The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

Condis Crystals of Small Molecules III. Thermal Analysis of Plastic and Condis Crystals of some Cyclosilanes

Three cyclic methyl and ethyl substituted silanes were synthesized and their thermal properties analyzed. All show a plastic crystalline state which permits also ring and/or side-chain conformational motion as judged from the enthalpies of transition to the isotropic state. Heat capacity data and entropies of disordering into the plastic crystal leave open the possibility of a condis (conformationally disordered) state below the plastic crystal state with a continuous, transitionless freezing of the conformational motion at lower temperature.     

Organosilane polymers. I. Poly(dimethylsilylene)

Poly(dimethylsilylene) higher polymers prepared by alkali metal coupling of purified dimethyldichlorosilane were found to be high melting, largely crystalline polymers, soluble in solvents at temperatures above 200°C.     

Possible Wormhole Solutions in (4 + 1) Gravity

We extend previous analyses of soliton solutionsin (4 + 1) gravity to new ranges of their definingparameters. The geometry, as studied using invariants,has the topology of wormholes found in (3 + 1) gravity. In the induced-matter picture, thefluid does not satisfy the strong energy conditions, butits gravitational mass is positive. We infer thepossible existence of (4 + 1) which, compared to their (3 + 1) counterparts, are lessexotic.     

Mach's principle and higher‐dimensional dynamics

We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP‐B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass of a body and its Newtonian state in space and time. One possible way to improve upon this situation in classical physics is to associate mass with an extra dimension. Indeed, Einstein's theory of gravitation can be locally embedded in a Ricci‐flat 5D manifold such that the 4D energy‐momentum tensor appears to originate from the existence of the extra dimension. An outline of such a 5D Machian extension of Einstein's general relativity is presented.     

On the Klein–Gordon Equation in Higher Dimensions: Are Particle Masses Variable?

We consider ways to generalize the 4D Klein–Gordon equation of particle physics to higher dimensions. The most promising approach implies that the mass which appears in the 4D relation is a term in the source-free 5D relation. We check this explicitly for the case of exact solitonic and cosmological solutions of the Kaluza–Klein equations. In general, particle masses are variable; but are constant for the Schwarzschild and late-universe cases, in agreement with data from the solar system and astrophysics. Our results have significant implications for cosmology, and can easily be extended to 10D superstrings, 11D supergravity and higher dimensions.