Energy conservation for a relativistic doppler shifted pulse

[Ham]

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
level are

Edwin F. Taylor and John Archibald Wheeler
"Spacetime Physics", 2nd Ed.
W. H. Freeman, 1992,
ISBN 0-7167-2326-3 (hardcover)
0-7167-2327-1 (paperback)

N. David Mermin
"Space and Time in Special Relativity"
McGraw-Hill, 1968
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)

Robert Geroch
"General Relativity from A to B"
University of Chicago Press, 1978,
ISBN 0-226-28863-3 (hardcover),
0-226-28864-1 (paperback)

-- jt]]

 

[a student]

On Jan 23, 4:28 am, Ham <nejatiha...@gmail.com> wrote:
> 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?

I'll have a go at this. The point is that the energy, the momentum,
and
other quantities of particles (eg, their speeds), can be different
from one
reference frame to the next. However, the laws of motion for these
quantities take the same form in every reference frame.

For example, energy is conserved in each reference frame for
collisions
between particles:
E1 + E2 = E1' + E2',
(where ' denotes a quantity after the collision),but the energy
values
E1, E2, etc actually depend on the frame of reference being used.
Similarly for momentum conservation.

This is not surprising, as it is the same in Newtonian mechanics. For
two Newtonian observers moving at different relative velocities, if a
particle is at rest relative to one observer, with zero kinetic
energy, then
it will be moving relative to the other observer, with non-zero
kinetic
energy.

The main differences between Newtonian (more properly Galilean)
relativity and special relativity, in the above respect, is that
energy
and momentum are somewhat differently defined in the two cases,
and that the transformations between reference frames mix space
and time (and hence momentum and energy components, and electric
and magnetic field components).

 

[SJGooch]

I believe the original responder has altogether misinterpreted the original questioner's question. Please allow me to restate the original question more succinctly:

If the predictions of special relativity are compared to those of a simple flat nonrelativistic light medium that is "stationary" in the observer’s frame (“classical theory”), SR’s physical predictions of what an observer sees are ALWAYS "redder" by the Lorentz factor.

Because E=hf, we may infer that any photon received by an observer which is in motion relative to the emitter is less energetic than was that same photon when it was emitted.

Imagine a closed system composed of a collection of dynamically moving objects which are emitting and absorbing radiation, such as a hot gas. Each time a photon is transmitted from one molecule to another, the aggregate energy of the system is reduced by the Lorentz factor as applied to the energy of that particular photon.

How can this be reconciled with the principle of conservation of energy?

Thank you.