The mathematics of measurement

[homology]

So when we try to \"observe\" an observable through an experiment we, in the process, \"collapse\" the state vector into one of the eigenstates of the observable. So my question is, how do we represent such an experiment mathematically? Are there \"measurement\" operators that do this collapsing?

Thanks in advance,

Kevin

[Tal]

the act of measurement is actually averaging the behavior of the desired observable.
The trace operation, which is done with different \"weights\" on the wave function, which can be considered as the operators, is what gives the collapse of the wavefunction (or split into multiple universes, for that matter).

[Xerxes314]

The mechanism of collapse is a highly-charged, poorly-understood subject. One might check out recent work on decoherence tho. Particularly Zurek.

Xerxes

[Tal]

true.
see also works by Peter Zoller, Ignacio Cirac, and the group from Potsdam.

In the field of atom optics, and especially atom chips, there\'s a lot of work on decoherence, both theoretical and experimental.

For example, fragmentation of ultracold atomic clouds or BECs as they approach current carrying structures which are themselves at room temperature, is a unique and interesting way to see how environment affects quantum systems - decoherence.

[homology]

the act of measurement is actually averaging the behavior of the desired observable.
The trace operation, which is done with different \"weights\" on the wave function, which can be considered as the operators, is what gives the collapse of the wavefunction (or split into multiple universes, for that matter).

Hmm, could you do an example (it doesn\'t need to be specific)?

Thanks,

Kevin

[Martin]

For an interesting discussion of collapse theories, see Collapse Theories. But QM, with its apparent incongruities, remains an unfinished theory, and there is much debate about different interpretations and alternative hypotheses. See the link that Xerxes provided. Also, you might find these of interest: Many Worlds, Everett, Bohmian Mechanics, and Goldstein/Weinberg.

-Martin

[Tal]

an example of work on decoherence:

Henkel et al., in the arxiv database, quant-ph/0208165

also:
Folman et al., quant-ph/0012061

Enjoy

[Xerxes314]

I just finished reading this piece by Schlosshauer, which is (IMHO) very very good:

Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics

It\'s got a general overview of decoherence followed by a description of the implications of decoherence for every major interpretation of QM. At the end, he suggests that decoherence may make the whole problem of interpretation essentially irrelevant; more a matter of personal taste than physical content. Personally, I think the MWI is elegant and well-justified physically.

Xerxes