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Is Planck's Law Inconsistent With Equations Of Momentum


JulianM

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Given that E = m.c^2

and that E = h.f

 

why can't we form a relationship for particles of light?

Shustaire is quite right of course. The energy momentum equation is the more general form, of which the famous E=mc² is a simplified special case. The more general form is able to account for entities such as photons that have zero rest mass but which nonetheless have energy and momentum. In fact the connection between it and E=hf is made via de Broglie's relation:

 

For a photon, the energy momentum relation reduces to E=pc. But de Broglie's relation tells us p=h/λ, so since  c=fλ, we can rewrite that as p=hf/c.  So we have E= (hf/c).c, i.e. E=hf.

 

Bingo!  And a rather nice connection between the two great discoveries in early c.20th physics: relativity and quantum theory. :)

Edited by exchemist
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