It's the "handwaving" part that is the fundamental question here! In
particular one has to ask the question if relativity can produce a
differential in radiation pressure by reason of differences in wave
propagation velocities. My point is and has been that if the author is
simply handwaving then it should be simple to look at his derivation
and say, Hey! Look right HERE, this is a bunch of handwaving! But as
far as I can tell nobody (me included) has bothered to do that.
Easy enough to do.
(a) Using eqn (1) to justify the dependence of radiation pressure on wave
speed is crap - v in (1) is _not_ wave velocity. This is worse than
handwaving.
(b) What is the difference in the force acting on the end plates (in the
rest frame of the resonator)? With propagation constant beta, wavenumber k
(which will be the free-space wavenumber), power P, angular frequency w,
and phase and group velocities vp and vg the force acting on an endplate
is F = 2P*beta/(ck) = 2P*beta/w = 2P/vp = 2P*vg/c^2. Therefore, equation
(6) is correct. The derivation, however, from the radiation pressure of a
beam at normal incidence, is handwaving, and looks wrong. Specifically,
the text between (3) and (4) appears to be using a result from [3] (alas,
not available via IEEE, and google scholar doesn't provide it - note that
the title given is probably wrong, so don't depend on it for searching),
which is either (i) a result for non-perpendicular incidence or (ii) for a
beam in a dielectric medium. Neither is mentioned. If (ii), the result is
wrong (it's 2 time the Abraham momentum of the beam, which is _not_ equal
to the force on the reflector). So, handwaving, but yielding the correct
result.
(c) Bottom of pg (4). Since with the resonator in steady-state, the
time-averaged force on each endplate is constant, why not just use F1 - F2
as the force difference? To use the relativistic velocity transformation
formula is needless, and potentially misleading (consider, for example,
the force-on-moving-stars paradox). Just find the thrust in the rest frame
of the resonator, and, if the resonator is moving fast enough, then use
the relativistic transformation law to find the thrust in the frame of
interest. At the top of page (5), "each operating within its own reference
frame" is handwaving of the worst kind - it's just wrong.
(d) Page 6, following figure 2. The statement that no force will be
exerted on a reflection-free interface due to a beam entering a dielectric
medium is wrong. This has been experimentally falsified (OK, the
experiment would have had some reflection, but you can compensate for that
by putting the beam through the interface both ways - the reflection force
would change direction, but other forces would not). The theory for this
was all done in the 1970s (if not earlier). Also, this claim directly
opposes the author's (correct, but note the problems with using the
Abraham force to predict the radiation pressure) claim that the momentum
flux of the beam changes upon entry into the dielectric medium.
(e) Use of the Abraham force only to predict the force on the
dielectric-immersed endplate is wrong. Note experiments done by R. V.
Jones (1948, and later, iirc 1960s).
(f) Entire paper: the force on the tapered walls of the waveguide is
ignored. Consider the vacuum-filled case: the force on the large endplate
is F = 2P*beta1/w (my P = Q*author's P, being the power flux in
the resonator, not the power provided by the microwave source), and F =
2P*beta2/w on the small plate. Note that the overall effect of the tapered
section is to convert beta1 to beta2, while leaving the wavenumber
unchanged. This requires the wavevector to change direction, and there is
a resultant radiation pressure force on the tapered section. This force
cannot be handwaved away, as it results from exactly the same process that
gives rise to the force on the endplates: a change in direction of the
wavevector. This force is equal to F = 2P*(beta2-beta1)/w, for a total
force of zero. Since the radiation pressure forces on the walls of a
vacuum-filled non-absorbing stationary waveguide result from the change in
the direction of the wavevector, it is instructive to consider propagation
in a closed path from point A to one end plate, reflection to the other,
and back to A - the wavevector at A is equal to the wavevector at A, in
both magnitude and direction, and hence the total force is equal to zero.
So, plenty of handwaving, claims that have been demonstrated to be wrong
by experiments done decades ago, a bizarre, un-necessary, and probably
wrong application of relativistic transformations, and the crucial error
of ignoring the force on the tapered section of the waveguide.
What more is needed?
However, if somebody wants to build it to test it, let them go ahead!
Cheap enough to do out of curiosity if one has the time available (and
likely enough to lead to publication in New Scientist, even if only as an
experimental refutation of the original NS publication). Of course, if the
would-be builders are deliberately scamming investors, then that's another
story.
