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a student
#2
Jan28-09, 05:00 AM
P: n/a
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).