What grade of decoherence to be a classical aparatus

1. Jun 9, 2013

StarsRuler

Books of quantum mechanics are very ambigous in this aspect. A classical apparatus that collapse wavefunction of a quantum system must "quasieliminate" the non-diagonal elements of density matrix, or have a quasiclassical wavefunction of the form
$ae^{iS\hbar^{-1}}$ where a is a real slowly changing in space and time and S is the classical action in the trayectory between 2 points of the wavefunction. But ¿ how much slow this change of a, and rapid oscillating S ?. There is qualitative but no quantitative answers in both forms of watch a classical system, in particular a measurement apparatus

Last edited: Jun 9, 2013
2. Jun 10, 2013

tom.stoer

I think the analysis is done in terms of the strength and time of the interaction with the environment, not in terms of the size of the measuring decives.

3. Jun 10, 2013

BruceW

books on QM are ambiguous exactly because decoherence is a concept based on a certain limit. In other words, as the classical apparatus causes the density matrix to tend to a diagonal matrix, the system decoheres more and more. generally, the density matrix will never become completely diagonal, but as it becomes closer to being diagonal, so too the system becomes more decoherent.

edit: and generally, there is no standard way to categorise the system to say if it is classical. And the definition 'quasiclassical wavefunction' also suffers from the same problem of being arbitrarily defined. In truth, we can only say that one wavefunction is more 'quasiclassical' than another. We cannot definitively say that a wavefunction is quasiclassical. This is pretty much the main idea of the measurement problem.

second edit: I guess you can say that a wavefunction tends to a quasiclassical wavefunction under a certain limit.

Last edited: Jun 10, 2013
4. Jun 10, 2013

StarsRuler

And what is done in praxis? If a certain apparatus is perceived like a classical system, then all the systems more classical than it we can be sure that his comportment will be classical too, I suppose. Is this the provisional solution to the problem??

5. Jun 10, 2013

BruceW

hmm. That makes sense to me. I think in most cases, classical measurement devices have such a large number of degrees of freedom that the off-diagonal terms of the density matrix decay very quickly, so that people just say "it is a classical apparatus" without putting much thought into it. another thing that could be considered is how easily quantum information leaks from the apparatus to its environment.

There is another thread going on, where someone called audioloop has given some nice links to some research into decoherence times, e.t.c. on pages 7 and 8 of this thread: https://www.physicsforums.com/showthread.php?t=682271&page=7 you might find these interesting.