The Relativistic Doppler effect has been explained and derived from the invariance of the wave equation in the case of light (or from Lorentz Transformations). In relativity, it was described as a phenomenon involving two different inertial frames, a consequence of Lorentz invariance.
Other simple methods have been used to give account to the Doppler effect for waves in acoustics.
Acoustic waves in material media, on the other hand, are neither Galilean or Lorentz Invariant.
It was considered so far that the wave equation in EM interaction is the same for the moving source and moving observers.
The Longitudinal Doppler effect in Nature is a detection of a frequency shift of oscillations originated by a transfer of a net energy and momentum due to non stationary positions of Emitters and observers.
It is properly obtained by adopting the conservation of energy and momentum of waves and matter interacting.
The Doppler Radar unveils a potential issue if one considers inertial both RADAR and a mirror, unless placing some external pressure, to a mirror of finite mass, which exactly counterbalances, the radiation pressure.
Preprint CONSERVATION LAWS and the Doppler effect through the Doppler RADAR
It is very interesting also that, according to a very recent work by Hrvoje Dodig,
Article The Wave Equation for a Moving Source and a Moving Receiver
the wave equation for stationary observers and sources cannot have the same form as the one for moving sources or observers for example.
Such feature should be related also to the fact that ENERGY AND MOMENTUM variations are involved and they play a role which may not preserve the wave equation form
Other questions are related:
https://www.researchgate.net/post/Is_the_doppler_effect_of_light_an_actual_energy_shift_of_photons_or_it_is_only_a_relativistic_connection_of_different_reference_frames
https://www.researchgate.net/post/Compton_scattering_and_the_moving_mirror_scattering_give_different_results_till_which_approximation_they_can_match
Preprint CONSERVATION LAWS and the Doppler effect through the Doppler RADAR
I put the work of
Hrvoje Dodig
Article The Wave Equation for a Moving Source and a Moving Receiver
In the inertial frame of the RADAR, for a mirror of finite mass m, receiving photons at frequency f0 the equation of energy conservation is this one
(gamma0-gamma1)mc2= h(f1-f0)
the variation of speed of the mirror of mass m, implies that there is a difference of the gammas.
The Doppler Effect of EM waves is a variation of frequency detected of EM waves, hence If there is no variation of speed there is no Doppler effect.
No variation of speed hence kinetic energy -> no difference of gamma-> no frequency difference-> no Doppler effect
For any realistic scenario Doppler RADAR occurs only in the case there is a small variation of speed of the reflector after absorption and re-emission, unless infringing conservation laws.
That is why the inertial version of the mirror can be used just as approximation, as it is in the case of the infinite wall in classical mechanics.
since there is a Doppler, there is a frequency difference there is a difference of gamma hence there is a variation of speed.
DOPPLER EFFECT -> VARIATION OF SPEED OF THE DETECTOR OR VARIATION OF SPEED OF THE SOURCE (atom emitter)
DOPPLER RADAR --> VARIATION OF SPEED OF THE REFLECTOR
a kinetic energy variation of the masses (emitter or receiver) is at the base of the Doppler effect
It is not a question infact, it is a discussion on being or not being that the true nature of DE is energy momentum exchange between matter and radiation.
- Badges
- Science topic
- Similar topics
- Methodology
- Research Methodology
- Research Papers