If E=mc2 and we know light exists, why is it that light doesn’t have …

If E=mc2 and we know light exists, why is it that light doesn’t have infinite mass and consequently why aren’t we all squashed? – M

The equation that you present is a simplification of the full relationship between energy, mass, momentum, and the speed of light, and is really only appropriate for stationary massive particles. In it, E is the particle’s energy, m is the particle’s rest mass, and c is the speed of light. Since light has no rest mass, the previous equation is simply not applicable to it. I should note that this equation is sometimes used to describe moving massive particles, in which case the m is allowed to increase to reflect the increasing energy of the moving particle. But the use of this equation for moving particles and the redefinition of mass as something other than rest mass often leads to confusion.

A better way to deal with moving particles, particularly massless particles, is to incorporate momentum into the problem. The full equation, correct for any particle, is E2=m2c4+p2c2. In this equation, E is energy, m is the rest mass of the particle (if any), p is the momentum of the particle (if any), and c is the speed of light. While light has no rest mass, it does have momentum and it’s this momentum that gives light an energy. Light travels along at the speed of light with a finite momentum and a finite energy. On the other hand, the momentum of a massive particle increases without limit as the particle approaches the speed of light and so does the particle’s energy. Thus massive particles can’t ever reach the speed of light.

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