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1Author    B. H. LavendaRequires 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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 TEI-XML for    default:Reihe_A/55/ZNA-2000-55a-0745.pdf 
 Identifier    ZNA-2000-55a-0745 
 Volume    55