An Extended Version of Hubble’s Law

Friedmann-like cosmological equations were derived by us in a recent paper by using axioms proposed by us for the so called empty Space. By using one of our cosmological equations we have derived in this paper a relation between the expansion velocity of the universe and the radius of the universe. This relation may be considered as an extended version of Hubbles’ Law. According to our relation derived here, the Hubble factor H goes on decreasing as the radius increases.

Zitterbewegung and the Electron

Starting from a probabilistic model of the electron, which explains spin and spin measurements in terms of a probability density distribution resulting from a rapidly changing angular momentum during an extended Zitterbewegung EZBW, a “light-like” model of the electron and other spin-1/2?particles is formulated. This model describes individual particles in terms of paths of a moving quantum. It is shown that this description allows one to reproduce observable properties as path-averages over a period of the fast EZBW in elementary calculations. The general topology of the paths may be described as a helical path, with a helix axis forming a circle around a fixed point in space. The radius of the helix and of the circle is equal and given by half the reduced Compton wave length of a photon of energy equal to the rest energy of the particle described. The paths depend on the relative velocity between the described “entity” and the observer, and represent the De Broglie wave. The merits of the proposed model are summarized and its role in relation to the established description by quantum mechanics is discussed. It is concluded that it supports the existence of the proposed EZBW, and offers a description of quantum behavior without quantum mechanics.

Inflation and Rapid Expansion in a Variable G Model

Cosmic inflation is considered assuming a cosmologically varying Newtonian gravitational constant, G. Utilizing two specific models for, G-1(a), where, a, is the cosmic scale parameter, we find that the Hubble parameter, H, at inception of G-1, may be as high as 7.56 E53 km/(s Mpc) for model A, or, 8.55 E53 km/(s Mpc) for model B, making these good candidates for inflation. The Hubble parameter is inextricably linked to G by Friedmanns’ equation, and if G did not exist prior to an inception temperature, then neither did expansion. The CBR temperatures at inception of G-1 are estimated to equal, 6.20 E21 Kelvin for model A, and 7.01 E21 for model B, somewhat lower than CBR temperatures usually associated with inflation. These temperatures would fix the size of Lemaitre universe in the vicinity of 3% of the Earths’ radius at the beginning of expansion, thus avoiding a singularity, as is the case in the ΛCDM model. In the later universe, a variable G model cannot be dismissed based on SNIa events. In fact, there is now some compelling astronomical evidence, using rise times and luminosity, which we discuss, where it could be argued that SNIa events can only be used as good standard candles if a variation in G is taken into account. Dark energy may have more to do with a weakening G with increasing cosmological time, versus an unanticipated acceleration of the universe, in the late stage of cosmic evolution.

General Relativity and the Tully-Fisher Relation for Rotating Galaxies

The flat limit of rotational velocity (vφ) approximately equal to the “edge”-velocity of a galaxy is related to the baryonic mass (MB) via the T-F relationship with n ≈ 4. We explore the connection between mass and the limiting velocity in the framework of general relativity (GR) using the Weyl metric for axially-symmetric galaxies that are supported entirely by their rotational motion. While for small distances from the center, the Newtonian description is accurate as one moves beyond the (baryonic) edge of the galaxy, Lenz’s law and non-linearity of the gravitational field inherent in GR not only lead to a flat velocity (obviating its Keplerian fall), but also provide its tight log-log relationship with the enclosed (baryonic) mass.