Collapse as conditional probability?

In my collapse challenge quant-ph/0505172 I describe the measurement problem in perhaps its simplest form: state collapse due to passing a screen. There is certainly a collapse in any interpretation, but it relates to different things in different interpretations.

1. If one identifies the state (the wave function modulo phase) with 'knowledge', one has the statistical interpretation, and the collapse is known to be simply the transition to conditional probability. It exists, but causes no problems.

According to this interpretation ('state=knowledge') quantum physics says nothing at all about reality, but only about mental processes in the observer, namely how his knowledge changes, when he takes notice of a measurement result and accepts it as genuine. (In other words, if he doesn't accept it, his knowledge doesn't change and the wave function remains unreduced!)

This is admittedly a consistent position. But to reduce physics to psychology is a move of desperation, not a solution of the fundamental problem.

2. The alternative is to identify the state with the object. This is what physicists do in practice when they plan and think through experiments. And this is what is in accordance with the practice of actual quantum measurements - as for instance described in the cited book by Braginsky and Khalili.

Then the state and the photon are identical at the level of the model, in the same way that an atom in the Bohr model is a pair of points in phase space.

Then the collapse is again present, but it is now an objective (observer independent) problem in statistical mechanics: the result of the interaction of a quantum system with a many-particle screen.

Before Jaynes, who came up with the unfortunate interpretation (1.) the default interpretation was, to my knowledge, (2.) Von Neumann and Wigner admittedly brought 'mind' into the picture, but they did not talk about 'state=knowledge'.

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

A theoretical physics FAQ