Q&A: How Does a Photon Have Momentum w/o Mass?

[Ed Aboud]

Sorry if this is a ridiculous queation, but how does a photon have momentum if it hass no mass?

 

[Crosson]

They do it with energy! The equation for energy in relativity is:

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

Where m is the mass, p is the momentum, and c is the speed of light. Put in $m = 0$ and you get E = p c, so any massless particle with energy E will have momentum p = E/c.

 

[dst]

From the relativistic mass equation - e^2 = (pc)^2 + (mc^2)^2. Since it has no rest mass, the latter term disappears but we still have e^2 = p^2 * c^2.

 

[Ed Aboud]

Ah I see, thanks very much!

 

[glueball8]

what is the relationship between P and E?

 

[Usaf Moji]

They do it with energy! The equation for energy in relativity is:

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

Where m is the mass, p is the momentum, and c is the speed of light. Put in $m = 0$ and you get E = p c, so any massless particle with energy E will have momentum p = E/c.

Another way of getting the same result is to use the more popular form

$$E = mc^2$$

and solve for m (which can be regarded as the "relativistic mass"). Then just multiply by the velocity, which is c, and treat it like any other problem. You'll see that you get the same result, p = E/c.

 

[malawi_glenn]

what is the relationship between P and E?

See post #2, if you mean P is the momentum?

 

[lightarrow]

Another way of getting the same result is to use the more popular form

$$E = mc^2$$

and solve for m (which can be regarded as the "relativistic mass"). Then just multiply by the velocity, which is c, and treat it like any other problem. You'll see that you get the same result, p = E/c.

...just by chance because the derivation is wrong. Photons are massless. The correct derivation is the one already written in post 2.