I have had some time to think more about quantum measurement
in general,

there are a few loose ends in the arguments I sent you which probably should be
filled in in any case.

Just as a matter of principle. So here they are:

First, the argument used the concept of "state" a lot. This needs
qualification, in two ways.

Qualification one:

The "states" of a an ordinary physical object, like an absorber or
back-body emitter, are normally

described thermodynamically in terms of probabilities of "lines" or
"energy levels" being visited.

And the Boltzmann is probability distribution is good enough most of the time,
for states

of relatively high energy. But in actuality -- these lines are not TRUE
eigenvectors of the system.

In an infinite universe of finite density, they are really just
"metastable" states, partial

eigenfunctions. But that is well known, and no surprise,
and it is

known that we can use Boltzmann anyway, to predict overall behavior in
practice. To make it all

VERY exact, we can take any of two standard approaches: (1) invoke radiation
flux in space as the mechanism

which keeps the Boltzmann distribution legit, even as we look forwards (or
backwards) in time, implicitly

noting that we are really using the Boltzmann distribution for the overall
universe; (2) consider the limits as V

goes to infinity of a compact period universe of volume V, in which the energy
levels are (increasingly good) approximations

to components of true eigenfunctions.

Anyway, the point is that we don't really need to elaborate. It is well-known
that they are really metastable, but that we can use

Boltzmann anyway. That's well-established in forwards time analysis. Thus the
backwards time discussion is fine, and it

isn't a contradiction to say that we observe a photon being emitted (in
backwards time) immediately "after" time t1.

The argument holds up fine, as regards that point.

Qualification two:

I implicitly assumed that "states" correspond to eigenfunctions of
the Hamiltonian operator H,

as in the conventional treatment of solid-state physics.

This is a more serious logical hole, which has the following resolution.

We are ultimately interested in two possible viewpoints on what the
"Schrodinger equation" MEANS.

We may take the many-worlds view, in which the wave function or density matrix
actually describes the state of reality.

When we say that the Schrodinger equation is the fundamental law of dynamics of
the universe, we implicitly say that

the wave function or density matrix represents the actual objective state of the
universe at some time. When we try to derive measurement

as a consequence of those dynamics, that's the logical way to proceed.

Alternatively, we may assume that the Schrodinger equation correctly represents
the dynamics of the universe (in some sense), but

is the statistical outcome of something more fundamental.

Unfortunately, the argument in the two cases is a bit different. It is more
complex in the former case.

In the former case, it is well established in solid-state physics that we do
not need to allow for arbitrary

probability distributions Pr(psi) or Pr(rho) in order
to specific the stochastic state of the universe;

all measurable differences between probability distributions are captured by
knowledge

of the density matrix. Furthermore, it is commonly assumed that
"states" or "pure states" of a solid

object do correspond to eigenfunctions of the dynamics.

These common assumptions are ADDITIONAL ASSUMPTIONS, and rightly labelled as
part of the COMPLETE

quantum measurement theory in use today. One may come up with arguments about
whether they may be derived

from basic dynamics and boundary conditions, or not. BUT IT IS ENOUGH for our
poses to say

that we would like to AVOID ASSUMING the most PROBLEMATIC PART of the
measurement formalism, the part

about applying measurement operators to states to derive probabilities; we have
found a way, for

this particular family of experiments, to DERIVE predicted probabilities
WITHOUT using that problematic assumption.

Yes, we do have to make a few smaller conventional assumptions to close the
loop, but at least we get rid

of the worst apriori assumptions, and we avoid having to make predictions about
the direction of time which come

DIRECTLY from apriori assumption. When we derive predictions DIRECTLY from a SUBSET
of the conventional assumptions,

from the Schrodinger equation and from local thermodynamics, we end up
with predictions which DIFFER

from the usual predictions, precisely for the class of experiments you have
proposed. (Though we do leave hanging

the status of experiments with extremely hot absorbers.)

For the underlying-realism assumption, the words "state" clearly have
meaning directly, and the argument goes through directly.

The caveat would be that "states" may correspond to equilibrium
ensembles of underlying physical states, but that does

not affect the validity of the logic.

=================================================================================

I did have a chance to read the new edition of Hawking's book,

where he characterizes his earlier claims as a "mistake." But in
explaining the "mistake,"

he basically says "I was wrong to assert that there logically MUST be
backwards-arrow

regions of space-time. My colleagues have explained to me that one can
construct alternative models."

But this certainly does not invalidate the earlier model, particularly when the
alternatives

are less parsimonious. Thus the earlier model still stands as an important
option

worthy of consideration, unless there are other arguments. Since he did not

present any other such arguments, and the new logic fully addresses the one

other argument we might anticipate... it stands as an option that should be
explored.

---------------------------------------------------

I have a few other new thoughts, most of which probably do not bear on the
immediate situation.

Earlier, I did ask myself: "Who has studied the question of whether
available OPTICAL frequency

"holes" (excitable modes) change a lot as temperatures rise
high?" (If they grew a lot,

this might possibly allow "photon attraction" effects by absorbers in
the laboratory. I haven't thought that through

SO far...) There is an obvious answer: laser
designers. So that's one other direction one might

think about in the future. But for now, I am mainly looking at other aspects,
more aligned with the formal

mathematical treatment.

Best,

Paul