Systematic approach to the relativistic Doppler effect based on a test theory

Numerous experiments have been carried out to validate the Lorentz transformation or to find possible violations of Lorentz invariance, based on test theories to test special relativity. The test theory of Mansouri and Sexl (MS) provides a general framework for the transformation of inertial frames, presuming a preferred system of reference. Based on the MS framework, this paper systematically approaches the relativistic Doppler effect such that its dependency on transformation coefficients and parameters can be investigated. The Doppler effect is formulated in a complex Euclidean space where time is represented with imaginary numbers. Two formulae of the Doppler effect, which have been derived in an arbitrary transformation within the MS framework, are presented: one between an inertial frame and the preferred one and the other between arbitrary inertial frames. It is shown from the former formulation that the Doppler effect is independent of the synchronization of clocks, which implies that the Doppler-shifted frequency in the absolute synchronization is the same as that in the standard synchronization. The latter formula can allow us to find Doppler shifts without information on the velocities of inertial frames relative to the preferred frame. Exploiting these theoretical results, we examine the transverse and the longitudinal Doppler effects in detail.

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Use of classical pertubation theories for the calculation of barycentric aberration and Doppler Effect

International Astronomical Union Colloquium ◽

10.1017/s0252921100074042 ◽

1978 ◽

Vol 48 ◽

pp. 127-129

Author(s):

P. Stumpff

Keyword(s):

Doppler Effect ◽

Inertial Frame ◽

Doppler Shifts ◽

The Earth ◽

Vlbi Observations ◽

Self Consistent ◽

The Mean ◽

Increasing Demand ◽

Stellar Aberration ◽

Total Velocity

Modern techniques have considerably improved the accuracy of radioastronomical measurements. Examples are the high resolution in frequency, time and position for spectroscopic, pulsar, and VLBI observations. There is an increasing demand for accurate reduction of such measurements to an inertial frame of reference, preferably the barycenter of the solar system and the mean equator and equinox of a standard epoch. Reductions of this kind include the computation of general precession, nutation, aberration and Doppler effect. For general precession and nutation, there are internationally accepted algorithms which can be programmed in form of self-consistent subroutines. Aberration and Doppler shifts are determined by the barycentric velocity of the Earth and by diurnal effects. Until now, as far as I know, a self-consistent algorithm of sufficient accuracy for computation of the barycentric velocity components of the Earth has not been available. The need for such an algorithm is indicated by the recommendations of Commission 4 (Ephemerides) of the IAU (1976), that “stellar aberration shall be computed from the total velocity of the Earth …”, and that “reductions to apparent places should be computed rigorously …”. In practice, this can be done by reading and interpolating ephemerides obtained from numerical integrations.

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Line-of-Sight Winds and Doppler Effect Smearing in ACE-FTS Solar Occultation Measurements

Atmosphere ◽

10.3390/atmos12060680 ◽

2021 ◽

Vol 12 (6) ◽

pp. 680

Author(s):

Chris D. Boone ◽

Johnathan Steffen ◽

Jeff Crouse ◽

Peter F. Bernath

Keyword(s):

Atmospheric Chemistry ◽

Doppler Effect ◽

Line Of Sight ◽

Measured Signal ◽

Mixing Ratio ◽

Model Calculations ◽

Doppler Shifts ◽

Solar Occultation ◽

Wide Range ◽

Wind Profiles

Line-of-sight wind profiles are derived from Doppler shifts in infrared solar occultation measurements from the Atmospheric Chemistry Experiment Fourier transform spectrometers (ACE-FTS), the primary instrument on SCISAT, a satellite-based mission for monitoring the Earth’s atmosphere. Comparisons suggest a possible eastward bias from 20 m/s to 30 m/s in ACE-FTS results above 80 km relative to some datasets but no persistent bias relative to other datasets. For instruments operating in a limb geometry, looking through a wide range of altitudes, smearing of the Doppler effect along the line of sight can impact the measured signal, particularly for saturated absorption lines. Implications of Doppler effect smearing are investigated for forward model calculations and volume mixing ratio retrievals. Effects are generally small enough to be safely ignored, except for molecules having a large overhang in their volume mixing ratio profile, such as carbon monoxide.

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Thermal waves emitted by moving sources and the Doppler effect

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2021.121098 ◽

2021 ◽

Vol 176 ◽

pp. 121098

Author(s):

Roberto Li Voti ◽

Mario Bertolotti

Keyword(s):

Doppler Effect ◽

Thermal Waves ◽

Moving Sources ◽

The Doppler Effect

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The Doppler effect is the same for both optics and acoustics

Optik ◽

10.1016/j.ijleo.2021.167565 ◽

2021 ◽

pp. 167565

Author(s):

Shukri Klinaku

Keyword(s):

Doppler Effect ◽

The Doppler Effect

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ON THE THEORY OF THE DOPPLER EFFECT IN A MOVING MEDIUM

Modern Physics Letters A ◽

10.1142/s0217732398000024 ◽

1998 ◽

Vol 13 (01) ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

BRUNO BERTOTTI

Keyword(s):

Solar Wind ◽

Doppler Effect ◽

Dispersive Medium ◽

Time Derivative ◽

Optical Path ◽

Moving Medium ◽

Perturbation Theorem ◽

Hamiltonian Theory ◽

The Doppler Effect ◽

Definition Of

The increase in the accuracy of Doppler measurements in space requires a rigorous definition of the observed quantity when the propagation occurs in a moving, and possibly dispersive medium, like the solar wind. This is usually done in two divergent ways: in the phase viewpoint it is the time derivative of the correction to the optical path; in the ray viewpoint the signal is obtained form the deflection produced in the ray. They can be reconciled by using the time derivative of the optical path in the Lagrangian sense, i.e. differentiating from ray to ray. To rigorously derive this result an understanding, through relativistic Hamiltonian theory, of the delicate interplay between rays and phase is required; a general perturbation theorem which generalizes the concept of the Doppler effect as a Lagrangian derivative is proved. Relativistic retardation corrections O(v) are obtained, well within the expected sensitivity of Doppler experiments near solar conjunction.

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