I have had some time to think more about quantum measurement
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.
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.
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