On Mar 28, 3:36 pm, PD wrote:
On Mar 28, 11:24 am, Koobee Wublee wrote:

OK, let’s do a recap. Are the following equations valid under the
Lorentz transform and SR?

** f’ / f = (1 + [v] * [c]) / sqrt(1 – v^2 / c^2)

Where

** [v] = Velocity vector between frames of f and f’
** [c] = Velocity vector of light
** [] * [] = dot product of two vectors

That equation is invalid, period.
You have a small problem with dimensions in that equation.
The fact that you derived an equation with dimensional problems should
tell you something about your derivation. If you believe that SR has
*also* produced equations with dimensional problems like this one,
perhaps you could point to some.

Good grief. The self-styled physicists have been calling (c = 1) for
almost 100 years, but nevertheless yes, it was a minor mistake of
yours truly in which it can be easily corrected if someone does not
half a brain. shrug The corrected equation is:

** f’ / f = (1 + [v] * [c] / c^2) / sqrt(1 – v^2 / c^2)

Where

** [v] = Velocity vector between frames of f and f’
** [c] = Velocity vector of light
** [] * [] = dot product of two vectors

Is the above equation valid under the Lorentz transform and SR?

If no, what do you think the correct equation for relativistic Doppler
shift is? shrug

If yes, WTF? The above equation simplifies into the following for
transverse Doppler shift. Please don’t bullshift this with
‘tangential Doppler shift’. shrug

Under the transverse case,

** f’ / f = 1 / sqrt(1 – v^2 / c^2)

Where

** [v] * [c] = 0

In that case, SR predicts a blue transverse Doppler shift, no?
shrug

This was checked mated several posts ago. In fact, this was
checkmated several years ago. It took this incidence to open up the
eyes of Einstein Dingleberries where they are caught using the time
transformation for transverse Doppler shift and the energy
transformation for longitudinal one. What an embarrassment, no?
MathemaGicians? shrug