Re: Energy conservation in moving frames

On Sun, 11 Mar 2006 robert.w.adams@xxxxxxxxxxx wrote:

I have a thought experiment that is puzzling to me.

Suppose there is a spacecraft headed towards earth. It has a laser on
board that emits a sequence of short pulses, aimed towards a receiver
on earth. These pulses have a duration T when measured by an on-board
clock, and a wavelength lambda. The repitition rate is fixed according
to the clock on the spacecraft.

Assume the spacecraft is accelerating twoards earth, so the pulses
received on earth are no longer evenly spaced in local earth time, and
the measured pulse duration T is also variable (and always shorter,
given that the spacecraft is accelerating). Also, the wavelength lambda
will be, in general, shorter.

Now assume that after some time, the laser stops emitting pulses, and
the total energy of the pulses (since the generator was turned on) is
measured both on the spacecraft and on earth. Will the answers be the
same? Does wavelength come into the energy calculation somehow, in a
way that compensates for the shorter pulse duration received on earth?

Don't bother making it more complicated by having a series of pulses, and acceleration. Just stick to a single pulse, from a spaceship moving at constant velocity towards the detector.

If the pulse is at a frequency f, as determined on board the spaceship, and consists of N photons, the spaceship-measured energy in Nhf, where h is Planck's constant.

For slow approach velocity v<<c, the detector-measured energy will be
Nh(f+df), where df = vf/c. This energy is different.

Note that the same thing will apply if a rock is thrown. A proper relativistic calculation for the Doppler shift of the pulse doesn't change the conclusion.

OK, so what does this mean? Firstly, while energy is conserved in an inertial reference frame, there is no required for energy to be the same as measured in different reference frames (something which has nothing to do with conservation of energy).

It also means that, as measured from the _accelerating_ frame of your shaceship, the energy of each already emitted pulse keeps getting less and less as the ship accelerates; this looks like a nice simple thought-demonstration that energy is _not_ conserved in accelerating reference frames. This would be the case under either Galilei transforms or Lorentz transforms.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.

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