摘要
The first proof (Sections 2 - 4), applies Doppler shifts to the Fourier time sine series. It shows if <i>K</i> = <i>f'/f</i> (frequency ratio of the shift, <i>f'</i> the shifted frequency), then the value of the series at time = t occurs in the shifted series at time = <i>t/K</i>. That is because in each harmonic the sin(<i>f't</i>) and cos(<i>f't</i>) became sin(<i>Kft</i>) and cos(<i>Kft</i>). The original series could be the number of photons in area of a beam with encoded information. Therefore the number of observed photons and information has the same resultant Doppler shift as frequency. Resultant is total effect of axial, transverse and gravitational shifts. Mass and energy of light do not have the same Doppler shift which may indicate missing parts that Doppler shift and that mass traveling at the speed of light is different from other mass and energy. The second proof (Section 5) the vector equations of space time require observed time to have 3 dimensions if the speed of light is constant in all directions, but the Doppler shift in each direction is not the same. The blue shift (compression) of time has paradoxes. If time has many dimensions, that would solve the paradoxes, but break conservation laws. No solution of that is given here. It is not expected that radical a solution will have any followers.
The first proof (Sections 2 - 4), applies Doppler shifts to the Fourier time sine series. It shows if <i>K</i> = <i>f'/f</i> (frequency ratio of the shift, <i>f'</i> the shifted frequency), then the value of the series at time = t occurs in the shifted series at time = <i>t/K</i>. That is because in each harmonic the sin(<i>f't</i>) and cos(<i>f't</i>) became sin(<i>Kft</i>) and cos(<i>Kft</i>). The original series could be the number of photons in area of a beam with encoded information. Therefore the number of observed photons and information has the same resultant Doppler shift as frequency. Resultant is total effect of axial, transverse and gravitational shifts. Mass and energy of light do not have the same Doppler shift which may indicate missing parts that Doppler shift and that mass traveling at the speed of light is different from other mass and energy. The second proof (Section 5) the vector equations of space time require observed time to have 3 dimensions if the speed of light is constant in all directions, but the Doppler shift in each direction is not the same. The blue shift (compression) of time has paradoxes. If time has many dimensions, that would solve the paradoxes, but break conservation laws. No solution of that is given here. It is not expected that radical a solution will have any followers.
