Missing Mass, Galaxy Ageing, Supernova Redshift, MOND, and Pioneer

I have revised the introduction to this. Any comments?

Does a Teleconnection between Quantum States account for Missing Mass,
Galaxy Ageing, Supernova Redshift, MOND, and Pioneer?


Introduction

Background
There are well known and substantial difficulties in formulating quantum
theories in curved spacetime (Dirac, 1964; Fulling, 1989; Wald, 1994).
Einstein (1930) found problems with electrodynamics in curved space
time, and suggested that the affine connection of general relativity
might be replaced with a teleparallel connection. Such a replacement can
also be motivated in the orthodox interpretation of quantum mechanics in
which it does not make sense to talk of position between measurements
and hence it does not make sense to talk of a path between an initial
and final state; e.g. we may not discuss which slit a particle passes
through in the Young’s slits experiment. By that token we should also
not talk of geodesic motion of a photon emitted from a distant star and
detected on Earth.

The methods used in this paper have arisen from research into
foundational issues in quantum mechanics, leading ultimately to a
rigorous quantum theory incorporating gravity (Francis, 2005). It is not
the purpose of this paper to discuss the theoretical aspects of that
model, but to report on its success in making verified empirical
predictions distinct from those of the standard model, and to point to
further tests not available from the resources of the author. In almost
every respect the model agrees with general relativity in the classical
correspondence, but late in 2004 it was found that it yields a different
result for cosmological red shift. This gave a means to directly test
the model against data collected by astrophysicists. In each case the
model has shown itself to be consistent with data, and, moreover, it
gives accounts of observed phenomena which the standard model has been
unable to explain.

Despite its theoretical origin, the model described here can be treated
as phenomenological, and assessed on the basis that, when confronted
with data, its predictions have exceeded those of the standard model. We
will use standard general relativity and quantum mechanics with one
change: the wave function is not modelled in curved space but in quantum
coordinates, as described in section 2.3, making use of coordinate space
vectors (defined in section 2.1) for position and momentum. The
mathematical implications of this change are described in section 2 and
its empirical validity may be assessed on the basis of its consequences,
as discussed in section 3.

Teleparallelism
This is not a theory of teleparallel gravity in the usual sense (see
e.g. Arcos and Pereira, 2004). Torsion will be removed as part of wave
function collapse and in the classical correspondence gravity is
described by curvature, as is normal in general relativity. It will be
seen that this prescription reduces to the affine connection in the
classical correspondence and that geodesic motion is preserved for
classical particles and for a beam of light.

In special relativity the metric may be determined from the behaviour of
light. In this paper the connection is also determined by using light
arriving at the detector to determine coordinates at the source, under
the assumption that there exists a coordinate space in which plane wave
states are defined. It will be seen that this can be done consistently
in an FRW cosmology. Momentum at source is defined teleparallel to
momentum at detection, and this determines a connection between the
initial and final states. The coordinate space itself is not considered
physical. Since the connection is only meaningful at the times of
measurement it will be called a teleconnection.

Comparison with the Standard Model
As described in section 3, the model predicts that the cosmological
redshift factor, 1+z, varies with the square of the expansion parameter.
The square law applies to cosmological redshift; gravitational redshift
is as in general relativity, as required by the principle of
equivalence. It follows that the rate of expansion of the universe is
half that predicted by the standard model, the universe is twice as old
as has been thought, and critical density for closure is a quarter of
the standard value, dispensing with at least the bulk of missing mass
and resolving any ageing issues arising from recent observations of
mature galaxies at z=1.4 and greater (e.g. Mullis et al., 2005; Doherty
et al 2005). The existence of mature galaxies at this red shift may
genuinely be described as prediction rather than retrodiction, since the
implications of the square red shift law were discussed in public forum
before the observations had been announced (Francis, 2004). It is also
predicted that as observations are made at greater redshifts, ageing
problems in the standard model will grow more severe.

The model predicts that cosmological redshift is present in all
measurements using Doppler. This has been observed. For some years the
Pioneer spacecraft have been sending back Doppler information appearing
to indicate an anomalous acceleration toward the sun (Anderson et al.,
2002). The anomalous data can now be understood as an optical effect due
to cosmological redshift not evidence of actual acceleration. No other
explanation has yet been given for the Pioneer redshift. The effect is
also 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). Again this
appears as an optical effect arising from the treatment of redshift, not
a real change to Newtonian dynamics. The MOND test is particularly
stringent as it uses data from a large number of stars, and because cold
dark matter does not give any explanation as to why the same
characteristic acceleration law should be found in all galaxies.

All astronomical measurement using redshift must be reinterpreted in
this model. In standard cosmology a best fit with supernova data is
found for the concordance model, Omega=0.3, Omega_Lambda=0.7 (Reiss et
al., 2004; Filippenko, 2004, and references cited therein). To first
order in z, for a closed cosmos with zero cosmological constant the
redshift magnitude relation found here is close to that of the standard
model with Omega=0.41 and Omega_Lambda=0.59. The fit improves when terms
O(z^2) are taken into account, but it remains to find the best fit
values of Omega and Omega_Lambda using a computer solution. Similar
results are found using the integrated Sachs-Wolfe effect (Afshordi, Loh
& Strauss; 2004; Boughn & Crittendon, 2004; Fosalba et al., 2003; Nolta
et al., 2004; Scranton et al., 2004) and are consistent with evidence
from the Two-Degree Field Galaxy Redshift Survey (2dFGRS; Peacock 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. Since all of them depend on
same relationship between redshift and expansion the optical distortions
due to the square redshift law will affect Omega and OmegaLambda in the
same way. However Spergal comments on discrepancies in the data on both
the largest and smallest scales, and this may provide a further test of
the model. This requires resources and data not available to the author.


Regards

--
Charles Francis