Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Ryen on 17/05/2008 18:31:53

Title: How do photons have momentum, but no mass?
Post by: Ryen on 17/05/2008 18:31:53

Ryen asked the Naked Scientists:

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?

Title: How do photons have momentum, but no mass?
Post by: lightarrow on 17/05/2008 20:28:27

Quote from: Ryen on 17/05/2008 18:31:53

Ryen asked the Naked Scientists:

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[2mE_k(1 + E_k/2mc²)]

where E_k = kinetic energy = E - mc²

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

p ≈ Sqrt(2mE_k) ≈ Sqrt(2m*mv²/2) = Sqrt(m²v²) = mv.

Title: How do photons have momentum, but no mass?
Post by: MacMac on 10/07/2008 05:39:03

Lightarrow might be interested in reading this paper: http://www.aias.us/documents/uft/a82ndpaper.pdf (http://www.aias.us/documents/uft/a82ndpaper.pdf)

Title: How do photons have momentum, but no mass?
Post by: Andrew K Fletcher on 10/07/2008 08:46:46

Quote from: MacMac on 10/07/2008 05:39:03

Lightarrow might be interested in reading this paper: http://www.aias.us/documents/uft/a82ndpaper.pdf (http://www.aias.us/documents/uft/a82ndpaper.pdf)

Interesting paper. Thanks for the link.