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Unformatted text preview: from which it is easy to show that Similarly, we can show that These are the Lorentz transformations for energy and momentum of a particleit is easy to check that . Photon Energies in Different Frames For a zero rest mass particle, such as a photon, E = cp , E 2 c 2 p 2 = 0 in all frames. Thus . Since E = cp , E = cp we also have . Notice that the ratios of photon energies in the two frames coincides with the ratio of photon frequencies found in the Doppler shift. As we shall see when we cover quantum mechanics, the photon energy is proportional to the frequency, so these two must of course transform in identical fashion. But its interesting to see it come about this way. Needless to say, relativity gives us no clue on what the constant of proportionality (Plancks constant) is: it must be measured experimentally. But the same constant plays a role in all quantum phenomena, not just those concerned with photons....
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