Do Waves have mass?

Question

Do any form of electromagnetic waves like visible light have mass? It is known that all electromagnetic waves have energy. According to Einstein's

$$ E^2=p^2c^2 + m^2c^4 $$

formula, the energy of a particle like photon, which shows wave properties as well, is derived from its mass and momentum. Some suggest that photons are indeed mass-less and that photons have energy due to there momentum, but momentum itself is equal to mass times velocity, $p=mv$.Then how can a body have momentum and not mass? The experiment on photoelectric effect by Einstein clearly proves Planck's theory of energy packets(photons) as correct, thus providing concrete evidence for the wave-particle duality of photons. Could anyone provide an explanation that is understandable to interested high-school students? Thank you:)

Waves do not have mass, but they do have relativistic mass. This link answers a similar question to yours http://physics.stackexchange.com/questions/2229/if-photons-have-no-mass-how-can-they-have-momentum — Sheepman, Apr 25 '15 at 05:35
Hi Sagnik. Your question has already been answered. See If photons have no mass, how can they have momentum?. — John Rennie, Apr 25 '15 at 06:23
I've just spent half an hour formulating an easy-reading answer to this question, only to find it's been closed, and that I can't post my answer, which I have nevertheless saved. — John Duffield, Apr 25 '15 at 09:52

score 0 · Answer 1 · answered Apr 25 '15 at 07:54

You want a high school level answer. I will try.

There are fundamental definitions established at the creation of the universe. Physicists have deduced many of these fundamental quantities, which define relationships between things like matter, energy and even time. One fundamental definition is the invariant speed of light, and the fact that by definition mass can't travel at the speed of light. However, observed effects of light require more. Light demonstrates the properties of a particle; it can't just be a 'wave'. Hence the photon, which carries specific packets (quanta) of energy and reacts like a particle. Another requirement of known physics is that photons have zero rest mass; they only exist at the speed of light. Photons are very special 'particles'. Photons are better thought of as a description defined by observation and theory. Formulas such as those you quote are simplified for use. For a full understanding, if that is even possible yet, you must move into quantum physics, which even Dr. Richard Feynman admits is rather weird. It's certainly a bit beyond high school, though you may want to refer students to Feynman's lecture series available on YouTube.

This doesn't seem to address the question of how massless photons can have a non-zero momentum. — John Rennie, Apr 25 '15 at 08:19

Do Waves have mass?

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