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mathfeel

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Suppose there is some EM wave in the vacuum with frequency and field strength [tex]\omega,E[/tex]

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?

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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