What becomes of the superposition principle?

In the traditional analysis of the measurement according to von Neumann, the situation is radically simplified (which is the cause of the problems) in that one understands measurements as reductions onto eigenvalues, and analyses general situations with the help of the superposition principle.

In the thermal interpretation this is a bit more complicated. When one repeats an experiment, the state of the rest of the world has changed, and one does not have exactly the same situation.

But is the same in the average. This makes all the difference. One cannot superpose whole universes. In any case I do not know how one could prepare such a situation. In the thermal interpretation there is only one state of the whole universe. All others are derivatives.

The superposition principle only applies to systems that are sufficiently small that one can produce and manipulate them in more or less arbitrary quantities. Macroscopic systems are definitely not in this category!

This restriction brings into play Wigner's classic argument
J.A. Wheeler and W. H. Zurek (eds.), Quantum theory and measurement. Princeton Univ. Press, Princeton 1983, Chapter II.2, see particularly pp. 285-288.
(see also the entry 'Does decoherence solve the measurement problem? in my theoretical physics FAQ)
which proves the incompatibility of unrestricted unitarity, the unrestricted superposition principle, and state collapse under measurement.

We will see this in more detail in the next entry, which deals with the measurement of a single spin.

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Arnold Neumaier (Arnold.Neumaier@univie.ac.at)

A theoretical physics FAQ