Re: Missing Mass, Galaxy Ageing, Supernova Redshift, MOND, Pioneer

Charles Francis wrote:
> I might describe this post as a pre-preprint. I have not yet sent it
> anywhere, and would like to get comments and criticisms before I do.
>
>
> Title
> Does a Teleconnection between Quantum States account for Missing Mass,
> Galaxy Ageing, Supernova Redshift, MOND and Pioneer?
>
> Author
> Charles Francis MA (Cantab) PhD (Lond)
>
> 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 investigates the empirical implications of
> using a teleparallel displacement of momentum between initial and final
> states quantum theory. An exact formulation is possible in a closed 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
> currently accepted rate, twice as old, and requiring a quarter of the
> critical density for closure. To first order, supernova redshifts
> indicating Omega_M=0.3, Omega_Lambda=0.7 in standard cosmology are
> consistent with a closed universe close to critical density and with
> zero cosmological constant. The effect of expansion is found in the
> anomalous Pioneer redshift and in the flattening of galaxies' rotation
> curves. Milgrom's phenomenological law (MOND) is precisely obeyed, and
> appears in the model as an optical effect, affecting observation but not
> dynamics.
>
> 1 Introduction
> 1.1 Teleparallelism
> 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
> 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 transport along a path.
>
> This is not a theory of teleparallel gravity in the usual sense, as
> described by e.g. Arcos and Pereira (2004). The connection is only
> defined for measured states and will be called a teleconnection. We
> require only longitudinal teleparallel displacement of momentum.
> Teleparallel displacement requires a preferred coordinate system. This
> will be determined from the requirements of wave mechanics and exhibited
> in the instance of a homogeneous isotropic cosmos. 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 shown that this prescription reduces to
> the affine connection and that geodesic motion is preserved for
> classical particles and of a beam of light.
>
> 1.2 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,
> not linearly. 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). 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
> with Farmer Oz before the observations had been announced.
>
> 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.
>
> All cosmological tests using redshift measurement will have to be
> reinterpreted to demonstrate the consistency of this model with data. In
> standard cosmology a best fit with supernova data is found for the
> concordance model, Omega=Omega_M=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.
>
> Further consistency tests are possible. The standard concordance model
> is consistent with 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). Evidence for dark energy and
> accelerated expansion also comes from the integrated Sachs-Wolfe effect
> (Afshordi, Loh & Strauss; 2004; Boughn & Crittendon, 2004; Fosalba et
> al., 2003; Nolta et al., 2004; Scranton et al., 2004). It will be
> necessary to analyse these tests and any of them could potentially
> falsify the model. It is not unreasonable to suspect that the optical
> distortion due to the square redshift law will, in each case, affect
> Omega and Omega_Lambda in the same way, but rigorous testing requires
> resources and data not immediately available to the author.
>
> 2 Teleparallel Quantum Theory
>
> 2.1 Coordinate Space
> Each local region, O, of a continuous manifold, M, can be considered as
> a subset, U is a subset of R^n, together with a map, psi:U->O. Let U be
> denoted by axes a=0,...,n.
>
> Definition: A coordinate space is any such subset, U is a subset of R^n,
> together with metric yta_a_b.
>
> Here yta is not the physical metric, but is an abstract metric used for
> mapping. Curvature is naturally conceived in terms of the scaling
> distortions of maps. In general straight lines in coordinate space are
> not geometrically straight, but for a sufficiently short line segment
> the deviation from straightness is not detectable, and, to first order,
> a short rod placed at x will appear as a small displacement vector, A^a,
> defined, as usual, as the difference in the coordinates of one end of
> the rod from the other. A coordinate space vector can be defined by
> inverting the scaling distortions of the map. This is done by choosing
> primed locally Minkowski coordinates with an origin at x. We define the
> matrix
>
> kappa^a_b(x)=x^aprime_,b(x). 2.1.1
>
> 2.1.1 applies pointwise; kappa is defined using different local
> Minkowski coordinates for each origin x. 2.1.1 is meaningless as a
> differential equation and gives paradoxical results when treated as one.
>
> For the vector, A^a, at position x, the corresponding coordinate space
> vector, barred to distinguish it from an ordinary, or physical, vector,
> is defined by
>
> Abar^a(x) = kappa^a_b(x) A^b(x). 2.1.2
>
> This ensures that the coefficients of a coordinate space vector are
> equal to the coefficients of the corresponding vector in the primed,
> Minkowski, coordinates and preserves the inner product:
>
> yta_m_n Abar^m Bbar^n
>
> = yta_m_n kappa^m_a(x) kappa^n_b(x) A^a B^b
>
> = yta_m_n x^m_,a(x) x^n_,b(x) A^a B^b
>
> = g_a_b(x) A^a B^b 2.1.3
>
> 2.1.3 is true for any vectors A, . So
>
> g_a_b(x) = yta_m_n k^m_a(x) k^n_b(x) 2.1.4




Mr. Francis invited comments,

Quoting C. Francis,

"Teleparallel displacement requires a preferred coordinate system.
This
will be determined from the requirements of wave mechanics and
exhibited
in the instance of a homogeneous isotropic cosmos. 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 shown that this prescription reduces to
the affine connection and that geodesic motion is preserved for
classical particles and of a beam of light."

Using the following in the same paragraph,

"preferred coordinate system", " wave mechanics",
"isotropic cosmos", "wave function collapse",
"normal in general relativity", "geodesic motion".

is really hard to understand. IMHO an article of
this sophistication ought to be expanded and given
a link. I'm unable to determine if the "preferred CS"
contradicts GR, because of the ambiguous conditions.

Regards
Ken S. Tucker

.