Core Propositions of the Thermal Interpretation

Quantum mechanics describes the universe as a whole, and in particular everything in it that one can measure in a reproducible fashion - including single systems, ensembles in the statistical sense, detectors, and physicists.

The universe as a whole behaves deterministically, and can be described with a classical Hamiltonian, with dynamics defined by a Hamiltonian function and a Poisson bracket. The classical variables in this dynamics are the fields and correlation functions traditionally called expectation values.

The universe has a classical state space, whose pure states are all the density matrices of quantum mechanics. (The traditional interpretation, in contrast, has a quantum state space, whose pure states are only the density matrices of rank 1. This restriction is the cause of the traditional interpretation problems.)

All properties of the physical systems in our universe are derived from a single mathematical model of the universe and its evolution. In particular, the state of every physical system is completely determined by the state of the universe.

The dynamics of such a system are given by projection of the dynamics of the universe onto the algebra of variables of the system, and can, in the Markov approximation, be described by a dissipative differential equation in Lindblad form. If the dissipation is negligible, one obtains the traditional von Neumann equation for the density matrix of the system.

An important feature of the thermal interpretation is the observance of the logical requirement that one must - apart from motivational remarks - talk only about objects with a mathematically precise definition.

This ensures a logically consistent model, in which the traditional components of our universe can be defined and analysed, together with their mathematical descriptions.

In particular, the measurement process is modelled by the mutual interaction of a quantum system with a detector, both understood as subsystems of the universe. In this way the Copenhagen interpretation's division of the world into quantum systems and classical measurement apparatuses is overcome. What a measurement represents is pinned down.

Chance and quantum leaps turn out simply to be consequences of a description of quantum system and detector which, as a result of the Markov approximation, does not completely take into account their mutual interaction with the rest of the universe.

In particular, the observable distribution of measurable random variables is in accordance with the statistical interpretation of quantum mechanics.

In the thermal interpretation the Born rule, in which probability is the square of the absolute value of an amplitude, follows directly from the projection of the many particle system onto the traditional reduced description by classical pointer variable of the detector plus quantum state of the measured quantum system.

The interpretation is therefore 100% compatible with the practice of quantum mechanics, but derives the probability interpretation from simple deterministic presuppositions, instead of making the inexplicable (and philosophically problematic) assumption that it simply counts as one of the mysteries of our universe.

Arnold Neumaier (
A theoretical physics FAQ