Why has no one before me thought of this?

There have certainly been plenty of attempts to understand quantum mechanics as a deterministic theory of the whole universe; however only a few have appeared in academic journals. The difficulty lies in constructing - out of philosophical deliberations - a precise, scientific formulation, from which the Born rule can be derived and which can convincingly refute the traditional counterarguments (in particular those from Wigner).

The two most important alternatives (Bohm, Many Worlds) have their own serious flaws and have therefore not been able to make much impact.

Much of Bohm's interpretation is counterintuitive, for example, the electron of a hydrogen atom in its ground state localises itself in a fixed position (relative to the atomic nucleus) and does not move! Thus this interpretation has only been accepted by a minority. See also: http://www.mat.univie.ac.at/~neum/papers/physpapers.html#bohm

In the many worlds interpretation, a multitude of alternative, unobservable worlds is postulated, and probability theory loses its traditional significance in the single, actually observed world. Therefore this interpretation is also very controversial. See also: http://www.mat.univie.ac.at/~neum/papers/physpapers.html#manyworlds

What is new about the thermal interpretation is the identification of observable variables with the slowly altering expectation values of microscopic variables, in the sense of statistical mechanics, instead of applying a statistical meaning to these expectation values. This provides a clear and intuitive background against which a self-consistent theoretical basis for the probability structure could be built.

In his book 'Directions in Physics' (1975) Dirac writes on page 10:

''And I think it is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinism and which will, therefore, justify the Einstein point of view.''

(He certainly did not mean the Bohmian mechanics by this, since at this point it already lay in the past, and therefore had obviously not been able to convince him.)

''But such a return to determinism could only be made at the expense of giving up some other basic idea which we now assume without question.''

What one must give up is the so far unquestioningly accepted interpretation of the expectation value as a statistical concept. (Dirac is referring above all to renormalisation problems in quantum field theory, which have not yet been eliminated, but perhaps appear in a new light; compare the comments about renormalisation in the extract “Two kinds of expectation values”).

There are some subtle indications that a few other authors, had they thought further in this direction, would probably have arrived at the same interpretation:

''In a statistical description of nature only expectation values of correlations are observable.'' (Christof Wetterich, 1997, in hep-th/9703006)

Wetterich is one of the current experts in non-equilibrium quantum field theory and the associated renormalisation theory, with numerically impressive results which can be tested experimentally.

''The only reasonable interpretation of the variables p and q is as mean values rather than truly sharp values since we live in a world where ħ is nonzero.'' (John Klauder 2001, in: quant-ph/0112010)

''One is almost tempted to assert that the usual interpretation in terms of sharp eigenvalues is 'wrong', because it cannot be consistently maintained, while the interpretation in terms of expectation values is 'right', because it can be consistently maintained.'' (John Klauder 1997, in: quant-ph/9710029)

Klauder is one of the physicists who has had success with modelling coherent states in quantum optics.

To give in to the temptation mentioned by Klauder would certainly be a risky venture, as one would be working in isolation. Yet pursuing it could lead to rich rewards...


Arnold Neumaier (Arnold.Neumaier@univie.ac.at)
A theoretical physics FAQ