Re: wave momentum

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding:
> I am a bit mystified by the comments on this thread:  There is no real  E/M
> wave -- we have given up the idea of an aether long ago have we not.  There
> _is_ real motion in a sound (or to stretch things, water wave) -- ie
> molecules do move and thus one can more easily imagine a momentum flow, but
> I am a bit nervous about this as well.  Am I being to "classical" -- (or
> worse, just ancient)???

No. You are just being incorrect.  Hertz discovered real EM waves well
over a century ago.  They were predicted by Maxwell who also identified
light an an example of them.

> Thus an e/m wave doesn't "carry" mass thus no momentum -- there is a charge
> at the "originating" site which does impose a force on the distant site
> thus it may cause some momentum at that site.   We just  imagine a  wave
> momentum which we hope will make calculations easier -- just as we talk
> about  E/M "fields" which are not "real" either but  are sometimes helpful
> to imagine.

This is simply incorrect. Denying the EM field degrees of freedom and
including only Coulomb-esque actions at a distance between charged
particle degrees of freedom is not equivalent to the Maxwell theory and
is inconsistent with experiment and special relativity.  Any attempt
(even at the purely classical, nonquantum level) to "integrate out" the
field degrees of freedom from the (charged matter + EM field + their
mutual interactions) Lagrangian results in a very nonlocal particle-only
theory which can only be solved perturbatively in inverse powers of c^2.
The lowest order theory is Coulombic electrostatics tied to Newtonian
dynamics.  The next order includes initial lowest order magnetic field
effects and leading order relativistic corrections (for moving
particles) to the Coulombic interaction between particles as well as the
leading order relativistic corrections to the particles' dynamics.  The
resulting Lagrangian for this (interacting particle-only) theory is the
Darwin Lagrangian.  The next order correction to this theory is much more
complicated and I don't know what the name of its Lagrangian is, or even
if it has a name.  It is only if an infinite order expansion is made
whose dynamical equations of motion result in an infinite set of coupled
*infinite order* differential equations that the Maxwell field +
particles theory is asymptotically reproduced as a particle-only theory.

Where did you get the idea that EM fields are not "real", or are somehow
less "real" than particles?  After all, we consider the so-called
'particles' to really be the classical limit (in terms of wave function
localization in position and momentum) of quantum excitations of
underlying dynamical *fields*.  In the case of electrons (& positrons) it
is the lowest mass lepton generation of a Dirac field coupled to the
Maxwell (i.e. EM) field via a local connection that happen to make a
global U(1) gauge invariance local.

> Of course I readily admit that action at a distance is not much more "real"

It's not any more real.  I think it is less real.

Somehow, I'm getting a sense of deja vu about this thread.  Am I the
only one?

David Bowman
dbowman@georgetowncollege.edu