Re: Ranging and Pioneer

[repeat of a presumably lost post]

Thus spake Igor Khavkine <igor.kh@xxxxxxxxx>
Oh No wrote:
Thus spake Igor Khavkine <igor.kh@xxxxxxxxx>

The quantum corrections to the classical behavior of these
objects are suppressed by the number of atoms or the number of photons
involved (very large in both cases), as well as hbar.

So, I return to my original question. Can you estimate the C*hbar/N
term and show that it can be sufficiently large to account for the
spectral shift anomaly?

I am not sure that we aren't at cross purposes here. According to the
theory the path of macroscopic objects is simply the classical Newtonian
path. Only the wavelength of the detected light/signal is shifted.

Then why doesn't light just obey Maxwell's equations?

Maxwell's equations assume the prior existence of space-time. This gets
us into the substantivalist/relationist debate which is a whole issue in
itself. Perhaps most physicists incline toward substantivalism, while
philosophers towards relationalism. Notably Einstein inclined toward
relationalism. see http://plato.stanford.edu/entries/spacetime-holearg/

I don't really want to get into that, which is something of an open
debate. I merely remark that to be scientific one should examine
predictions in both models. In quantum theory we cannot define paths of
photons. I am suggesting that this principle should also be applied to
photons from distant stellar objects. Using Maxwell's equations makes an
assumption which I cannot justify empirically, because I can only
measure space-time coordinates for physical events, not for photons in
empty space.


If you model
everything classically (including radiation) and still get a shift,
then why use quantum mechanics in the first place?

Classically means assuming the affine connection holds at points in
empty space. This will give standard general relativity with no shift.

If you get no shift
classically, or rather not enough to account for the anomaly, then your
model seems to be predicting the shift as a quantum correction, in
other words an O(hbar/N) effect.

One could call it a quantum correction, but it is not an 0(hbar/N)
effect.

While few-photon light intensities can
be produced in modern optics labs, I sincerely doubt it that the signal
from the Pioneer spacecraft is that weak. In other words, I'm skeptical
about any model that predicts quantum radiation effects significant
enough to account for the anomaly. That is, unless I'm proven wrong by
an explicit estimate of the size of such an effect.

For a strong signal the size of the effect is still the expectation of
the size of the effect for a single photon. If each photon is subjected
to the same shift, the signal is also subjected to that shift.

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.

Wow... "plane waves"? I thought there weren't going to be any wave
functions here.

The whole point is to retain this aspect of quantum mechanics.

I don't see why. The reason I asked about the abstract state
formulation of QM is that it removes most explicit references to
coordinates and makes one less susceptible to confusing a wave function
with something like a fluid density. In principle any quantum system
can be described both using wave functions and the more abstract
approach, they are equivalent. However, sometimes, one approach or the
other makes things clearer.

In this case, the abstract state formulation makes things much clearer.

So, does your formulation of quantum mechanics allow you to express
everything in terms of abstract states and operators, without reference
to wave functions?

I use an abstract ket formulation of quantum mechanics. The wave
function is simply the inner product <x|f>. It is important not to think
of this as some sort of fluid density since this will create confusion.
Note that the bra <x| refers to a measurement result which can actually
be done, not to a coordinate in empty space where we cannot do a
measurement. In other words the wave function simply appears as a
mathematical abstraction, not as a description of a fluid density or
similar physical entity.

Then I don't like your proposal. I'm not happy (nor would a very large
number of working physicists be) when someone hands me a coordinate
system to use without giving me a choice in the matter.

I don't think there is a choice in the matter. It is a mathematical
deduction from assumptions, hence it gives you no choice once the
assumptions are accepted. Apart from minor tweaks in the quantum theory,
the assumptions are basically just the assumptions of quantum mechanics
together with the assumptions of general relativity less the affine
connection. In fact the affine connection seems to me the only really
questionable assumption in the standard theory, either gtr or qm. By
replacing it I have a formulation of quantum theory which is consistent
with gtr. As qm and gtr are known not to be consistent together, to give
a mathematically exact formulation of qm in an FRW cosmology seems
worthwhile - reservation: I only have a fully rigorous formulation in a
homogeneous isotropic cosmology. Applying it to rotation curves means I
have to use a heuristic argument, nonetheless I think it works.

First, a technical point. GR presumes a metric tensor. For each metric
tensor, there is a unique torsion-free affine connection compatible
with it. You are free not to use it, but it is there, hence not
eliminated. It also pops back up in the definition of the geodesic
equation, if you need to use that one. And if you've lost geodesics as
well, then you've also lost GR.

It is true that I lose GR for quantum phenomena, but I recover it for
classical phenomena.

Second, if your assumptions lead you to the conclusion that there is
one coordinate system that is better than all others, then the
assumptions must be seriously reconsidered. Any observer is free to use
her own coordinate system. Forcing everyone to use the same one is like
trying to make every person on Earth speak the same language. That's
just not going to happen. Therefore, you should be able to formulate
your theory independent of a choice of coordinates, especially if you
claim to be compatible with GR (and background independence, which
comes with the package). If you can't, then it's another point against
your proposal.

This brings into play the fundamental incompatibility between quantum
theory and gr. Although quantum theory is normally applied on very small
scales it requires us to write down integrals over all space. Since "all
space" is not Minkowski, quantum theory can only be an approximation.
The only way I can write down an exact formulation with an integral over
all space is on a synchronous slice at constant cosmic time. This in no
way inhibits our ability to use any local coordinate system to describe
local physical laws, or indeed to formulate quantum theory in any
locally Minkowski coordinate system as a very accurate approximation.
But light from distant stellar objects is not a local phenomenon, so we
should be cautious of studying it using local coordinates.


You misunderstood what I was trying to say. There are basically two
situations: a shift detected equivalent to MONDian motion or Pioneer
acceleration, or no shift detected, Newtonian motion (noisy signal near
the crossover). In fact it is always Newtonian motion, but if the
wavelength is small compared to the accuracy of measurement of position,
one gets to see a shift which is essentially the effect of the expansion
of the universe on the wave function.

Again, why does the *accuracy of measurement of position* play a role
in *whether* there is a shift.

Because measurement of position induces the collapse of the wave
function. Accurate measurement of position is equivalent to frequent
wave function collapses, tending to continuous motion in the classical
limit in which position can be measured continuously. I am suggesting
that if we are using a signal with a period greater than the frequency
of wave function collapse, then we measure an average motion and get the
classical result. Only by using a signal with a period less than the
frequency of wave function collapse can we measure the quantum
prediction.

Never mind the detection part. There
either is a shift or not, independent of whether someone measures it or
not. It still sounds to me like you're saying that the existence of the
spectrum shift depends on someone measuring it and the accuracy of his
apparatus. Am I still misunderstanding?

I don't think so. Greater accuracy of position measurements gives more
frequent wave function collapse, so that a higher frequency in the
signal is needed to avoid measuring Doppler averaged over several
quantum cycles, i.e. the classical result.

In principle, it should be possible to use very loud signals and drown
the noise. Then the cycle slip could be observed. Actually it is
possible that it has been observed already. VLBI measurements of IM
Pegasi have detected a sudden (over one hour) jump in its motion by
2/3rds its diameter. The researchers are looking at other explanations,
but if I am right this sort of observation will become more and more
common as astrometry improves. For example Hipparcos has made some odd
parallax measurements of the Pleiades and some other open clusters. When
Gaia goes up in five years time it will produce stacks of anomalies at
the accuracy with which it can measure.

If this is indeed a prediction of your model. You should make it
falsifiable. If these cycle slips are *not* see, under what conditions
can your model be ruled out?

At the moment we can only measure the rotational velocity of the Milky
way using methods which depend on wave function effects, like Doppler or
VLBI. These give a speed of c220km/s for the orbital velocity of the
Sun. After a sufficient period of measurement of sufficient accuracy we
will be able to measure the orbital velocity of the Sun by direct
geometrical means. I am predicting a figure of c160km/s, i.e. the
velocity predicted by Newtonian gravity in the absence of a cold dark
matter halo. I think that would be pretty conclusive. At the moment
there are a range of other tests, but they may not be considered
conclusive.

Tests so far:

Supernova redshift. Marginally better fit to m-z relation than standard
for both Riess and Astier data sets, using a no Lambda model with
density Omega=1.89. A substantial number of observations of supernovae
at z>1.5 will be needed to eliminate either model. There is a probe for
such supernova currently in design stage.

Galaxy ageing. Observations of high z galaxies are out of kilter with
galaxy evolution models, but data is too preliminary to say this is
conclusive. Next generation of very large telescopes should find more
evolved galaxies at considerably higher redshifts. In the teleconnection
model these are not as far back in time and the universe is much older.

Lensing. Observations of galaxy profiles using lensing are not
consistent with profiles from galaxy rotation curves, and neither are
consistent with analytic evolution models. They are consistent with the
teleconnection no CDM model.

MOND and Pioneer. The teleconnection offers an explanation not afforded
in the standard model.

Other tests are suggested. Notably Hipparcos parallax distances to
certain open clusters produce anomalies and there are unexplained
anisotropy in the microwave background. Analysis is complicated, I have
no training in astrometry and feel like an old dog who can't learn new
tricks, but I am working on Hipparcos parallax. Also further VLBI
observations of stars over long timescales may produce apparent jumps in
motion like that of IM Pegasi. Full data on IM Pegasi is not due to be
published till next year.


Regards

--
Charles Francis
substitute charles for NotI to email

.

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