The third paper of the series about the foundations of quantum physics explains how measurements are seen from the point of view of the thermal interpretation. Unlike in traditional interpretations, single, non reproducible observations do not count as measurements since this would violate the reproducibility of measurements. This difference is most obvious in the interpretation of single discrete microscopic events.
Generally, the measurement principle says that a macroscopic quantum device qualifies as an instrument for approximately, with uncertainty $\Delta a$, measuring a Hermitian quantity $A$ of a system with density operator $\rho$, if it satisfies the conditions of uncertainty bounded from below and reproducibility. There are statistical and deterministic measurements with the corresponding nature of the relationship between the state of the system and the state of the measurement instrument. An event-based instrument is a statistical instrument measuring the probability of events modeled by a discrete (classical or quantum) statistical process. The correspondence between eigenvalues and observables is only perfect for sharp observed quantities with zero uncertainty.
Mathematically, elementary particles are causal unitary irreducible representations of the Poincare group. In an interacting quantum field theory, only asymptotically free particles exist. Specifically, the particle concept is only valid if the semiclassical approximation holds and geometric optics can be applied. Otherwise, the S-matix calculated from renormalized quantum field theory is needed. From the quantum optics point of view, the photoelectric effect can be described as the measurement of a free classical or quantum electromagnetic field by means of a photomultiplier. Stokes’ description of a partially polarized quasi monochromatic beam of classical light behaves exactly like a modern quantum bit, including Born’s rule (Malus law) and Schrödinger’s equation.
In the thermal interpretation of statistical physics, the state of the system is described by the density operator of Gibbs states from statistical mechanics and the usual hierarchy of approximations from nonequilibrium statistical mechanics to thermal equilibrium exists. The Koopmann representation can then be used to unify classical and quantum mechanics, such that states of classical mechanics are represented by diagonal density operators and states of quantum mechanics contain off-diagonal elements. The functions of expectation values follow Hamiltonian dynamics given by Poisson brackets and the classical limit can be explained by the law of large numbers and coarse graining. The information ignored by coarse-graining leads to the intrinsic quantum probability. Empirical randomness is taken to be an emergent feature of deterministic chaos implicit in the deterministic dynamics of the Ehrenfest picture. To describe applications between the classical and quantum regime, quantum-classical models based on the Liouville and Hamilton equations are often used. This results in Ehrenfest equations where the l.h.s. is replaced by classical variables. The Lie algebra of the quantities is the direct product of the Lie algebra of the classical sub-system and the Lie algebra of the quantum subsystem, which results in non-linearities responsible for chaotic behavior of the system.
Compared to other interpretations, the Copenhagen and statistical interpretation can be seen as limits of the thermal interpretation. In the thermal interpretation, the Heisenberg cut is replaced by the choice of relevant variables that describe the coarse grained deterministic system. Particles appear only as detection events created by the detector and mediated by fields and the “collapse” is a result of coarse graining. In a statistical interpretation, all statements claimed about single quantum systems are non-minimal. In particular, the minimal interpretation does not address the foundational problems posed by the ensembles of equilibrium thermodynamics.
As Arnold Neumaier explicitly says, the thermal interpretation is inspired by what physicists actually do rather than what they say. It is therefore the interpretation that people actually work with in the applications (as contrasted to work on the foundations themselves), rather than only paying lip service to it. Accordingly, this third paper in the series features some really nice discussions of real-world measurements and interesting thoughts about real-world measurements from a wide range of applications.
However, refuting single measurements on microscopic systems and their scientific legitimacy is probably not something everybody agrees with. Even if in particle physics experiments, the interpretation could be changed to avoid particles, I personally see no strong need for doing so. Also, quantum field theory is rather seen as a framework about fields and their excitations than about beams as in geometric optics for example. There is nothing wrong with anti-particles showing up in the formalism of relativistic quantum field theory.
Stokes' description of the quantum bit by means of polarized light in classical optics is rather interesting. And modeling the discrete outcomes of measurements by multistable systems is a nice idea worthwhile to follow up. However, the notion explicitly stated that the thermal interpretation gives a deterministic picture of QM, God does not play dice but moves fast to produce randomness, makes me feel rather uncomfortable. At a fundamental level, the world is surely not quantum-classical but quantum, even though it might, for computational physics purposes for example, be possible to model quantum uncertainty by deterministic chaos.
If the thermal interpretation were rather intended to be an interpretation of statistical mechanics and a unified framework to describe experimental practice in a wide range of applications than to revise and change microscopic theoretical quantum mechanics, I could more fully embrace it. The presented need to change some well established views and concepts, about things such as the existence of particles, the inherent randomness of quantum mechanics, or the observability of single microscopic systems, is for me personally not strong or urgent enough.
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