Abstract
We were inspired by three great concepts: 1. Pythagorean means, 2. Pierre de Fermat´s principle of the least time, 3. Michael Faraday´s concept of vibrating rays in longitudinal and transverse directions. We have formulated an extended Doppler formula for rectilinear motions in the absolute spacetime where both postulates of the special relativity are valid. The second postulate of the special relativity for rectilinear motions was derived as the harmonic mean speed based on the Pythagoras-Fermat-Faraday (PF2) model. The null result of the Michelson-Morley experiment is valid for the arms of that interferometer separated by the angle π/2. However, for the angles smaller than π/2 a predicted fringe shift should be observed. For the circular motions the Doppler formula combines the longitudinal and transverse speeds in such a way that the frequency of the rotating light beam is diluted by a factor [1-(v/c)2]0.5 and the wavelength of that light beam is extended by the same factor. The Doppler formula for light beams can be tested for the rotating source and the detector placed close to the rim of that rotating disk in a defined position. In order to obtain new experimental data we propose to construct the Michelson-Morley-Harress-Sagnac interferometer where rotating disks have being attached to both arms of the Michelson interferometer. In rotating disks we might prepare light beams with defined independent values of their longitudinal speeds and after the mixing of these two light beams on their return path to the detector we might observe predicted fringe shifts. In these circular paths the second postulate of the special relativity is not valid. The full composition of Doppler formula is given by the interplay of the macro Doppler effect (the relative motion of the source and observer) and the micro Doppler effect (the combination of the longitudinal and transverse vibration speeds of that oscillating particle – the elasticity of the photon wave).
Highlights
The famous quote of Heraclitus “Nature loves to hide” was described in details by Hadot (2008)
1) The extended Doppler formula was derived as two contributions: the macro Doppler effect and the micro Doppler effect
2) The second postulate of the special relativity was derived as the harmonic mean speed of the longitudinally oscillating particle
Summary
The famous quote of Heraclitus “Nature loves to hide” was described in details by Hadot (2008). Faradays lecture “Thoughts on Ray Vibrations” presented in London on 3rd April 1846 influenced many researchers and stimulated the formation of valuable models This concept several time appeared and disappeared from the focus of researchers (e.g., for references see Bilbao et al, 2014). All these activities were stopped by the second postulate of the special relativity – vibrating rays models based on Galilean speed additions were experimentally falsified. We have described the second postulate of the special relativity as the harmonic mean speed of longitudinal vibrations of the oscilating particle for the rectilinear motions. The full composition of Doppler formula is given by the interplay of the macro Doppler effect (the relative motion of the source and observer) and the micro Doppler effect (the combination of the longitudinal and transverse vibration speeds of that oscillating particle – the elasticity of the photon wave)
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