| | 1 | Author
| S. J. Prokhovnik | Requires cookie* | | | Title
| The General Solutions of the Robertson-Walker Null-geodesic and their Implications  | | | | Abstract
| The Robertson-Walker metric gives mathematical expression to three widely-held assumptions about the nature of the observable universe. It is shown that the null-geodesic of this metric has little-known solutions for the speed and distance of a light-signal relative to its source. Some implications of these results are considered, the most interesting of these being that only in a universe whose 3-space is Euclidean (k = 0) will the behaviour of light on the cosmological scale be compatible with .our understanding of light behaviour on the local scale. It is shown in an Appendix that the derived implications of the metric are entirely consistent with Special Relativity, its underlying principles and its consequences. | | | |
Reference
| Z. Naturforsch. 48a, 915—924 (1993); received December 3 1992 | | | |
Published
| 1993 | | | |
Keywords
| Cosmology, Special Relativity, Light propagation | | | |
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| default:Reihe_A/48/ZNA-1993-48a-0915.pdf | | | | Identifier
| ZNA-1993-48a-0915 | | | | Volume
| 48 | |
| 2 | Author
| S. J. Prokhovnik, A. E. Paparodopoulos | Requires cookie* | | | Title
| Light Propagation in a Curved-Space Friedmann Universe | | | | Abstract
| It was shown [1] that, in a Friedmann universe considered as an expanding ensemble of fundamen tal particles and whose 3-space is Euclidean, the propagation of light and its associated wavelength(s) partake in the expansion of the universe. In consequence, a light-signal emitted from any source will reach and pass every fundamental particle in its path at the same speed, c, despite the systematic mutual recession of any pair of such particles. This result, derived from the Robertson-Walker metric, is in full accord with all local physical experience of light transmission and with the requirements o f Einstein's Special Theory of Relativity. It is shown here that the same result also applies to any curved-space Friedmann universe. | | | |
Reference
| Z. Naturforsch. 49a, 543 (1994); received February 7 1994 | | | |
Published
| 1994 | | | |
Keywords
| C osm ology, Light propagation, Special Relativity | | | |
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| default:Reihe_A/49/ZNA-1994-49a-0543.pdf | | | | Identifier
| ZNA-1994-49a-0543 | | | | Volume
| 49 | |
| 3 | Author
| Sean Bohaty | Requires cookie* | | | Title
| Theoretical Determination of the Mass of a Roton | | | | Abstract
| For 56 years, researchers have sought, with varied success, to determine the mass of a roton. However, with the recent emergence of the author's theory of superfluid 4 He, the time may soon be at hand when the roton's mass is determined unequivocally. This letter reports the first quantitative results of the new theory of helium II. Using data from a neutron scattering experiment, the mass of a roton was calculated. It was found that the roton mass is 2.12 x 10 -* 7 kg or approximately 0.32 m He , where m He is the mass of a helium atom. | | | |
Reference
| Z. Naturforsch. 52a, 561—563 (1997); received May 13 1997 | | | |
Published
| 1997 | | | |
Keywords
| Rotons, Special relativity, Superfluid helium-4 | | | |
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| default:Reihe_A/52/ZNA-1997-52a-0561.pdf | | | | Identifier
| ZNA-1997-52a-0561 | | | | Volume
| 52 | |
| 5 | Author
| B. H. Lavenda | Requires cookie* | | | Title
| Is Relativistic Quantum Mechanics Compatible with Special Relativity? | | | | Abstract
| The transformation from a time-dependent random walk to quantum mechanics converts a modi fied Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order o f the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel function o f an imaginary argument is the solution o f the finite difference differential Schrödinger equation whereas the same function o f a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition o f the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of 7r/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components o f a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms o f ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms o f a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral o f the modified Bessel function and determines the paths o f steepest descent in the classical limit. If the definitions of frequency and wave number in terms o f the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation o f causality. In order to get surfaces o f constant phase to move at the group velocity, an integrating factor is required which determines how the intensity decays in time. The phase correlation between neighboring sites in quantum mechanics is given by the phase factor for the electron to reverse its direction, whereas, in special relativity, it is given by the Doppler shift. | | | |
Reference
| Z. Naturforsch. 56a, 347—365 (2001); received February 14 2001 | | | |
Published
| 2001 | | | |
Keywords
| Random Walks, Quantum Mechanics, Special Relativity, Ordinary and Modified Bessel Functions | | | |
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| default:Reihe_A/56/ZNA-2001-56a-0347.pdf | | | | Identifier
| ZNA-2001-56a-0347 | | | | Volume
| 56 | |
| 6 | Author
| B. H. Lavenda | Requires cookie* | | | Title
| Special Relativity via Modified Bessel Functions | | | | Abstract
| The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the 'k calculus' which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle's position are Gaussian and Poisson, respectively. | | | |
Reference
| Z. Naturforsch. 55a, 745—753 (2000); received May 11 2000 | | | |
Published
| 2000 | | | |
Keywords
| Special Relativity, Recursion Relations of Modified Bessel Functions, Lattice Jumps, Size and Mass of an Electron, Doppler Effect | | | |
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| default:Reihe_A/55/ZNA-2000-55a-0745.pdf | | | | Identifier
| ZNA-2000-55a-0745 | | | | Volume
| 55 | |
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