Re: The time it takes to emit one photon

> 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.

> 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.

> 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. To continue with chess analogy,
von Neumann follows up variations all the way to check mate while
you're talking only about how much material your next legal move can
capture, insisting that this one-move capture value you got is all
there is to be said about the position.

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.
All this is about the properties of the model itself (where T1, T2,...
belong), there is no confusion between the 'reality' realm (e.g. how to
measure T1, T2,..) with the 'model' realm (how to compute, at least in
principle, T1, T2,..).

The reason for pointing out this absence of the algorithm within the QM
formalism for computing T1, T2,... was to indicate why did von Neumann
(and numerous other 'anti-realists' since) have to reach beyond the
formalism (outside of the model) for a deus ex machina, e.g. observer's
consiousness, to execute the missing algorithm. The linear QM/QFT with
its Measurement Theory is either a defective theory or an inconsistent
theory (e.g. if you abandon von Neumann's self-consistency requirement
which leads to the existence of defect and requires deus ex machina as
a temporary patch until a genuine solution is found), and that is the
source of over seven decades of unsettled arguments. (I am using term
"defect" instead of the usual characterization of the problem as
"incompleteness" since the latter implies one can merely add the
missing piece without abandoning the rest [and retaining it only as one
among possible computational approximations]. The position of the
present QM/QED vs Barut's self-field ED is analogous to the position of
Newtonian physics with respect to the Special & General Relativity --
the older theory is fundamentally defective in both cases.)

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. It
was only in Barut's work, that the Einstein's program, at least as far
as QM/QED, had clicked together. Barut has shown explicitly what
Einstein (and few others since) had conjectured five decades earlier --
the linear QM/QFT is merely a linearized approximation of the coupled
Maxwell-Dirac/Schrodinger classical fields. The linearization is
achieved by switching from the deterministic but nonlinear evolution of
the original Maxwell-Dirac fields to the indeterministic/ensemble
evolution (obtained via under-constrained variation of the action
performed by the Barut's ansatz, which is a special case of Carleman
linearization in variational form) of the QM/QED.

While these developments may appear obscure at present (especially if
one doesn't know what the question is that is being answered), I think
the beauty and the conceptual clarity of this approach, along with many
new possibilities it opens (e.g. genuine computation of the fundamental
constants, such as alpha, which Barut sketched but never completed and
which with todays computers should be within reach) will win eventually
over the 'quantum magic' dominating the current zeitgeist.

.

Relevant Pages