How do we know light has no mass?

Question

Our understanding of the speed of light and many other things is predicated on the fact that light has no mass. As we can’t weight it directly like on a scale I am wondering (outside of mathematics) how we can test and prove this theory? Is it possible that light does have mass, it is just very very very small?

Further, if light has no mass, does it also have no energy? e=mc2 means energy for something massless would be 0. We know light has energy, so how does this equation work?

In: 42

Answer 1

If light had mass a whole bunch of our physics wouldn’t work. You are looking at it a bit the wrong way around; it isn’t that so many things are predicated on light having no mass, but that all those things are evidence that light has no mass.

> Further, if light has no mass, does it also have no energy? e=mc2 means energy for something massless would be 0.

*E = mc^(2)* in its simplest form comes from Special Relativity, which doesn’t apply to massless things. The slightly more general version of this is a bit more complicated:

> E^2 = (pc)^2 + (mc^(2))^2

where *p* is the object’s momentum. Mass is just one expression of energy, momentum is another way energy can be expressed. So a normal object has some energy from just existing (it’s “mass” energy), and some from moving (its “momentum” energy).

If something is “at rest”, with no momentum, that equation simplifies down to the normal *E = mc^(2)* that we all know.

Photons, or light, can never be at rest, so we can never simplify it down that way. For a massless object we get:

> E = pc

which is perfectly fine. If the photon is moving it will have momentum, so will have energy.

This has some fun results. If we take the photon energy of *E = hf* and plug that in, with a bit of algebra we get:

> p = h / λ

where λ is the wavelength of our light, and h is Plank’s constant. This encouraged de Broglie to wonder if anything with momentum also had a corresponding wavelength, and that led him down the path of thinking about matter waves, and wave-particle duality; that all things we think of as “particles” have a wavelength based on their momentum, and behave in wave-like ways sometimes, just as how wave-like things (like light) behave in particle-like ways sometimes.