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A Static Cosmological Model, MOND and the Galactic Rotation Curve
By Kathleen A. Rosser, Quemado Institute
November 20, 2016
View PDF (17 pages)
[Also available on viXra]

 Click to enlarge. Hubble Ultra Deep Field 2014 - Image Credit: NASA, ESA, H.Teplitz and M.Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst(ASU), Z. Levay (STScI) -- Galaxies fill the Hubble Ultra Deep Field 2014. The dimmest galaxies are more than 10 billion times fainter than stars visible to the unaided eye and represent the Universe in the extreme past, a few 100 million years after the Big Bang. The image itself was made with the significant addition of ultraviolet data to the Hubble Ultra Deep Field, an update of Hubble's famous most distant gaze toward the southern constellation of Fornax. It now covers the entire range of wavelengths available to Hubble's cameras, from ultraviolet through visible to near-infrared. Ultraviolet data adds the crucial capability of studying star formation in the Hubble Ultra Deep Field galaxies between 5 and 10 billion light-years distant.

CLICK TO ENLARGE. Hubble Ultra Deep Field 2014 – Image Credit: NASA, ESA, H.Teplitz and M.Rafelski (IPAC/Caltech),
A. Koekemoer (STScI), R. Windhorst(ASU), Z. Levay (STScI) — Galaxies fill the Hubble Ultra Deep Field 2014. The dimmest galaxies are more than 10 billion times fainter than stars visible to the unaided eye and represent the Universe in the extreme past, a few 100 million years after the Big Bang. The image itself was made with the significant addition of ultraviolet data to the Hubble Ultra Deep Field, an update of Hubble’s famous most distant gaze toward the southern constellation of Fornax. It now covers the entire range of wavelengths available to Hubble’s cameras, from ultraviolet through visible to near-infrared. Ultraviolet data adds the crucial capability of studying star formation in the Hubble Ultra Deep Field galaxies between 5 and 10 billion light-years distant.

A static cosmological metric is derived that accounts for observed cosmic redshift without the requirement for an expanding universe. The metric is interpreted in such a way as to predict a universal potential that accounts the anomalous acceleration of outlying stars of spiral galaxies (the galactic rotation curve), obviating the need for dark matter or modifications to general relativity.

  1. Introduction

The Big Bang (BB) theory has been questioned over its 85-year history for a number of fundamental reasons. That all the matter in the universe was created instantly at a single point some finite time in the past defies intuition as well as established conservation laws. That the dynamic general relativistic Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, which forms the basis of the BB theory, is orthogonal in the space and time coordinates raises questions about its mathematical validity, a concern expressed by Friedmann himself in his original paper of 19221. That Hubble deep-field images displaying thousands of distant galaxies reveal no apparent galactic structural evolution seems to suggest the universe is much older than the BB theory purports. Well-established patterns of stellar evolution indicate some stars predate by billions of years the event of the Big Bang, pointing to a flaw in the theory. Questions may also be raised about the superluminal expansion predicted by the FLRW metric, implying possible violations of locally observed special relativity. That Einstein himself believed singularities can’t exist casts doubt on the singular origin of matter. These objections are foundational.

It is also unsatisfying that the BB theory fails to predict more recent observations, such as the apparent increase of expansion rate known as cosmic acceleration2,3,4, currently explained by reintroducing Einstein’s abandoned cosmological constant Λ and/or by postulating an ad hoc mysterious quantity called dark energy. The BB hypothesis also does not account for early-epoch cosmic inflation5, nor does it accommodate the unexpectedly large rotation velocities of outlying stars in spiral galaxies, whose anomalous centripetal acceleration is often attributed to an unidentified substance called dark matter. A further defect in the theory is the premise of homogeneity. The universe in fact manifests large-scale inhomogeneities in the form of clusters, walls and voids. Averaging over these density variations has introduced difficulties of its own, a problem known as back-reaction6.

Generally, astrophysicists as a community acknowledge these problems inherent in the BB hypothesis7,8,9. Scores of papers are published annually in peer-reviewed journals such as Physical Review D exploring possible solutions to these problems10,11,12. Nevertheless, the FLRW metric of the expanding universe remains the basis for modern cosmology, and is widely accepted among physicists as a valid model. This standard theory of cosmology has been dubbed the Lambda-Cold-Dark-Matter (ΛCDM) model due to its reliance on Einstein’s cosmological constant to account for cosmic acceleration, and its appropriation of cold dark matter to explain the galactic rotation curve.

The ΛCDM model is the most comprehensive gravitational model of the universe currently known, and has a distinct appeal in that it preserves general relativity (GR) in its original form. Numerous theories of modified gravity, including bimetric,  bigravity or massive gravity theories13,14, scalar-tensor theories (eg. the Brans-Dicke theory15), tensor-vector-scalar (TeVeS) theories16, vector-tensor theories17, modified Newtonian gravity (MOND)18, and f(R) gravity theories that modify Einstein’s field equations (EFE)19,20,21,22, have been investigated, but so far none have proven sufficiently compelling to replace GR as the prevailing theory of gravity. Many such variations suffer problems in the limit of solar system scales, where, to agree with observation, they must predict the same results as GR, giving rise to complicated schemes such as the chameleon mechanism23,24,25 and Galileon fields26. Many of these theories fail the test of Occam’s Razor.

The present article discusses the results of an investigation into an alternate description of the universe. This description obviates the need to modify general relativity, while also eliminating any requirement for dark matter. It accounts in a natural way for the redshift-distance relation, and postulates a simple metric explanation for the galactic rotation curve. . . . MORE>> View PDF (17 pages)

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Anomalous Magnetic Moment and the g-Factor

One of the most curious properties of elementary particles is their anomalous magnetic moment. This is calculated from what is called the “g-factor”, which is based on the ratio of the magnetic moment due to the spinning particle’s charge, and the angular momentum due to its mass.  For classical objects, such as planets, g = 1. But for quantum objects such as electrons, protons, neutrons, muons, mesons and quarks, g can in principle have any value. What this means is, it seems as if the charge of the particle is spinning at a different rate from its mass.

For the electron, g is almost exactly 2, naively implying the electron’s charge is rotating twice as fast as its mass. This would seem to mean the electron has internal structure. But accelerator measurements of its cross section indicate it has a radius of zero. Or so they say. But in fact, the Standard Model of particle physics, which comprises a disjointed collection of calculational techniques and equations,  does not really offer a picture of the electron’s structure, if it has one, nor a definite way of predicting its properties. Indeed, the g-factor is an ongoing area of research into physics beyond the Standard Model.

Several papers in Physical Review D, the preeminent particle physics journal, appear each month on the subject of the g-factor and anomalous magnetic moment, which is usually defined as (g-2)/2. This has become a curious subject because the sum total of human knowledge cannot yet explain it.

The g-factor is the most critical parameter distinguishing one particle from another.  Some of the g-factors are (approximately) 1 for the photon, 0 for the mesons, 2 for the electron and muon, about 5.6 for the proton and about minus 3.8 for the neutron. Quarks also have g-factors, but these are known only vaguely. Why the g-factor is more critical than say, other distinguishing properties such as charge, spin (quantized angular momentum), and mass, is that the g-factor plays a profound mathematical role at the very foundations of theory.

This can be understood as follows. The particles that physicists most often deal with are the photon (a quantum of electromagnetic radiation with spin 1), the meson (particles of charge +,- or 0 and spin 0), the proton (a positively charged particle that occupies the nucleus of the atom and has a spin of 1/2), the electron (a light negatively charged particle that surrounds the nucleus like a cloud and has a spin of 1/2), the neutron (a neutral spin 1/2 particle that also occupies the nuclei of atoms), and the quarks (particles that form the interiors of protons, neutrons and mesons, and have charges of 1/3 or 2/3). Oddly, all of these particles are described by different equations, equations that have very different structures and appearances and seem irreconcilable. These include the Dirac Equation, which is a relativistic generalization of the Schroedinger equation familiar from quantum mechanics and which describes the electron and its antiparticle the positron; the Klein Gordon equation, another completely different relativistic generalization of the Schroedinger equation that applies to spin-0 mesons; and Maxwell’s Equations, which describe the photon. There are others.

It turns out, however, that all of these equations can be combined into a single General Particle Equation that takes the g-factor as a parameter. When the g-factor is inserted into the General Particle Equation and the expression simplified by ordinary algebraic methods, the result is either the Dirac Equation, the Klein-Gordon Equation, or Maxwell’s Equations, depending on the value of g. So, for example, if you plug g=2 into the General Particle Equation and simplify, the result is the Dirac Equation, ie the equation for the electron.

The interest here is not so much the mathematics, as that the g-factor is so fundamental, it makes a particle what it is: an electron, a photon, a proton, and so on. So even though a photon seems very distinct from an electron, the two are fundamentally the same phenomenon except  for their values of g. This very property is at the forefront of particle physics research today. Its nature surpasses the limits of our present understanding, and enormous work is going into its precise calculation and the theories that should, physicists hope, predict its value.

 

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