Derivation of the photon energy

[shaiyefet]

Hi everyone,

Anybody knows if the photon energy (frequency * Planck's constant) can be derived from more basic physical principles or this formula was "invented" to explain the photo-electric effect or black body radiation?

If you know a way to derive it, please share.

Thanks a lot !

 

[mfb]

Everything is fundamentally based on observations. Our theories are made based on those observations, and have to agree with them.
Special relativity would not work if energy would not be proportional to frequency. From the observation that physics, and in particular the speed of light, is the same for all observers, and quantization from quantum mechanics, you can derive E/f = constant. This constant is then called Planck constant.

 

[shaiyefet]

Thanks for your comment,
Do you know any specific textbook that shows how to derive E/f=const. ?
Thanks

 

[f95toli]

You can't really derive it, it was (and is) an experimental observation.

 

[mfb]

Well, you can derive it based on other assumptions (in particular, those of special relativity). Lorentz transformations require that both E and f scale in the same way. Otherwise you would not get the same invariant mass of systems of two photons or photon plus massive particle.

Special relativity is not based on quantized light, although both were introduced in the same year by the same person. Lorentz transformations are actually a bit older.