Re: Looking for a concept
- From: thomas_larsson_01@xxxxxxxxxxx
- Date: Sun, 12 Feb 2006 18:47:20 +0000 (UTC)
There is a quite simple argument why we need a theory which
explicitly incorporates the observer.
The Hamiltonian of the universe consists of three terms,
H_U = H_S + H_O + H_SO,
which describe the system, the observer, and the system-observer
interaction, respectively. Time evolution of the universe is
always unitary. In the absense of observation, H_SO = 0 and H_O
decouples, so the time evolution of the system alone is also
unitary. The standard formulations of observation introduce
concepts which a foreign to QM - wave-function collapse, breaking
of unitarity, etc. However, my objection is that by looking at the
system alone, you cannot correctly describe the time evolution of
the universe.
There is of course a well-developed and sophisticated mathematical
formalism for extracting numbers from QM - finding the Gelfand
spectrum of a von Neumann algebra or whatever. I do claim to
understand this theory very well, and I certainly do not question
its validity. However, it deals with the system alone, and it does
not depend on the physical properties of the observer. Therefore,
it can not correctly describe the time evolution of the universe,
i.e. the outcome of an actual experiment, which clearly depends on
H_O and H_SO. Hence we need a formalism which explicitly
incorporates the observer's physical properties.
Let us perform a simple Gedanken experiment. Prepare our system -
a laser beam, say - in a plane-wave state with 4-momentum k.
According to standard QM, we should observe an energy spectrum
with a sharp peak at E = k_0. However, this is not what is
recorded in a real detector. Even if we ignore that a plane-wave
state is an idealization, the peak will still be broadened
because the detector recoils. By dimensional analysis, we expect
that the peak will have a width of order k_0^2/M, where M is the
mass of (the active part of) the detector. The peak will only be
sharp in the limit that M -> infinity, i.e. that the detector is
macroscopic and hence classical. Hence an implicit assumption
about a classical observer has sneaked into classical QM.
There is a conceptual difference between this kind of observer and
an observer in SR. In SR, an observer is simply a choice of
Lorentz frame. If we observe our plane-wave in different Lorentz
frames, the peak will be red-shifted or blue-shifted because of
the Doppler effect, but it will remain sharp. In contrast, the
interaction between the photons and the detector broadens the peak
but does not move it.
.
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