On Monday, May 30, 2022 at 4:06:45 AM UTC-5, Lou wrote:
We are all familiar with the equations to quantify energy of EMR from a single wavelength or frequency. But I have been unable to find any
reference on how to calculate energy from a *range* of wavelengths or frequencies. In particular with reference to Doppler shifted emr For instance: Can one calculate what difference in energy , if any, an
emitted source of emr between 100-200nm would have if it was redshifted
to 200-400nm?
At first I thought the answer was obvious, but then I thought about it a little more and realized I needed to think about it more carefully.
It is easiest to think of this quantum mechanically, I think. The number of photons does not change, but their rate is reduced proportional to the frequency. This gives a factor of 1/2 to the rate of photons. In addition each photon is now half the frequency, so the energy per photon is also
reduced by 1/2. So the total power in the band 200-400nm would be 1/4
the power in the 100-200nm band prior to being red shifted.
Doing this calculation in classical EM would require transforming the EM
tensor F^{\mu\nu} via the Lorentz transform to get the correct EM field amplitudes, from which the energy density can be calculated. The QM
argument is much simpler.
Rich L.
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