How can light carry energy via momentum, but have no mass??
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For particles traveling close to (or at) the speed of light, momentum isn’t directly related to (rest) mass. The usual equation p = mv does not apply at high speeds, and you need the full relativistic equation E^2 = (mc^(2))^2 + (pc)^(2) (where E is energy, m is rest mass, p is momentum, and c is the speed of light). At low speeds, and for non-zero masses, this reduces to the usual p = mv as a very very close approximation, but like most formulas in classical physics it’s just an approximation to the true relativistic formula.
Put another way, light *does* have mass(-energy). It just doesn’t have *rest* mass. But since a photon is never *at* rest, it isn’t massless in the sense that you wouldn’t feel it if it bumped into you.
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