How Momentum is Transferred via Massless Photons

[MetaJoe]

Hi, this is my first post, and I'm sure this is a very basic question: Suppose two electrons collide, and thus momentum is conserved. Momentum, as we all know, is defined as the product of mass and velocity. But the means of transferring momentum between these electrons is a photon, which is massless. So, it seems there must be some point at which momentum is being transferred, but at which the magnitude of the momentum is zero, and thus is not conserved. So, I'm confused: just how is momentum transferred via massless photons while also being conserved? Thank you very much!

Joe

 

[Doc Al]

Momentum, as we all know, is defined as the product of mass and velocity.

That's true for massive particles moving at nonrelativistic speeds. It's not true for massless particles like photons. Even though massless, photons carry energy and momentum.

 

[MetaJoe]

Thanks for the response. So, how is momentum, when it's carried by a photon, defined?

 

[Doc Al]

Thanks for the response. So, how is momentum, when it's carried by a photon, defined?

Relativity tells that for any particle, energy (E), mass (m), and momentum (p) are related by this:
$$E^2 = p^2c^2 + m^2 c^4$$

For photons, m = 0, so:
$$p = E/c = hf/c$$

 

[Hootenanny]

Thanks for the response. So, how is momentum, when it's carried by a photon, defined?

Momentum of a photon is defined as

$$P = \frac{h}{\lambda}$$

Where P is momentum, h is plank's constant and $\lambda$ is the wavelength of the photon.

Edit: Doc Al beat me to it

 

[MetaJoe]

Excellent. Thank you very much!