Suppose there is some EM wave in the vacuum with frequency and field strength [tex]\omega,E[/tex](adsbygoogle = window.adsbygoogle || []).push({});

In the frame of someone moving along with the light, the frequency and field become:

[tex]\omega^{\prime} = \alpha \omega\,, E^{\prime} = \alpha E\,,

\alpha = \sqrt{\frac{1-\beta}{1+\beta}}[/tex]

Suppose both observers want to estimate the photon number. They do:

[tex]n \propto E^2/\hbar \omega[/tex]

in their respective frame and will come up with a number that differ by a factor [tex]\alpha[/tex]

So photon number is not a Lorentz scalar or function of one? That's not a big deal. But usually there'd be other related quantity (like time and space is related) that is transforms with n. What it is?

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# Estimating/counting photons in two frames

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