 1  Author
 S. J. Prokhovnik  Requires cookie*   Title
 The General Solutions of the RobertsonWalker Nullgeodesic and their Implications    Abstract
 The RobertsonWalker metric gives mathematical expression to three widelyheld assumptions about the nature of the observable universe. It is shown that the nullgeodesic of this metric has littleknown solutions for the speed and distance of a lightsignal relative to its source. Some implications of these results are considered, the most interesting of these being that only in a universe whose 3space 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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 ZNA199348a0915    Volume
 48  
2  Author
 S. J. Prokhovnik, A. E. Paparodopoulos  Requires cookie*   Title
 Light Propagation in a CurvedSpace Friedmann Universe    Abstract
 It was shown [1] that, in a Friedmann universe considered as an expanding ensemble of fundamen tal particles and whose 3space is Euclidean, the propagation of light and its associated wavelength(s) partake in the expansion of the universe. In consequence, a lightsignal 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 RobertsonWalker 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 curvedspace 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/ZNA199449a0543.pdf    Identifier
 ZNA199449a0543    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 helium4   
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 ZNA199752a0561    Volume
 52  
5  Author
 B. H. Lavenda  Requires cookie*   Title
 Is Relativistic Quantum Mechanics Compatible with Special Relativity?    Abstract
 The transformation from a timedependent 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 nonnearest neighbors, whose solutions are the chirality components o f a freeparticle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the KleinGordon 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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 ZNA200156a0347    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, onedimensional 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 wellknown relativistic formula for the addition of velocities. In the nonrelativistic and ultrarelativistic 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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 55  
