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If photons have no mass, how do they have momentum?

@megzican asked the Naked Scientists: If photons have no mass, how do they have momentum?

... then I may consider moving it to 'new theories'.

...Use Euclid's postulates and from there explain as simple as you can where, and how, you see photons getting a mass through the new geometry. You may have a point, but I have difficulties following how the change redefines a photon?

"If photons have no mass, how do they have momentum?"Agreed (I think) the key equation is p = h / λ h is plank's constant, λ is wavelength of the light.So, the shorter the wavelength the more the momentum. The "envelope" of the photon has the same spatial distribution regardless of wavelength. That means there are more waves in a short wavelength photon than a long one. Each wave gives a little electromagnetic push to a charge and imparts some momentum. That is one way of understanding this relation.

Objects with mass are actually the more complex case, as their interaction can still be considered to be via virtual force carriers

like (and usually) photons, but generated by a "reservoir" from the velocity of the mass in some way. I'd like to understand properly how that's supposed to work. What's going on that's different between a massive object and a large collection of photons when each imparts its momentum? I hope that question makes sense.