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How can a photon have no mass and still travel at the speed of light?

First of all I am not a professional physicist. I was curious as to how a particle of light can reach the maximum speed of light c given that particles experience an increase in mass as they approach c ?

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A photon does not "reach" light speed, it is "born" with that velocity. And because the photon has no rest mass, there is no problem inherent.

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