Physics – Mathematical Physics
Scientific paper
2005-05-10
Physics
Mathematical Physics
20 pages, minor correstions installed, to appear in Rep. Math. Phys
Scientific paper
10.1016/S0034-4877(05)80074-6
We show that the key problems of quantum measurement theory, namely the reduction of the wave packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument, may be rigorously resolved within the traditional framework of the quantum mechanics of finite conservative systems. The argument is centred on the generic model of a microsystem, S, coupled to a finite macroscopic measuring instrument, I, which itself is an N-particle quantum system. The pointer positions of I correspond to the macrostates of this instrument, as represented by orthogonal subspaces of the Hilbert space of its pure states. These subspaces, or 'phase cells', are the simultaneous eigenspaces of a set of coarse grained intercommuting macroscopic observables, M, and, crucially, are of astronomically large dimensionalities, which incease exponentially with N. We formulate conditions on the conservative dynamics of the composite (S+I) under which it yields both a reduction of the wave packet describing the state of S and a one-to-one correspondence, following a measurement, between the pointer position of I and the resultant state of S; and we show that these conditions are fulfilled by the finite version of the Coleman-Hepp model.
No associations
LandOfFree
On the mathematical Structure of Quantum Measurement Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the mathematical Structure of Quantum Measurement Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the mathematical Structure of Quantum Measurement Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-313023