/sci/ - Science & Math

>>15033720
>This is because he is considering the difference in between the moving object at two times (marked S and S').
Considering that a wavelength is the distance between two wave crests, you need to consider at least two moments of time, separated by at least one period.
Nathan assumed for simplicity (later in the paper he considers the general case) that the end point would line up with the receiver forming a right triangle.
You do this yourself later, when considering your isosceles triangle.

Making t infinitesimal, and thus vt infinitesimal, does not change this fact.

You are right that if the period of emission aligns such that it begins at angle θ and ends at angle π-θ between receiver and source, forming an isosceles triangle, then the wavelength will stay the same (but a distortion of the waveform would still be observed, still dependent on β), but such a fortuitous case is not the subject of the Ives-Stilwell experiment, which tests the case I showed above, namely for a factor of the order of β^2 when θ = 90° that is thought not to be there classically, but actually it is very much present.

I'm the guy who is not Nathan, by the way.