How can light have momentum if it has zero mass?

bcrowell

How can light have momentum if it has zero mass?

The relativistic expression for the momentum of a massive particle is p=mγv. It's possible to get confused if one tries to apply this to a particle with zero mass, since it seems as though the result would have to be zero, and yet we know based on Maxwell's equations that light has momentum. (For example, let a light wave strike an ohmic surface perpendicularly. The electric field excites oscillating currents, and the magnetic field makes a force on these currents that is shown by the right-hand rule to be in the direction of propagation.)

The resolution of the apparent contradiction is that massless particles always travel at c, and γ approaches infinity as v approaches c. That means that mγv can't be evaluated simply by plugging in values for the variables. One could instead use calculus to take the appropriate limit. An easier approach is to use the relation m²=E²-p² (in units with c=1), which relates a particle's mass, total mass-energy, and momentum. This equation is valid for both zero and nonzero values of m. The result for m=0 is p=E (or, in units with c≠1, p=E/c), which agrees with Maxwell's equations.

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