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How can light have momentum?

So, I have been watching a lot of videos on physics, and a few of them have eluded to the fact that light has momentum. For instance, minutephysics video "E=MC2" is incomplete states that the full equation to describe objects with momentum and mass is E^2= (mc^2)^2 + (pc)^2 and he also says "The energy of a massless particle is the same as it's momentum". What I don't understand is this: The equation for an objects momentum is P=(mv)/(sqrt(1-(v^2/c^2))) which is basically just p=mv but because of gamma you have to do that annoying thing in the denominator. But EITHER WAY when mass=0, momentum equals zero. And light is massless. So... I'm confused. Please help.
Thanks!

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Robert S. | Robert Math PhysicsRobert Math Physics
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for light E=pc       
 
where E is the energy of the photon (light)
p is the momentum and c is the speed of light
 
since light waves have a wavelength or frequency associated with it
using planks equation E= hf f is the frequency and h is planks constant
the momentum in terms of frequency is p = hf/c
using c = lf where l is the wavelength then p = h/l
 
a photon can strike and move an electron using the momentum above
 
 
Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (143 lesson ratings) (143)
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George,
 
        Volumes have been written about this. The modern concept of light was started by Plank and Einstein. The photoelectric effect gave experimentally that the energy of a photon is a function of it's frequency only. The zero mass was an hypothesis initially but has been verified experimentally to a high precision. Quantum mechanics is full of non-intuitive results when viewed from the perspective of classical mechanics. Relativity is an extension of classical mechanics when velocities are near the speed of light. 
       If you want to get a really good introduction get a copy of Richard Feynman's book "QED" Quantum Electro Dynamics.
 
Hope this helps a little
Jim