Re: The time it takes to emit one photon

> I don't see any magic here. In my previous post I used analogy
> with a classical die with 6 faces. ...

You use "magic" (the unspecified non-physical collapse) to get around
the _mutual exclusivity_ of the two forms of evolution/change of Psi in
time. The "magic" part is the switchover between the two (which, being
incompatible / mutually exclusive, cannot both specify the evolution
simultaneously). When and how does Psi (of the _whole_ system, the
object plus aparatus and anything interacting with either) stop
evolving via the linear unitary evolution and start evolving via the
projection postulate? When and how does it then somehow stop evolving
via the projection postulate and resume the unitary evolution? What is
the formal counterpart in the QM that describes (in time and space
parameters) this switchover between the two modes of evolution?

The von Neumann's answer is as complete as any here -- he simply said
that the observer's consciousness performs the collapse. At least he
recognized that the unitary evolution cannot accomplish the required
transition. You can hand-wave it in many other ways tried since,
without in essence getting beyond the von Neumann's euphemistic
admission of the inadequacy of the unitary formalism to account for the
most basic empirical fact -- the occurence of a single result. His
solution is, of course, nothing but a magic trick -- a psychological /
didactic device, entirely outside of the formalism, creating an
appearance (at the verbal, handwaving level) of overcoming the core
shortcoming of the linear formalism. But, as the many decades of
persistent confusion among the physics students testify, it never
answers it at the formal level, within the theory or physical model
itself.

Your level of argument doesn't appear to even recognize the mutual
exclusivity of the two modes of evolution, carrying on as if the two
modes can guide the change of Psi simultaneously and it is a mere
matter of convention and convenience which description one chooses to
use (as your dice example illustrates). Once you recognize the mutual
exclusivity of the two (they cannot both guide the change of Psi
simultaneously), then the questions posed at the top (and the von
Neumann's euphemistic answer 'I don't know') make sense and remain
unanswered within the QM orthodoxy. Note also that the von Neumann's
proof of movability of the cut (the transition point between the two
modes) does not answer (within the formalism) where and when does the
projection mode occur -- he puts that part outside of the formalism
("consciousness" performs the collapse; what is "consciousness" in the
formalism? when, where and how "it" does it? the other conventional
answers merely substitute "consciousness" and its magic with other
equally vague and magical work-alikes).

One legitimate semi-answer, which at least clearly recognizes the
mutual exclusivity of the two modes, is the GRW spontaneous collapse
extension of QM -- here the switch between the two modes is a part of
the formalism, entering as an additional formal and genuine QM
postulate. Unfortunately the GRW spontaneous collapse solution is
grafted in superficially, as a quick & dirty patch of the gaping hole
in the formalism, but without any connection to other physics, with no
dynamical basis or the empirical tests (other than providing, by
declaring it, the 'single result'). Thus while GR & W do lay out the
problem correctly and cleanly, without having to call upon deus ex
machina from outside the formalism (consciousness, splitting of
universe, irreversible macroscopic measurement, decoherence), this
semi-answer still doesn't really add any useful physics (beyond von
Neumann's answer) to the QM.

Einstein did state what the genuine answer ought to be (which was
worked out in detail decades later by Barut and his students [see the
ref's cited earlier] confirming in full Einstein's intuition on this
problem):

" At the present time the opinion prevails that a field theory must
first, by "quantization," be transformed into a statistical theory of
field probabilities according to more or less established rules. I see
in this method only an attempt to describe relationships of an
essentially nonlinear character by linear methods." ["The Meaning of
Relativity", 5th ed, Dover 1956, pp 165].

This is precisely what Barut has demonstrated -- he constructs the
explicit linearization procedure, a variant of Carleman linearization
(without referring to it, being apparently unaware of its existence and
use in applied math), of the coupled nonlinear PDE system
(Maxwell-Dirac classical fields) of the very type suggested by
Einstein. (Similar view of the QM and QFT was shared by de Broglie,
Schrodinger, Fermi, Jaynes etc.)

.

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