# The Naked Scientists Forum

### Author Topic: How do photons have momentum, but no mass?  (Read 7336 times)

#### Ryen

• Guest
##### How do photons have momentum, but no mass?
« on: 17/05/2008 18:31:53 »

We were debating at work if over time the weight of the Earth increases due to photon bombardment from the Sun.  Then we found that apparently photons have no mass, yet they have momentum.  Could you please explain how this is possible?

What do you think?

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How do photons have momentum, but no mass?
« Reply #1 on: 17/05/2008 20:28:27 »

We were debating at work if over time the weight of the Earth increases due to photon bombardment from the Sun.  Then we found that apparently photons have no mass, yet they have momentum.  Could you please explain how this is possible?

What do you think?

At school you learn that momentum p is equal to mass multiplied velocity, but that formula is not correct, it's only approximately correct, for objects with mass, at low speeds, and it's wrong for objects without mass.
The correct equation is:

p = Sqrt[(E/c)2 - (mc)2]

E = total energy; m = mass

In that equation, valid at any speed and for massive or massless objects, put m = 0 (the case of photons) and you will find p = E/c; so photons do have momentum even if they are massless.

From an empirical point of view, switch on a very powerful laser in a certain direction, and you'll be able to measure a recoil in the opposite direction; this is the experimental prove that light has momentum.

If you want to find the approximated formula p = mv at low speeds for massive objects, write the above equation in this way (after some computations):

p = Sqrt[2mEk(1 + Ek/2mc2)]

where Ek = kinetic energy = E - mc2

At low speeds, Ek << mc2 so you can neglect Ek/2mc2 obtaining:

p ≈ Sqrt(2mEk) ≈ Sqrt(2m*mv2/2) = Sqrt(m2v2) = mv.
« Last Edit: 17/05/2008 20:42:07 by lightarrow »

#### MacMac

• Jr. Member
• Posts: 11
##### How do photons have momentum, but no mass?
« Reply #2 on: 10/07/2008 05:39:03 »

#### Andrew K Fletcher

• Neilep Level Member
• Posts: 2331
• KIS Keep It Simple
##### How do photons have momentum, but no mass?
« Reply #3 on: 10/07/2008 08:46:46 »
Lightarrow might be interested in reading this paper: http://www.aias.us/documents/uft/a82ndpaper.pdf

Interesting paper. Thanks for the link.

#### The Naked Scientists Forum

##### How do photons have momentum, but no mass?
« Reply #3 on: 10/07/2008 08:46:46 »