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 shi...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.展开更多
In writings on relativity time, the various relations are only changed by the transverse shift. This paper proves that the axial Doppler shift does that as well and gives some impacts of that on common differential re...In writings on relativity time, the various relations are only changed by the transverse shift. This paper proves that the axial Doppler shift does that as well and gives some impacts of that on common differential relations in physics. When a modulated signal lasting a time = T is subjected to an optical Doppler shift K (either axial or transverse or both), where K is shifted frequency/original frequency, the Doppler shifted signal will last T/K. This because all shifted harmonics of its Fourier series (with a fundamental period of T) will last 1/K times the period of the original harmonic. The reader can graph any Fourier series and then graph its shifted series. The reader will see the shifted period is T/K. The Fourier series of the original repeats when time is greater than T and the shifted one when time is greater than T/K, which means the original series only represents the signal from time = 0 to T and the shifted series represents the shifted signal from time = 0 to T/K. Hence, the shifted one has all of the information in T/K as the original has in T. Therefore everything in the series including information is T/K long in the shifted series. Therefore, both the axial and the transverse Doppler shift change time periods in a vacuum, independent of material involved. That has not been obvious for over 100 years the axial shift changes time from the definition of frequency = 1/time.展开更多
Reasons are given for a Doppler shift on the number of observed (sensed) photons in a light beam not just a shift in frequency, also a similar (non-relativistic) effect on the number of observed (sensed) particles (wi...Reasons are given for a Doppler shift on the number of observed (sensed) photons in a light beam not just a shift in frequency, also a similar (non-relativistic) effect on the number of observed (sensed) particles (with non-zero rest mass) in a particle beam. Optics texts have neither effect.展开更多
文摘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.
文摘In writings on relativity time, the various relations are only changed by the transverse shift. This paper proves that the axial Doppler shift does that as well and gives some impacts of that on common differential relations in physics. When a modulated signal lasting a time = T is subjected to an optical Doppler shift K (either axial or transverse or both), where K is shifted frequency/original frequency, the Doppler shifted signal will last T/K. This because all shifted harmonics of its Fourier series (with a fundamental period of T) will last 1/K times the period of the original harmonic. The reader can graph any Fourier series and then graph its shifted series. The reader will see the shifted period is T/K. The Fourier series of the original repeats when time is greater than T and the shifted one when time is greater than T/K, which means the original series only represents the signal from time = 0 to T and the shifted series represents the shifted signal from time = 0 to T/K. Hence, the shifted one has all of the information in T/K as the original has in T. Therefore everything in the series including information is T/K long in the shifted series. Therefore, both the axial and the transverse Doppler shift change time periods in a vacuum, independent of material involved. That has not been obvious for over 100 years the axial shift changes time from the definition of frequency = 1/time.
文摘Reasons are given for a Doppler shift on the number of observed (sensed) photons in a light beam not just a shift in frequency, also a similar (non-relativistic) effect on the number of observed (sensed) particles (with non-zero rest mass) in a particle beam. Optics texts have neither effect.
