# Collapse and quantum measurement

Experiments involving measurements are oftern interpreted in terms of a collapse of the state of the system. However, they can be interpreted without any collapse.

In particular, in photon experiments, the collapse interpretation is never applicable since a measured photon stops existing rather than collapsing into an eigenstate of the measured operator.

Instead, a collapse is just a change of the description level. The moment one changes the description level, everything changes everywhere instantaneously, without making the slightest change to the underlying reality.

One has the same instantaneous change already on the classical level. We can calculate the probability that a star is of a certain kind. This probability depends, however, on what we consider to be the relevant ensemble. If we change the ensemble by restricting to a subensemble, the probability may change. And it does so throughout the universe, instantaneously, just by making our subjective decision to consider only the subensemble instead of the whole ensemble. This is nothing special to physics, it is an experience of everyday life. It is as simple as this:

(*) collapse = restricting to a subensemble = replacing a probability by a conditional probability.
The mathematical justification of the equality (*) is easy to see by considering only commuting observables, in which case quantum mechanics reduces to classical probability theory. Now measure just one of a complete set of commuting observables, and interpret the resulting formula classically.

It is up to the subject making a study when she will switch to the conditional probability, and has nothing to do with her knowledge. But once the ensemble is replaced by a subensemble (by conditioning with respect to a partial observation on her side of the system), the view changes instantly, since it happens only in the subjects head -- she decided to remodel the situation, and so it changes accordingly.

But as long as one keeps fixed what is the system considered, we have objective physics to tell us what happens with the system, as far as it can be told at all.

The objective state of a physical system is a state of the total system considered, and not one of its many partial traces, which only give the perspectives of local observers.

Of course, the partial trace is observer-dependent. The dependence comes from the freedom of a subject to choose what it will consider as the system.

This is the _only_ subjectivist element in physics. It is already present in classical physics, where changing the (subjective) coordinate system changes everything. There we are trained to know that these subjective elements are to be ignored, and that what counts is just the coordinate-independent part of physics.

We know that ordinary optical perspective is something subjective, and we correct for that by developing a more general objective framework of space in which each perspective has its place. In this objective framework, perspective is seen to reduce space by one dimension, hence hiding information that objectively exists and can be modelled but is ignored by the view.

This reduction of a scene by viewing it in a particular perspective is in complete analogy to the reduction in quantum mechanics, where the choice of which subsystem to consider affects the resulting view.

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