# Mass and Traveling at the Speed of Light

Lymitra
I have read somewhere that you need to have zero mass to be able to travel at the speed of light; is this true? Also, light is a wave, waves contain energy, and energy and mass are interchangeable according to E=mc^2, so wouldn't light have mass and thus contradict the first statement?

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Parlyne
Energy and mass are not interchangeable. Mass is one form of energy. However, in switching back and forward between mass and other forms of energy, you also must conserve momentum. It is for this reason that you can't just consider energy in any form to be the same as mass.

Light carries both energy and momentum. And, with some work, you can show (starting from Maxwell's equations) that the momentum carried by light is related to its energy by $E = |\vec{p}| c$.

For a particle with mass, the relationship is more complicated, since the particle's mass also contributes to its total energy: $E^2 = |\vec{p}|^2 c^2 + m^2 c^4$.