# Q & A: Heavy Light

Q:
Does light have mass? I’ve been told it has momentum.
- Jim Eyrich
Hoopeston, IL, USA
A:
Jim,

Light does not have mass, although as you point out it does have momentum. At first this might seem contradictory since you may be used to the classical physics relation P=MV, which says that an objects momentum is the product of its mass and its velocity. If light has no mass, how can it have momentum?

The answer is that P=MV is not true for things that are moving extremely fast, where "fast" means close to or at the speed of light. Is such cases we have to use Special Relativity (invented by Albert Einstein), to describe the behavior of things. One of the statements of special relativity is that an objects energy E, it's momentum P and it's mass M are related by:

E^2 = (PC)^2 + (MC^2)^2

Where ^2 means "squared" and C is the speed of light.

In this case, if the mass M is zero, we get

P = E/C

Which says that the momentum is just the energy divided by C. We know light carries energy (the sun warms us) so we see that according to Special Relativity light should also have momentum.

(published on 10/22/2007)