I don't get this... how can light have momentum?

December 13, 2010 2:54 PM

How can light have momentum?

From this article, it seems that photons are imparting momentum, but since momentum is is expressed as mv, and m for a photon is zero, how does this work?

Problem Einstein?

posted by dougrayrankin to Science & Nature (9 answers total)

p=mv is the Newtonian equation for momentum. This is a special case for Einstein's special relativity.

Einstein's equaion is E^2 = (mc^2)^2 + (pc)^2, where:
E = energy or particle
m = mass
p = momentum
c = speed of light.

You'll see that in the case of photons, m=0, and momentum is non zero and completely dependent on the energy. Energy is proportional to frequency of light, so higher frequency light has more momentum. Blue light hist you harder than red light!

(The other special case in the above equation is for a particle with mass, at rest. So when p=0, E=mc^2 )

The concept of light having momentum has been verified by experiments, and has lots of potential uses, such as in spaceflight.

Lesson: Don't try to troll Einstein.
posted by auto-correct at 3:01 PM on December 13, 2010 [3 favorites]

Somebody has asked this question before on the Internets, and it looks like a couple decent answers were provided: http://www.newton.dep.anl.gov/askasci/phy00/phy00332.htm
posted by Perplexity at 3:01 PM on December 13, 2010

Pertinent typo above: E = energy of particle
posted by auto-correct at 3:03 PM on December 13, 2010

Response by poster: So it's akin to the photoelectric effect in so much as although they don't have momentum in the sense that a traditional Newtonian projectile might, there's the getting round it because the energy of the photon is imparted?
posted by dougrayrankin at 3:04 PM on December 13, 2010

Kind of. The momentum of the photon is totally "real". When a photon hits you, it passes momentum to you in the exact same was a massive particle of the same momentum would. It's just that the definition of "momentum" is a lot broader than the simple Newtonian case.
posted by auto-correct at 3:08 PM on December 13, 2010

Yeah this Wikipedia article on the Lorentz factor might be helpful. As you can see from that, the relativistic formulation for momentum which is p = gamma*m*v reduces to the Newtonian formulation for low v (and thus gamma ~ 1). When v ~ c gamma is huge ("infinity" when v = c) and thus p turns out to be a finite quantity despite m = 0.
posted by peacheater at 3:15 PM on December 13, 2010

this was answered at Ask A Physicist recently - How can photons have energy and momentum, but no mass?

short form (as others have said) is that P=mv only when v << c.
posted by russm at 9:03 PM on December 13, 2010

You might be interested in the solar sail, which works because light can impart real momentum when it hits something — not just directionless scalar energy, but linear momentum in whichever direction the light is traveling.

As of last summer, there's an actual real-life not-science-fiction solar sail en route to Venus.
posted by nebulawindphone at 8:15 AM on December 14, 2010

Equivalent classical-physics answer: light is a wave in the electromagnetic field. Go to the beach and let some water waves knock you down --- you'll always get knocked towards the shore. The waves carry momentum, even though the water stays in the ocean and doesn't climb up the beach.
posted by fantabulous timewaster at 10:38 AM on December 21, 2010 [1 favorite]