Doppler effect definition

I guess that this a good definition of the Doppler effect in SR scenarios (no gravity or acceleration), where the comparison yields the relative speed between emitter and observer. In GR, there can be gravitational redshift/blueshift on top of Doppler effects, which invalidates the above definition, IMO. In other words, the comparison of periods of the emitter and observer does not give the Doppler effect alone.

 

Well what do you mean by the period of emission?
Why not simply use frequency instead, seems less ambiguous to me.

 

I think one of the best descriptions for the relativistic Doppler effect is the one given by Einstein

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

A period corresponds to the difference between two clock-readings (i.e. a spacetime arc-length) along a worldline. IMHO, geometrically and operationally, the period is more natural.

 

True, you are correct.
On the other hand, if you look at the Einstein derivation , pulsation turns to be the better choice. As an aside, trying to explain the Ives Stilwell experiment in terms of period is rather tough, whereas the pulsation explanation falls out really nicely.

 

I suppose one can refer to Frequency (f), Wavelength (Lambda) or Period (T = 1/f) for Doppler measurements, but Doppler shift is normally expressed in terms of wavelength. Period, unless specifically defined, can be ambiguous though, as pointed out in previous posts. Your question: frequency counters normally count the number of cycles received per second, using the local clock.

 

It might be good to note that:

the k-calculus in Special Relativity starts by relating the period of emissions (a proper time along an inertial source) with the period of receptions (a proper time along an inertial receiver). The k-factor is later identified as the doppler factor, usually expressed in terms of the relative velocity between the source and receiver. From there, one then discusses frequency and wavelength, which are convenient for "practical" astronomical-type measurements via spectral lines etc.

in the standard Lorentz transformations, spacetime displacements are emphasized. A spacetime displacement along an inertial worldline involves its elapsed proper-time. Neither frequency nor wavelength are spacetime displacements. Of course, one can write the lorentz transformations in terms of the doppler-factor (since k and 1/k are eigenvalues of the Lorentz transformation) by using light-cone coordinates instead of rectangular ones.

It seems to me that proper-time is more primitive from a geometric perspective. Frequency and wavelength are secondary, derived concepts.