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The Casimir force between parallel conducting plates is a real,
macroscopic effect. It has now been measured to a precision of about
one percent and is beginning to be developed as a source of mechanical
action in microelectromechanical systems (MEMS) devices (see "Force
from empty space drives a machine" in the Feb. 10, 2001 Science News).
The force is due to the virtual particles and electromagnetic
fluctuations that constitute the quantum vacuum. However the force can
be very easily calculated by assuming that there is a real underlying
sea of zero-point energy in the form of a zero-point field, and that
certain modes of the field (shown for illustrative purposes on the
left as simple standing waves) are excluded in the region between the
(blue) plates (see "Radiation pressure from the vacuum: Physical
interpretation of the Casimir force," Milonni, Cook & Goggin, Phys.
Rev. A, 38, 1621, 1988; also "Repulsive Casimir force as a result of
vacuum radiation pressure," Hushwater, Amer. J. Phys., 65, 381, 1997).
Thus irrespective of the real vs. virtual ontology of the zero-point
field, calculations assuming it to be real result in the accurate
prediction of a very real force.

Our approach to inertia is similar. If we represent the
electromagnetic quantum vacuum as a real zero-point field and use the
techniques of stochastic electrodynamics, we predict the existence of
a zero-point energy flow in accelerated reference frames which we call
the Rindler flux. Now physically, the Rindler flux must consist of
virtual photons. Yet if we allow this virtual flow of energy to
interact with matter in a manner analogous to the Casimir force
interaction, we also arrive at a force: a reaction force that has the
"proportional to acceleration" characteristic that might account for
the origin of inertia.


VISUALIZING THE ORIGIN OF THE RINDLER FLUX

Stochastic electrodynamics models the electromagnetic quantum vacuum
in the approximation that it may be represented by propagating plane
waves of electromagnetic radiation, usually called the zero-point
field. In a customary spacetime diagram, electromagnetic radiation
(light) propagation is represented by lines at 45 degree angles. We
wish to show pictorially the origin of a Rindler flux of quantum
vacuum radiation by examining the flow of electromagnetic radiation
which a detector will measure in three different cases.



CASE 1: DETECTOR STATIONARY IN LAB FRAME -- The blue worldline in each
figure represents a detector with a shutter. It is fixed in place but
advancing in time, with time increasing from the bottom to the top. At
a given moment in time, the shutter opens and admits a certain amount
of radiation. It then closes again. In the left-hand diagram, light is
propagating from left to right, i.e. in the +x direction. In the
right-hand diagram, light is propagating from right to left., i.e. in
the -x direction. Clearly in both cases the same amount of radiation
will enter during the open-shutter interval.



CASE 2: DETECTOR IN CONSTANT MOTION WITH RESPECT TO LAB FRAME -- We
now have a situation in which the detector is in motion with respect
to our laboratory frame. The blue worldline of the detector is
therefore at an angle since its x-coordinate increases as time
advances. The time interval of the shutter opening is the same as in
case 1. But clearly now there is an asymmetry from the perspective of
the lab frame. Some of the radiation from the left will not be
detected because the shutter closes too soon. On the other hand the
shutter stays open beyond the last depicted light ray from the right.
More radiation (not shown) can continue to flow in from that direction
before the shutter closes. In the frame of the detector, of course,
there is no asymmetry. The detector judges itself to be case 1.

The situation is analogous to time dilation in special relativity. If
I am in rapid enough motion with respect to an observer, that observer
will notice that my clock appears to be moving more slowly than his.
But my clock looks fine to me. In fact, I see the observer's clock
running slowly. So the bottom line is that the lab frame observer
would expect there to be a net flow of energy through the detector,
but the detector would see no such flow.



CASE 3: DETECTOR UNDERGOING CONSTANT ACCELERATION -- No Rindler flux
is ever experienced by a detector in case 2 because the detector is
always at rest with respect to itself. Moreover the strength of the
Rindler flux in case 2 depends entirely on the relative motion of the
detector and the lab frame, which can be take on any value. The case
of acceleration is more subtle and involves more than just one
instantaneous reference frame. When accelerating, an object
continuously changes references frames, and this does lead to an
effect since dynamics necessarily involves time-dependent processes
over some time interval dt. When accelerating, the detector
continually undergoes a change of reference frame with respect to its
own previous reference frame. Each moment of time that the detector
experiences is connected to a previous moment in time in which it was
in a slightly different reference frame. This change of frame is no
longer arbitrary, but in fact depends on the curvature of the
worldline, which is hyperbolic for the case of constant acceleration.
What we have shown (Rueda and Haisch 1998a, 1998b) is that this minute
change in the energy flux results in a reaction force that acts upon
the detector with the "proportional to acceleration" characteristic
that might account for the origin of inertia.

There is a connection as well to an event horizon. As shown, the
hyperbolic worldline of the constantly-accelerating detector
asymptotically approaches, but never reaches, the topmost lightcone in
the left-hand diagram. Nothing to the left of that lightcone can have
any influence on the accelerating detector. The relationship of an
event horizon in this case to the black hole event horizon responsible
for Unruh-Davies radiation needs further elucidation.

CASIMIR FORCE
Depending on where in frequency one chooses to cut off the zero-point
field in the SED representation, the total energy density, call it E,
is enormous. This energy density is arguably improperly defined (due
to the unknown cutoff) and not physically real, yet in spite of that
one can calculate a very precisely defined difference in energy
density inside a Casmir cavity vs. in free space, E(free space)-E(in
cavity), and this tiny difference very accurately translates into a
radiation pressure which can account for the Casimir force.

INERTIA REACTION FORCE
In an infinitesimal time interval dt an accelerating object will move
from one coordinate frame into another. The Rindler flux in each frame
is arguably improperly defined and not physically real, yet one can
show that there does exist a very well defined difference in that flux
as perceived by an accelerating detector in any infinitesimal time
interval dt. That difference proves to be proportional to acceleration
and hence can be associated with a resulting reaction force which acts
like inertia.

(RF figures by Marsha Sims)

The concept of the "mythological" "Rindler Flux" and "Quantum Vacuum" ("Zero
Point Energy Field"), etc. as described by "Stochastic Electrodynamics", have
recently been totally disproved in a paper written by me (Jeff Lee of the
Center for Reality Physics), as it was revealed that the very diagram, on their
website illustrating the concept of "Rindler Flux", contains, within it, a
direct causality violation, which immediately exposes the fundamental error
within this line of reserach, totally destroying any and all possible vilidity
they may have misassumed that they had.

The "head guy" knows about it because I sent him a copy of the paper, but he
(and some of the others) said they will ignore any more of my e-mails. - I just
can't imagine why?

all the best,

Jeff Lee CENTER for REALITY PHYSICS