Energy conservation for a relativistic doppler shifted pulse
I am new to the field of relativity. I read the Lorentz transformation
between different system of coordinates. I have a question. Let's
suppose that we have a Doppler shifted pulse in frequency (time
dilation). This pulse has the same amplitude as the pulse seen by a
moving observer. That is strange for me while it contradict with
energy conservation. Even in an easier way E=hf. When the frequency is
changing the energy is changing so we have more energy as the one
generated!!!! I also looked into energy-momentum conservation but I
could not digest the point. Can anybody describe it to me please?
[[Mod. note -- From past discussions in this newsgroup, I think the
type of problems you're having may be too subtle to be fully resolved
in a newsgroup discussion. I strongly recommend that, in addition
to whatever you learn from this newsgroup, you also read some other
relativity books: Another book will often explain things just enough
differently from the one(s) you started with that things "click".
My personal favorites among relativity books at roughly the right
Edwin F. Taylor and John Archibald Wheeler
"Spacetime Physics", 2nd Ed.
W. H. Freeman, 1992,
ISBN 0-7167-2326-3 (hardcover)
N. David Mermin
"Space and Time in Special Relativity"
Waveland Press, 1989
ISBN 0-88133-420-0 (paperback)
and (even though it's nominally about general relativity, it also has
a lot of insights into special relativity)
"General Relativity from A to B"
University of Chicago Press, 1978,
ISBN 0-226-28863-3 (hardcover),