Mass and Traveling at the Speed of Light

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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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: $E^2 = |\vec{p}|^2 c^2 + m^2 c^4$.

Nabeshin
A problem here is that the word mass as is commonly used in speech actually has two meanings. A photon is said to have no rest mass; that is, if a photon were stopped its mass would be equal to zero. But it does have mass due to relativity. Particles with nonzero rest mass cannot accelerate to the speed of light. Also, it seems to me that with no rest mass the particle has no choice but to move at the speed of light.

tiny-tim