Koobee Wublee says...

On Mar 27, 9:01 am, Daryl McCullough wrote:
On Mar 26, Koobee Wublee wrote:

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?

[So] checkmate

You are deeply confused. You haven't pointed out any
disagreements.

It should be very clear at this stage the Doppler shift no matter how
you fudge it to be should agree with the energy transform as described
below.

You never derive any of your results, which makes them useless
for the purposes of discussion. You have made claims, without
deriving those claims, and every single claim has proved to be
false.

As I explained, there are two different questions:
(1) Given an electromagnetic wave described by attributes:
k_x, k_y, k_z, w
in one frame F, what are the attributes in the frame F' of
an observer moving at speed v in the x-direction relative to
F?

This is easily answered by realizing that phase is an invariant.
So

k_x x + k_y y + k_z z - w t
=
k_x gamma (x' + v t') + k_y y' + k_z z' - w gamma (t' + v/c^2 x')
= gamma (k_x - wv/c^2) x' + k_y y' + k_z z' - gamma (w - k_x v) t'

So it is clear that in frame F', the wave attributes are given by:
k_x' = gamma (k_x - wv/c^2)
k_y' = k_y
k_z' = k_z
w' = gamma (w - k_x v)

This is exactly the same as the transformation of the energy-momentum
four-vector:

p_x' = gamma (p_x - Ev/c^2)
p_y' = p_y
p_z' = p_z
E' = gamma (E - p_x v)

I don't know why you think that there is some kind of incompatibility.

This means SR predicts a blue Doppler shift in the transverse
direction, and that is totally wrong

According to what, or who?

The bottom line is that SR does not produce what is observed in
experiments.

The bottom line is that you have made many false claims and
that's another.

--
Daryl McCullough
Ithaca, NY