On Mar 24, 4:50 am, Daryl McCullough wrote:

Phi = kx - wt

To compute w' in a new coordinate
system, you rewrite x and t in terms
of x' and t':

x = gamma (x' + vt')
t = gamma (t' + v/c^2 x')

So in the frame F', we have:

Phi' = gamma k (x'+vt') - gamma w (t'+v/c^2 x')
= gamma (k-vw/c^2) x' - gamma (w-vk) t'

So
k' = gamma (k-vw/c^2)
w' = gamma (w-vk)

To get the nonrelativistic limit, you just
take the limit in which v/c is small, so
gamma is approximately 1, and v/c^2 is approximately
zero. This produces:

k' = k
w' = w-vk

In the Galilean case, there is no shift for *wave-length*
(k = 2pi/L, where L is the wavelength), but there is still
a shift for frequency (w is actually 2pi f, where f is
the frequency).

Yours truly was preparing to ruin a celebration, but the victory dance
never came. Why? So, here it is.

What is the transverse Doppler effect under relativity? According to
the energy transformation and also your derivation, it should predict
a blue shift while experiments time after time all have indicated
red. Oops! shrug

This disagreement of SR with experiments is serious and fatal, no?

checkmate