Post by Fjolsvit
Einstein attributed the idea that light has momentum to Maxwell.
IIRC, Feynman gives an example of how radiation will push an electron
in the direction of the wave. I will look for that when I get a
Is there a decent online discussion of how radiation pressure can be
derived from Maxwell's equations? The discussions I've found rely on
the QM explanation.
I know it goes something like this. The electric field drives a
charged particle in a direction perpendicular to the Poynting vector,
and parallel to the electric field, The moving charged particle
experiences a Lorentz force due to the magnetic field which is
perpendicular to both the Poynting vector and the electric field.
The particle is therefore accelerated in the direction of the
pointing vector. That's an heuristic explanation, but it isn't
quantitative. It also assumes the Lorentz force law, which I don't
believe Maxwell relied on.
This gives about the same treatment as Feynman. Feynman's treatment is
more quantitative than I remembered.
It's still somewhat unsatisfying because a charged "point" mass cannot
absorb all of the momentum without either changing its rest mass (which
electrons, for example, don't do) or violating the law of conservation
See Exercise 2.15
What I'm really interested in is the momentum and energy of a pulse of
radiation treated classically. In particular how these quantities
behave under a Lorentz transformation.
My expectation and goal is to show that they give the same results as
are given by quantum physics. The difficulty is that classical E&M
doesn't give a simple relationship between frequency and 4-momentum.
I'm pretty sure what I need to do is consider a 3-space volume selected
as follows: consider a plane wave moving in the x-direction. Select a
unit square in the y-z plane. Mark one point on the x-axis at the
leading edge of the pulse. Mark the other end at the trailing edge.
Integrate over the volume to get the total momentum and energy therein.
Then I need to do something like transform this volume. The problem
is, I no longer have a volume representing an instant in time, in terms
of the new reference frame.
So I should probably describe a similar spacelike slice in the new
reference frame. But then I'm not sure who to compare the 4-momenta of
the two samples.
Another approach which doesn't seem as satisfying is to transform the
change in 4-momentum of our above mentioned test particle.