P=mv so if photons have no mass, then shouldn't they have 0 momentum?
This is one that’s stumped me for a long time, and now finally I think I’ve found the answer. It’s to do with Einstein’s E=mc².
Rest masses
The concept of rest masses was first proposed by Einstein in his Special Relativity. A rest mass is the mass of an object when it isn’t moving at all, it has no velocity. Special relativity says that when an object is moving it’s mass increases.
So technically speaking you’re heavier when you’re walking around than when you’re stood still, but the effect is TINY.
Because the photon is constantly moving at the speed of light, technically it has mass, even though it’s rest mass is 0. And a photon never slows down so technically it always has mass. But it also technically doesn’t.
??? Please explain what this has to do with E=mc² ???
Well a photon’s energy can be calculated by the following formula:
E=hf
Energy = Planck's constant x Frequency
This formula means that all photons have energy, and that it’s proportional to it’s frequency. If we know that photons have energy then we can use this in the formula E=mc².
Einstein’s special relativity says that if something has energy, it also has mass
What does E=mc² even mean?
When Einstein published his paper on Special Relativity, he actually wrote the formula as m=E/c² and not E=mc² as we usually see it today. Why? His point with the formula E=mc² wasn’t that mass can be converted into energy, it was that mass IS a form of energy.