Under what conditions can a wave be said to carry momentum? Defining
momentum as the time integral of a force, light carries momentum, which
manifests itself as an electromagnetic force on a surface it reflects off
of. We can understand this purely classically by considering the electric
and magnetic fields interacting with a surface electron.
We can also get the momentum quantum mechanically (QM) from p = h/lambda.
Finally, from special relativity (SR) we could invoke "relativistic mass" m
and correctly get it from E = mc^2 and p = mv (with v = c) so that p =
E*v/c^2 (= E/c for photons).
The QM and SR relations also give the correct momentum for a massive
particle such as an electron, where v is now its speed and lambda its de
Broglie wavelength.
But what about mechanical waves? For phonons, h/lambda gives the "crystal"
momentum, but that's not a true momentum in the sense of exerting a force,
I'm told. Is there any meaning to the quantity E*v/c^2 where v is the
phonon speed of sound and E = h*nu?
Intuitively it seems a mechanical wave doesn't carry momentum since there's
no mass flow. A cork on the surface of the sea just bobs up and down (okay,
the bobbing is slightly circular, but never mind that). I assume surfing
requires interaction with the drag force from the sea bottom near the beach
as the wave breaks, so that still doesn't necessarily mean a water wave
carries momentum.
Comments? Carl
Dr. Carl E. Mungan, Assistant Professor http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL 32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu