Thread: Help on the photon

I am very sure this has been and will be discussed time and again but i hope you have enough patience to please answer this one more time.

If the photon is masless, how can it possess momentum and energy ? The 2 things just seem to go together. When they say massless they do mean mass = 0 right ? Then p = mv, therefore if m=0 then p=0

And when AH COmpton derived the formulas to calculate momentum of a photon, he used the equation E=mc^2 right ? So therefore, the photon must have a mass, because m = E/C^2 which can never = 0 but it will be a really really small number like ##x10^-36.

And if the photon does have a mass no matter how miniscule, then when it travels at c its mass will become infinite according to special relativity.

I am a really confused high school physics student, please help me out, dont let me rot in the darkness.

thank you

The momentum of a photon equals it's energy over the speed of light. The p=mv formula that you learn in highschool only works for finding the momentum of objects with mass. The energy of a photon equals Plank's constant times the wavelength.

Note that nowhere in the equations from the energy or momentum of a photon is mass used. Photons have no mass, but do have energy and momentum.

Another way to look at it that might help is in the following equation:

E^2 = (m c^2) + (p c)^2

For a particle with mass you can have p=0 and then E = m c^2, so a particle with mass is at rest in some inertial frame, where the energy is just the mass energy.

But for a particle with no mass m=0 the formula becomes just E = p c, so if a massless particle has energy it must have momentum. This means that we are forced to conclude that a massless particle cannot be at rest in any inertial frame.

Looking at the velocity addition formula in relativity, we find that this means that a particle with mass can never travel at the speed of light and a massless particle always moves at the speed of light.
v = (v0 + vf)/(1 + v0 vf /c^2)
This says that if the velocity of a particle is v0 then in an inertial frame moving at velocity vf with respect to it (in the same direction as v0), its velocity will be v.

So if there is an inertial frame in which the velocity of a particle is zero (v0 = 0) then in all inertial frames (vf<c) the velocity of that particle, v is less than c. (An inertial frame cannot have vf = c).

For any v0 less than c you can find an inertial frame (vf = -v0) in which the velocity v is 0. So if there is no inertial frame in which the velocity is zero as is the case with massless particles then the velocity must be c, for if v0 = c then in all inertial frames (vf<c) the formula gives v = c. (Notice that if you try putting vf = -c, you get v = (c - c) / (1 - 1), which is undefined).