Re: FarmingFisicistsFumble

Thus spake Oz <Oz@xxxxxxxxxxxxxxxxxxxx>
>
>This is really nice, charles. I wonder if anyone will sit up and take
>note?

Here is the first section. The first two paras are new, and there has
been a bit of change in the rest. Could do with criticism.
>
Does a Teleconnection between Quantum States account for Missing Mass,
Galaxy Ageing, Supernova Redshift, MOND, and Pioneer Blue-shift?



Abstract:
There have been previous suggestions, notably by Einstein, that the
affine connection in general relativity might be replaced with a
teleparallel one. This paper carries out a preliminary investigation of
the empirical implications of a teleparallel displacement of momentum
between initial and final quantum states, using conformally flat quantum
coordinates. An exact formulation is possible in an FRW cosmology in
which cosmological redshift is given by 1+z = (a_o/a(t))^2. This is
consistent with observation for a universe expanding at half the rate
and twice as old as indicated by a linear law, and requiring a quarter
of the critical density for closure. Supernova redshifts indicate a
universe a little over critical density and are consistent with zero
cosmological constant. Quantum coordinates exhibit an acceleration in
time, resulting in the anomalous Pioneer blue-shift and in the
flattening of galaxies’ rotation curves. These appear as optical effects
and do not affect classical motions. Milgrom’s phenomenological law
(MOND) is precisely obeyed.


1 Introduction
1.1 Background
There is growing concern in Cosmology about unexplained empirical
phenomena. The standard model of accelerating expansion is successful in
matching parameters to observation, but, while there is no true
reconciliation between general relativity and quantum mechanics, science
should remain open to the prospect that these phenomena may have some
deep underlying reason in new physics. Any new model of physics should
adhere to fundamental principles such as the cosmological principle and
the principle of relativity, but the true test is whether predictions
match observation, and whether a model is capable of making new
predictions or providing explanations where previously there were none.
This paper carries out a preliminary investigation of the empirical
implications of a modification to general relativity adhering to
fundamental principles. It is found that observation is consistent with
a universe of just above critical mass, with no cold dark matter or
cosmological constant, and no apparent timescale problem (Table 1). As a
bonus the model predicts the flattening of galaxies’ rotation curves and
the observation of Pioneer blue-shift, without requiring either a change
to Newtonian dynamics or galactic haloes.

Table 1: Properties Compared
Connection Affine Teleconnection
Topology Open Any
W 0.26+-0.05 1.1+-0.2
WL 0.74-+0.05 -0.1-+0.2
WB 0.025-0.05 0.1-0.2
Age of universe 14X10^9 yrs 16-20X10^9yrs
Age at z=6 7x10^8yrs 4.5x10^9yrs
Baryon:Non-baryon ~15:1 4-9:1
Expansion rate adot/a=H0 adot/a=H0/2
Pioneer blue shift unexplained ap=H0c
MOND CDM aM=H0c/8
wave motion curved space? flat space
classical motion geodesic geodesic

Table 2: Magnitude-Redshift Relation
first order comparison
affine: m-M ~ 5logz + 1.086(1-q)z
teleconnection: m-M ~ 5logz + 1.086(2-q)z

It is known on theoretical grounds that new physics is required to
reconcile general relativity and quantum theory (Dirac, 1964). Eppley
and Hannah (1977) showed that if gravitational measurement causes wave
function collapse in curved space, violation of the uncertainty
relationships can only be avoided by giving up conservation of momentum.
Individual detection of photons from distant stars strongly suggests
that we cannot be certain of the interpretation of redshift without
first having a rigorous formulation of quantum motions in curved space
time. Einstein (1930) found problems with electrodynamics in curved
space time, and suggested that the affine connection used in general
relativity might be replaced with a teleparallel connection. Such a
replacement can be motivated in the orthodox interpretation of quantum
mechanics; if it does not make sense to talk of position between
measurements then it is also without sense to talk of geodesic motion of
a photon emitted from a distant star and detected on Earth. Since the
connection is meaningful only at the times of measurement it will be
called a teleconnection. Standard general relativity and quantum
mechanics are assumed, excepting that wave functions are defined using
quantum coordinates (section 2.3), not in curved spacetime. It will be
seen that this can be done consistently in an FRW cosmology, that the
prescription reduces to the standard affine connection in the classical
correspondence, and that geodesic motion obtains for classical particles
and for a beam of light (section 2.4).

For the purpose of analysis a closed universe with zero cosmological
constant and no cold dark matter will be discussed. Other models are
possible but up to the accuracy of the tests applied here this simple
model is consistent with data, gives accounts of observed phenomena
which the standard model has been unable to explain and makes clear
predictions about future tests. In the instance of galactic rotation
curves testing has been done, not through direct statistical analysis,
but by deriving general laws (the magnitude-redshift relation and MOND)
and comparing them with empirical laws already established through
detailed statistical analysis. The distance-redshift relation has been
analysed using data sets from Riess (20040 and Astier (2005) and is
consistent with a universe with just over critical mass and no
cosmological constant.

1.2 The Teleconnection
The mathematical description of a teleconnection is given in section 2,
but it is useful also to develop an intuitive understanding of the
concept. This is not a teleparallel theory using the Weitzenbröck
connection (see e.g. Arcos and Pereira, 2004). Torsion will be removed
as part of wave function collapse and in the classical correspondence
gravity will be described by curvature, as is normal in general
relativity. In general relativity it is an assumption that photon
momentum is parallel transported through large distances. This
assumption takes no account of the propagation of a photon wave function
in a curved space-time, which would imply that a photon of precise
momentum at time of emission would not have precise momentum at
absorption. Here it is assumed that there exists a coordinate space in
which plane wave states are defined (2.3.1). Momentum at source is
teleparallel to momentum at detection, and this determines a connection
between the initial and final states.

In classical general relativity there is no local meaning to expansion
because length is defined locally, by an empirical procedure based on
local matter. If all matter locally were to “shrink”, including
ourselves and all the matter contained our measuring apparatus, then our
fundamental length scales would “shrink” in direct proportion; there
would be no change in numerical results of local distance measurements
and there would be no local means to detect the fact. To talk about
matter shrinking we have to compare a length scale defined here and now,
using here and now clocks and rulers, with a length scale defined at
some time in the past. In practice we can do this by studying light from
the past and analysing redshift provided that we know how light behaves.
The definition of a teleconnection assumes that if momentum has a
precise value at one place and time then it also has a precise value
other places and times and is empirically justified in so far as
observation yields precise values for cosmological redshift after
allowing for dispersion due to dust or other known factors. This is a
fundamental assumption in this model, of equal importance to the
assumption of the constancy of the speed of light in special relativity.
Like that assumption, if it were dropped we would be left, not with a
different theory, but with no known consistent theory.

Let Alf be an observer on a space craft or a distant planet, and let
Beth be an observer on Earth, such that Alf can signal to Beth. At the
time of emission of a photon passing from Alf to Beth, Alf defines
synchronous, conformally flat, co-ordinates in 3 dimensions at constant
cosmic time t. In a closed cosmos the universe can mapped onto a finite
space, which will be called Alf’s map. Beth defines Beth’s map in
exactly the same way, to the same scale, at the time of detection of the
photon, cosmic time t0. For a closed universe in three dimensions Alf’s
and Beth’s maps each consist of the interior of a sphere. Let a(t) be
the scale factor and let a0=a(t0). If the universe expands during the
time of travel of the photon from Alf to Beth, then Beth’s map is larger
than Alf’s map. Because the maps are conformally flat, they can be
placed in direct correspondence by enlarging Alf’s map by a factor
a0/a(t). The teleconnection is defined such that photon momentum is
represented by an arrow of equal length and direction on Beth’s map and
on Alf’s enlarged map.

Quantum coordinates define a four dimensional map found by considering
all the times and positions where Alf and Beth might be, with the time
axis scaled so that light is shown at 450. This is a Penrose diagram in
each time-radial plane. In these coordinates the arrow representing
photon momentum is of constant length and direction everywhere, so that
plane wave motions obtain for light. Beth can compare the scale of her
map to that of Alf’s map by studying red shift. There are two scaling
effects. First Alf’s map has been enlarged by a factor a0/a(t). In
addition, the scaling on the map changes as you move from one point to
another. That gives another factor a0/a(t). Thus, the model predicts
that the cosmological redshift factor varies with the square of the
expansion parameter 1+z = (a_o/a(t))^2.

On Beth’s map, Alf, and all physical objects in Alf’s locality such as
rulers, appear enlarged. This is torsion. In measurements in quantum
mechanics there is both an initial and a final measurement and the
coordinate system is scaled to the measuring apparatus at the time of
each measurement. Rescaling coordinates removes torsion and renormalises
momentum so that in the classical correspondence gravitational redshift
is as in general relativity, as required by the principle of equivalence
and for geodesic motion (section 2.4).

1.3 Comparison with the Standard Model
The cosmological microwave background defines the reference frame in
which photons are emitted. This scales coordinates at the time of the
production of CMB photons and the usual linear red shift law applies.
The analyses of big bang nucleosynthesis and of decoupling are
unaltered, but the density of baryonic matter becomes 0.064<Omega_B h^2
<0.096 after normalising Wcr to 1 (3.2.2). Thus baryonic matter forms
10-20% of critical mass, and at an extreme, the ratio of non-baryonic to
baryonic matter need only be 4:1 for closure, within the range of values
which might be accounted for by a massive neutrino.

The square law applies when all the information about the initial state
is contained in the detected light, as in the observation of
astronomical bodies. It follows immediately that the rate of expansion
of the universe is half that predicted by the standard model, the
universe is twice as old as would be indicated by a linear law, and
critical density for closure is a quarter of the standard value. An
immediate consequence is that there is no timescale problem for a closed
universe with greater than critical density and zero cosmological
constant. If observations at high red shift had revealed the expected
activity of the early universe it would have falsified the square red
shift law; in fact it receives support from the observation of mature
galaxies at z=1.4 and greater (e.g. Mullis et al., 2005; Doherty et al
2005, and references cited therein). As described by Glazebrook (2004),
there is poor agreement between current theoretical models of galaxy
evolution and empirical data. To explain this it has been suggested
(Cimatti et. al, 2004) that the theoretical models may be inaccurate.
This model presents an alternative, that a square redshift law means we
have to revise the ages of red galaxies. A value of Hubble’s constant
h=0.72 places an upper bound on the age of the universe of eighteen
billion years, so that at redshift 6 the universe would have been about
4.5 billion years old. A detailed study is required to assess
consistency between observation and theory, but this certainly appears
to alleviate the difficulties. Hopefully future observation and analysis
will be conclusive.

For some years the Pioneer spacecraft have been sending back Doppler
information interpreted as an anomalous acceleration toward the sun
(Anderson et al., 2002). No accepted explanation has been given for the
anomalous blue-shift, but if it were not observed it would be fatal to
this model. It is seen as an optical effect due to expansion (section
3.3). Here wave packets do not follow geodesics and there is disparity
between the solution of a wave function projected back in time from a
final measurement and the classical motion of a body. The disparity is
removed when the wave function collapses and coordinates are rescaled,
but it leads to an anomalous blue-shift in Doppler measurements of
stellar objects and the model predicts blue-shift simulating constant
acceleration toward the origin of coordinates, that is toward the
observer on Earth. This is a quantum effect; consistent with NASA’s
findings, there is no corresponding classical acceleration and planetary
motions are unaffected. A future test is planned which will determine
whether the acceleration is toward the Sun, toward the Earth, in the
direction of motion of the craft, or along the spin axis (Nieto et. al.
2004). If the direction is not toward the Earth the test will falsify
this model.

The Pioneer blue-shift is present in the observation of distant
galaxies, and precisely accounts for flattening of galaxies' rotation
curves consistent with MOND, the phenomenological law found by Milgrom
(1994; a review of MOND is given by Sanders & McGough, 2002). This
anomaly appears as an optical effect arising from the treatment of
redshift, not a change to Newtonian dynamics (section 3.3) or evidence
of cold dark matter. Similarly the accelerations of galaxies in clusters
are in the MONDian regime, and after revising the redshift-age relation;
there is no immediate evidence that CDM is necessary for galaxy
evolution. The MOND test is particularly important for several reasons.
Firstly, data fits have been given for over 100 galaxies and thousands
of stars, secondly, because cold dark matter does not give any
explanation as to why the precisely same acceleration law should be
found in galaxies of many sizes and types, thirdly, because there is no
other empirical evidence for CDM haloes, fourthly because there is no
satisfactory theory of CDM in particle physics, and finally because if
galaxies' rotation curves did not obey MOND it would refute this as a
‘no CDM’ model.

In standard cosmology a best fit with supernova data is found for the
concordance model, W_s=0.26, W_Ls=0.76 (Astier 2005, Reiss et al., 2004;
Filippenko, 2004, and references cited therein). To first order in z,
for a closed cosmos with zero cosmological constant the magnitude-
redshift relation found in section 3.1 is identical to that of the
standard model with W_s=0.33 and W_Ls=0.67, but examination of residual
Hubble diagrams, figures 1-3 shows that the fit is better for the lower
value of Ws, and direct analysis of supernova data indicates a universe
with slightly more than critical mass.

The concordance model is supported by the integrated Sachs-Wolfe effect
(Afshordi, Loh & Strauss; 2004; Boughn & Crittendon, 2004; Fosalba et
al., 2003; Nolta et al., 2004; Scranton et al., 2004) using evidence
from the Two-Degree Field Galaxy Redshift Survey (2dFGRS; Pea*** et al.
2001; Percival et al., 2001; Efstathiou, 2002), and from the Wilkinson
Microwave Anisotropy Probe (WMAP; Spergal, 2003, and references cited
therein). In practice these measurements determine cosmological
parameters rather than test consistency, and they depend on the
distance-redshift relation. Acceleration depends only on distance and
time, so that, if the standard model is consistent, a change in the
distance-redshift relation can be expected to give a consistent change
in the deceleration parameter in different tests. It is thus to be
expected that Ws~0.3 corresponds to W~1 in the teleconnection model
whether it is determined from Supernova or from WMAP and 2dGFS.

The first order analysis of WMAP appears unchanged in the teleconnection
model, as we expect isotropy and a gaussian random distribution. However
Spergal comments on discrepancies in the WMAP data on both the largest
and smallest scales, and Copi et al (2005) report on unexplained
alignments in the data. It is not presently possible to say whether
these are caused by higher order corrections in the analysis of data;
for example it may be necessary to take account of pioneer blue-shift
when removing foreground contamination.
>



Regards

--
Charles Francis
Please reply by name
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