.
To explain how probabilities and statistics are treated in the thermal interpretation, the classical formalism for probability notions is introduced by means of expectations along the lines of Whittle. Due to the weak law of large numbers, quantities become arbitrarily significant with increasing size of the sample.  Deterministic  reasoning  is then  appropriate  for  all  sufficiently significant quantities.  Statistical reasoning is necessary for noisy quantities, and requires that these quantities are sufficiently similar and sufficiently independent to ensure that their mean is significant. Measuring probabilities by a relative frequencies gives in principle arbitrarily accurate results due to the law of large numbers. Generally, a stochastic description of a deterministic system is obtained by applying a reduced or coarse grained description.
In rigorous terms, quantum field operators are distribution valued operators. The quantities in quantum field theory are smeared fields, described by local space-time integrals using an appropriate test function. In the thermal interpretation, the observables of QFT  are the q-expectations of those smeared quantum fields and correlations of them. The dynamics of theses q-expectations are given by generalized covariant Ehrenfest equations in the Ehrenfest picture and generalized covariant von Neumann equations in the Schrödinger picture. Depending on the specific situation, the Ehrenfest equations are equivalent to the  hydrodynamic or Boltzmann-like equations or to thermodynamic equations of state in thermal equilibrium.  Generally, in the thermal interpretation everything is based on the expectations of the smeared quantum fields, including the universe as a whole. Three different notions of relativistic causality are introduced. Particularly new is the extended causality for correlated systems with spatially separated parts. This new notion of causality, together with calling entangled entities an extended system (or object) are used to resolve some apparent paradoxes in Bell type entanglement experiments.  The apparent FTL propagation of information is resolved by the propagation of conditional information.

The thermal interpretation stretches quantum mechanics, which is usually considered to be a theory for the microscopic regime, far beyond its original purpose. It is explicitly meant to be an IOE (interpretation of everything) and indeed it seems to me to be some kind of a merger of theoretical, experimental, and applied quantum mechanics. In the thermal interpretation, macroscopic and microscopic considerations are mixed in a rather unusual way. By trying to simultaneously describe physics at all scales at once, it seems to reject the Wilsonian concept of effective description of physics that are only valid at specific scales. As the thermal interpretation is based on the Ehrenfest picture, where the q-expectations calculated from tracing over the statistical operator are the dynamical variables, the distinction between the uncertainty for a single quantum system (conventially seen as limitations to predictability/deterministicity  of quantum mechanics) and the uncertainty when actually doing the measurements, is eliminated. Instead, the thermal interpretation “fills” the quantum uncertainty by extending the microscopic objects considered. The conventional quantum uncertainty as well as the microscopic physics is  some kind of “hidden” in the density operator of the thermal interpretation.
Calling correlated objects in quantum mechanics (spatially) extended objects in a literal sense is highly unusual. Quantum entanglement is just correlation, which by definition does not provide any causal relationship between the entangled objects.
Statistical correlations due to preparation of the entangled parts of the system have nothing to do with dynamical propagating of information. So for me personally that's all that is about Bell-type and other entanglement experiments and I don’t see the need for new constructs such as conditional information in this context.

To me it seems that the thermal interpretation is motivated by a strong preference for what can be observed at everyday human scales, whereas the reality of everything else (such as for example fundamental particles, or physics at astronomical/cosmological regimes that is assumed to have happened before humans were present or takes place too far away) is questioned. However, most theoretical physicists see the movement of science away from what can just be directly observed at human accessible scales to smaller and larger regimes  (by theoretical extrapolations or complicated indirect measurements) as legitimate scientific progress.
For those reasons it seems that the thermal interpretation is more appropriately an interpretation of (experimental) statistical mechanics or thermodynamics, than of theoretical microscopic quantum mechanics.

reviewed Mar 6 by (4,935 points)
edited Mar 12 by Dilaton

Thanks for the review; here some comments:

Paragraph 2: The equations of hydrodynamics (and the other equations mentioned) are dissipative, hence not equivalent to the conservative Ehrenfest equations; they arise from the latter only through coarse-graining (dropping from the dynamics as irrelevant all multipoint correlations).

Paragraph 3: The Wilsonian picture of quantum field theory does not conflict with the thermal interpretation. Effective field theories are simply coarse-grained approximations to more fundamental theories, obtained by integrating out the energies above the desired scale.

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