The thermal interpretation

Here I present my own interpretation of quantum mechanics, the thermal interpretation.

The traditional interpretation of the orthodox formalism is modified in that - contrary to the tradition in which only von Neumann measurements of eigenvalues are treated as objective - it will be assumed that all raw measurements are measurements of expectation values of certain operators (or concepts that can be derived or calculated from them) and that the quantum mechanical expectation values have nothing directly to do with statistical expectation values (in the sense of mean values of sequences of measurements).

The resulting interpretation enables one to describe all measurements consistently without changing quantum mechanics. The only thing that needs to be changed is the interpretation of the orthodox calculus, in accordance with the fact that thermodynamics, hydrodynamics and kinetics - in other words the theories described by our measurement devices - all appear in the context of statistical mechanics as theories of expectation values.

The observed quantum probabilities are explained by sensitive dependence of the measured expectation values on the prepared expectation values - exactly as observed in the Lorentz attractor. Random behaviour appears precisely when this sensitivity is present. (This is easily verified by semiclassical calculations involving quantum chaos.)

Details will be given in the following FAQ entries.

A small part of the thermal interpretation has already been published in: quant-ph/0303047 = Int. J. Mod. Phys. B 17 (2003), 2937-2980, hereafter referred to in this FAQ as EEEQ.

EEEQ shows how the thermal interpretation developed out of my analysis of the foundations of quantum logic, but it says nothing about the consequences of the new interpretation and the analysis of actual measurement processes. A publication on this subject is in preparation.

However in EEEQ I take a two-pronged approach, and describe the traditional statistical interpretation at the same time.

In the abstract ensemble concept which is the basis of my account, a probabilistic interpretation is possible but not necessary, and for individual systems not meaningful.

When one leaves out Section 6 (Probability) the remainder is:
1. completely understandable,
2. 100% compatible with the actual practice of quantum mechanics,
3. physically interpretable,

although the word ’probability’ has no longer passed our lips.

The ’squared probability amplitude’ formula (24), which is the basis of the traditional interpretation of quantum mechanics, is only a marginal comment in Section 6, and thereby completely unimportant to the interpretation. I included this section only to show that my axioms are completely sufficient to derive the traditional probability concept (if one wants to).

One habitually starts from this formula and thereby creates all of the problems of interpretation.

In this way one destroys the close relationship between classical and quantum mechanics, and rediscovers it (for most students at least a year later) only when one learns about the density matrix in statistical mechanics.

By then so much havoc has been wrought that a hopeless chaos reigns in the understanding of quantum mechanics, and order is hard to restore…

Arnold Neumaier (
A theoretical physics FAQ