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Allen D. Allen
local time: 2023-09-21 07:57 ( )
Allen D. Allen (Abstracts)
Titles Abstracts Details
  • Time Dilation and the Spatial Interval for which dx/dt is Speed (1988) [Updated 6 years ago]

    The principle of relativity requires that the speed v<A, B> of A with respect to B be the same as the speed v<A, B> of B with respect to A for all ordered pairs <A, B>. It also requires that the interval Deltax used to calculate dx/dt = v<A, B> be defined for a particular experiment by resting endpoints. The rest frame of the endpoints is preferred for the experiment in that only the Lorentz contraction of Deltax applies to dx/dt = v<A, B> = v<B, A>. Consequently, relativistic time dilation is asymmetrical, the clocks in the frame of Deltax running faster than the clocks in a moving frame for all observers. This is analogous to the way in which the zero-momentum frame must be used to predict the outcome of dynamic particle experiments. In general, the principle of relativity does not say that for a given experiment E there is no preferred frame R(E). Rather, it states that there is no one preferred frame R for all E; that is, no absolute frame.

  • Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy (1988) [Updated 6 years ago]

    By direct substitution from E = mc2 and lambda = h(mv)−1, energy becomes E = hc2(lambdav)−1. This reduces to Planck's equation if, and only if, v = c. It follows from Snell's law that a photon undergoing refraction will gain energy sigmaE = hc2[(lambdav)−1 − (lambda0C)−1], where lambda0 is its wavelength in vacuo. This very small energy gain arises from work done on the photon's mass by the refracting medium in decelerating the photon from c to v. The medium therefore looses internal energy while the photon is passing through, regaining it when the photon leaves to resume speed c. Photon momentum is a linear, monotone-increasing function of speed, p = hc(lambda0v)−1. The reason photons do not have rest mass is because they cannot rest in space (v = 0) for the same reason massive particles cannot rest in time (v = c): In either case the energy would be infinite. EPR-type paradoxes can be resolved by replacing the notion of self-interference with recognition of the fact that lambdax is the extent of the x-axis that is instantaneously occupied by a particle.