Re: The time it takes to emit one photon

"nightlight" <nightlight@xxxxxxxxxxxxxx> wrote in message
news:1123904389.771197.20890@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> > I think you are making a mistake by trying to assign some physical
> > meaning to formal mathematical objects. These objects have no
> > physical meaning. There are no wavefunctions flying around us
> > as little clouds ...
>
> Psi(x,t) describes exactly how wavefunction 'flies around'. For
> example, the quantized EM field (in Heisenberg picture) evolves via
> plain Maxwell equations through vacuum or through linear optical
> elements.

Correct mathematical description of quantum dynamics of particles (and
fields)
is provided by vectors and operators in infinite-dimensional Hilbert (or
Fock)
spaces. Only in rare occasions (e.g., the position-space wave-function of
a single particle) this description can be visualized as a "cloud of
probability"
in the real 3D space. I think that your attempts to visualize Hilbert space
creatures as
living in our real world brings more harm than good. Please leave them where
they belong - in their mathematical world.

> > and "collapsing" time to time.
>
> Apparently you haven't read von Neumann's discussion from his 1932
> monograph, where the need for the two forms of state evolution within
> the linear QM is explained (which is probably still the best discussion
> on that topic). Within the linear unitary theory, the collapse is
> necessary to maintain the self-consistency of the theory. Only if you
> abandon the linearized QM/QFT, as some physicists have done, from de
> Broglie and Schrodinger in 1920s, through E.T Jaynes in 1970s and A.
> Barut in 1980s (he died, unfortunately, in 1994, while his self-fields
> ED developments were in full swing:
> http://phys.lsu.edu/~jdowling/barut.html ), you can avoid von Neumann's
> conclusion on the necessity of the collapse.

What's wrong with the collapse? The collapse is a part of the mathematical
model
which, as I am trying to explain here, has very little to do with reality
(only final numbers calculated by this model can be compared with
experiment).
The collapse in the mathematical world of wave functions does not imply
that real physical systems evolve by jumps. You can arrive to this (wrong)
conclusion only if you identify the wave function with the physical system
itself. I refuse to do that. I say that these two beasts live in different
worlds.

> > The only connection between this mathematical world and real
> > physical world is established when quantum mathematical formulas
> > arrive to some probability distribution or expectation value of an
> > observable. Only these numbers can be directly compared to what
> > is measured.
>
> The part that you're missing, and which was von Neumann's starting
> point, is that you can apply these same operational rules (the Born
> probability postulate you're talking about) in different ways, depening
> on how you choose to define aparatus and object. Then, the requirement
> of self-consistency of the theory, specifically the independence of the
> final results on the choice/convention of the object-aparatus boundary,
> carries implication that go beyond the simplistic one-move-ahead
> conclusions you seem to be stuck on.

If you accept that wave functions and their collapses belong to the abstract
mathematical world, then there is no problem in selecting the boundary
between the physical system and the measuring apparatus. No matter how
you choose this boundary, the predictions of quantum mechanics will agree
with experiment.
You should only remember that the word "predictions" refer only to
experimentally observable effects. I agree that with different choices of
the boundary
the QM descriptions may look strikingly different. But these differences
are related only to the non-observable mathematical world.

> Returning back to (A1)-(A3) -- that whole argument is in the model
> space-time using the rules of the model (the QM, the unitary evolution
> and the collapse). The model (the QM formalism) has time parameter,
> too, and that is what the T1, T2,... refer to. The point of that
> argument is to show that QM (via Measurement Theory, the projection
> postulate) implies the existence (we're in the model realm here) of
> values T1, T2,... which cannot be computed, not even in principle, by
> the theory. Unlike the 'electron position' before the measurement
> (which you keep bringing up) about whose existence the QM has nothing
> to say, here the QM says that there are values T1, T2,... yet it can't
> compute them because it has no algorithm within the formalism to do so.

Are these times T1, T2,... related to some observable events? I guess no.
Then I don't care if QM cannot predict them. If QM couldn't predict
the lifetime of a radioactive nucleus, then I would worry very much.
Luckily, this doesn't happen. QM can predict (the probabilities of)
everything that can be measured.

> Einstein, along with Schrodinger, de Broglie, ... through Jaynes and
> Barut in recent times, offer a much more acceptable (in the long run)
> way out -- drop the linearity and the measurement problem goes away.

I am not sure if you can abandon the linearity of quantum mechanics
(the existence of linear superposition of states) so easily. The rules of
quantum mechanics follow from the postulates of quantum logic. These
postulates have very precise and (in principle) experimentally verifiable
meaning.
Any non-linear "generalization" of QM must violate some of these postulates,
i.e., violate some fundamental properties of measurements.

Eugene.

.

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