Ranging and Pioneer

[[Mod. note -- This thread seems to be moving out of s.a.r ("astronomy")
and over to s.p.r ("physics, in particular quantum mechanics"). Perhaps
future discussion should be only in s.p.r and not cross-posted to s.a.r?
-- jt]]

Thus spake Igor Khavkine
Oh No wrote:
Thus spake Igor Khavkine
Oh No wrote:

1. Which objects are you treating classically and which quantum
mechanically?

I treat the emission of a photon from a distant object and its detection
on Earth quantum mechanically. The distant object is a conglomeration of
quantum particles.

That is a very complicated way to model anything big, bigger than, say,
a few millimeters. For macroscopic objects, we usually have the
relation

(quantum treatment) = (classical treatment) * (1 + C*hbar/N + ...),


where N is roughly the number of particles in the object. If you assert
that a quantum treatment is necessary, then you have to provide an
estimate of the constant C and compare it to hbar/N in magnitude.
That's what I asked in question (3.). However, I still don't see how C
would be large enough.

This indicates to me that you take a very different approach to quantum
theory from me. My starting point is to use axiomatic quantum theory, in
the manner of Von Neumann, and to set up a Fock space of quantum
particles. I take a classical object to have properties of a large
population of such particles. Classical properties can be found by
taking expectation values of quantum observables. But as far as the red
shift relation is concerned, I am only looking at individual photons.


2. Can you rephrase all your references to "wave functions" in terms of
the language of an abstract Hilbert space of states and operators
observables?

Yes. In fact that is where I come in. I find that it is necessary to use
coordinates which are conformally flat in the time-radial plane in order
to do this, so that quantum mechanics is effectively formulated on a
Penrose diagram in the time-radial plane.

First, I'm not sure what a coordinate choice has to do with Hilbert
spaces and operator observables. So, I can't see how my question was
answered.

The coordinate choice is fixed because I require plane wave motions in
the time-radial plane, or more properly that momentum in the final state
is teleparallel to momentum in the initial state.

Second, what if I don't like your choice of coordinates, can
I or someone else redo your calculations in global inertial coordinates
(if in Minkowski space) or in arbitrary coordinates (if in arbitrary
space-time)?

No (see above). In Minkowski space the formulation reduces to standard
quantum mechanics - but then there is no expansion and cosmological
redshift is 0, so the results are null. To write down the wave function
I am using a closed FRW space-time, with global coordinates given by

ds^2 = a^2(4(dt^2 - dr^2) - 1/4 sin^2(r)(dtheta^2 + sin^2(theta)dphi^2))

Teleparallel displacement of momentum imposes that dt^2 and dr^2 have
the same coefficient. The factors 4 and 1/4 come in because teleparallel
displacement results in cosmological redshift being proportional to the
square of the expansion parameter (I think this is related to electrons
having spin 1/2 but I have not explored that). A classical motion is
considered to be continuously observable and so is modelled as a
sequence of quantum motions

initial state - final state = initial state for next part of motion

When the final state becomes the initial state for the next part of the
motion the quantum theory has to be rescaled, with the consequence that
momentum is renormalised. This removes a factor of the expansion
parameter. Since the initial state and final state are infinitesimally
close together the connection reduces to the standard affine connection
of classical gtr at this point.

3. If you are proposing a quantum treatment of macroscopic objects like
stars or the Pioneer space craft, can you demonstrate with a
back-of-an-envelope estimate that said quantum effects would be
observable?

The quantum effects are observable when the accuracy of measurement of
position is less than the effective wavelength of the Doppler signal.
For Mars we have measurement accurate to about 10m, so the shift should
be present in optical frequencies in measurement of Mars, [...]

Hold on there... What if I use my naked eye to look at Mars? Then the
measurement uncertainty would be much larger, on the order of AU even!
Do you mean that I will then observe an overall shift in Mars' spectrum
by some very small frequency? Usually when two observers (say, at the
same place and at the same time) make the same measurement, but with
different instruments, they get different uncertainties (depending on
the instruments). But their uncertainty ranges should at least overlap.
Doesn't look like that's happening in what you are describing.
According to what you are saying, two obsevers may easily get
non-overlapping uncertainty ranges for the shift measurement.

No. The observed shift in Mars spectrum is equivalent to the Doppler
shift of ~0.4 m/s, way below the resolution of any apparatus we have to
measure it.

[...] Potentially this can be
tested from the original Pioneer tapes, because cycle slip is a
prediction of the model (associated with collapse of the wave function).

Can your model distinguish between a "collapse induced" cycle slip and
one that's due merely to noise during detection?

I don't see how, but I am not an expert on data analysis. I think
collapsed induced cycle slip should take place at approximately equal
intervals dependent on the apparatus used to measure it, but I would
think it is likely to be drowned by noise. If a test could be set up
with very low noise, then perhaps.



Regards

--
Charles Francis
substitute charles for NotI to email