How Can Photons Have Momentum If They Have No Mass?

[3dsmax]

Wikipedia says that photons have momentum. How can that be possible since p=mv?

 

[Creator]

Wikipedia says that photons have momentum. How can that be possible since p=mv?

The Poynting vector,S, gives momentum of light, and is given by:

S = E X B...E= electric field
B= magnetic field
X is cross product

However, this is the classical answer...and maybe this answer should be in classical section.

 

[George Jones]

Wikipedia says that photons have momentum. How can that be possible since p=mv?

According to relativity, the spatial momentum of a "particle" that has rest mass $m$ is

$$p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}.$$

To consider a photon, let $m \rightarrow 0$ and $v \rightarrow c.$ This gives zero over zero, which is indeterminant, and can be anything (including non-zero values), depending on how the limits are taken.

Also, relaltivity says that for any particle,

$$E^2 - (cp)^2 = \left(mc^2\right)^2.$$

Even if $m=0$, $p$ is non-zero when $E$ is non-zero. In fact,

$$E = cp$$

for a photon.

 

[3dsmax]

i wish that i was in a higher physics class so that i could understand you.

 

[pmb_phy]

Wikipedia says that photons have momentum. How can that be possible since p=mv?

The inertial mass M (aka relativistic mass) of a photon is defined just like the mass of all particles, as M/i] = p/v = p/c where p is the magnitude of the momentom and v is the particle's speed. I believe that you're thinking about a photon's proper mass m, which is zero for all photons.

The definition of the mass of a particle allows the following relation to be derived (let m = proper mass)

p = sqrt[1-(v/c)sup²]/c

This can be solved for m which in turn will be a function of the energy and momentum and when E = pc me will always turn out to be 0.

Pete