Thursday, August 26, 2010

An indefinite outcome for decoherence

Previously I asked a few fundamental questions about quantum theory. One was:

Why doesn't decoherence solve the quantum measurement problem?

This is a subtle question with subtle answers. I have hesitated on posting on this because the more I read the less sure I am of what the answer is. Basically, it seems there are a few key (distinct but related) aspects to the problem:
  • how does a measurement convert a coherent state undergoing unitary dynamics to a "classical" mixed state for which we can talk about probabilities of outcomes?
  • why is the outcome of an individual measurement is definite for the "pointer states" of the measuring apparatus?
  • can one derive of the Born rule which gives the probability of a particular outcome?
It seems that decoherence only solves the first problem, but not the last two.
An accessible brief summary is given in a Book Review by Anton Zeilinger. He states:

Fullerenes .... showing quantum interference in two-slit experiments whereas they can be seen in a tunnelling electron microscope, for instance, at classically well-defined locations. This shifting boundary is confirmed by the decoherence mechanism. But to argue that this is evidence against the Copenhagen interpretation, as the author does, is unjustified: the Copenhagen interpretation itself says that whether an object is classical or quantum is a function of the chosen experimental set-up.
Decoherence is, to follow physicist John Bell, for all practical purposes sufficient to describe the loss of quantum features for large systems. There are still unanswered questions. It is well known, which Schlosshauer also stresses, that the interference terms never strictly vanish, so decoherence can tell us only that the interference terms disappear effectively but not rigorously. Even after accepting that approximation, we are still left with the system represented as a mixture of various possibilities, like being in two places at once. In the classical world, we know that the system is always at this place or at that place. To explain the two as equivalent is again, for all practical purposes, sufficient. Yet it involves, as Bell points out, another interpretive leap.
A more detailed technical discussion is in Why decoherence has not solved the measurement problem: a response to P.W. Anderson, by Stephen L. Adler.


  1. I don't really understand what your point (2) means. Interpreted one way, it's a basis-dependent statement, as a measurement of x does not yield a definite answer in the p basis. Interpreted another way it seems somewhat trivial; the measuring apparatus is designed to couple to a system observable O, so when the measurement happens O gets perfectly correlated with "system sees O." This (apparently) pushes the paradox outwards to why we observe the measuring apparatus to have a definite value, but this is because the measuring apparatus is coupled in some basis to its environment (which includes us), and so on all the way up to astronomical length scales.

  2. Sarang, Thanks for the comment. I slightly edited the post to try and make it clearer.