**A Theorem of Mass Being Derived
From Electrical Standing Waves**

**- by -**

**Jerry E. Bayles**

*(Electrogravitational Research, quark137@aol.com)*

**This paper formalizes a concept presented in my book,
"Electrogravitation As A Unified Field Theory", (as well as in numerous
related papers), the concept of mass being the result of standing waves.
More exactly, the result of electrical standing waves.**

**First, the electric mass equation developed in previous
papers will be presented in terms related directly to the rest mass energy
of the electron. This is done so as to establish the fact that ordinary
parameters such as the permeability of free space, the charge squared of
an electron, and the classic electron radius directly establish the mass
of the electron. Then we will develop an actual standing wave on a transmission
line of arbitrary load resistance and line impedance. Using currents derived
from charge and time related to frequency, the mass-gain involving the
current squared times the wavelength squared feature of the developed mass-energy
equation will be presented. This suggests that an electrical mass creation
may be nonlinear to the forth power by reason of the current squared times
the wavelength squared.**

**Then the naturally negative mass feature involving
the phasor form of purely reactive current is presented which suggests
that purely reactive energy has a built-in negative mass associated with
its field. From that, we launch into a transmission line analysis involving
standing waves and examine the results of a standing voltage and current
wave given some arbitrary input voltage, line impedance, and load. From
the current derivation, we utilize the mass-energy equation to plot a resulting
mass wave buildup on the transmission line. Note that in Mathcad, the parameters
of the equations are active and can be changed for analysis purposes. If
you do not have your own Mathcad 6.0+ or later, you can download the Mathcad
Explorer for free from Mathcad website. (Link at: http://www.electrogravity.com).**

**Next, the current and mass-plot is animated relative
to increasing l/4 wavelength steps to show how the mass builds to a limit
at one end of the transmission line. Then the electric-mass equation is
analyzed for its relationship to force, momentum, inductance, (A) vector,
B vector, Poynting power, rest mass, and the quantum Hall ohm. Finally,
we reach back to the beginning statement for equation 11 of a standing
wave and compare it with the quantum equation for a standing wave, equation
51. The nearly identical structure of the macro-system equations verses
the quantum system equations suggests that the method of electrically created
mass may indeed be possible. The relative parameters of analysis are presented
immediately below.**

**The Electric Equivalent of Mass**

**
Magnetic permeability.**

**
Electron rest mass.**

**
Electron charge.**

**
Speed of light in a vacuum.**

**
Plank constant.**

**
Classical electron radius.**

**Let:**

**
Current multiplier for analysis.**

**Let:**

**
eq. 1**

**and:**

**
eq. 2**

**Now let:**

**
Solving for d:
eq. 3**

** (has the below solutions)**

**Note that the me term is proportional to the
square of the current term since c ^{2} is a constant.**

**Where:**

**
eq. 4**

**and:**

**
eq. 5**

**Check:**

**
eq. 6**
**(= Compton wavelength of the electron.)**

**Quantum mass check of the above:**

**
eq. 7**
**(= rest mass of the electron.)**

**Note that the mass is proportional to the current squared
for a fixed wavelength, d. Then related to current, the mass would increase
exponentially.**

**Let us calculate the effective mass related to the
current squared in an antenna with the following parameters:**

**Let:**

**and**

**Then:**

**
or, **

**Then the effective mass is given by:
eq. 8**

**
or, **

**(A significant mass increase over the mass of the electron.)**

**Note that the above macroscopic effective mass calculation
now is proportional to the square of the current as well as the square
of the wavelength. If we consider the case for purely inductive or capacitive
current, then the following applies:**

**Let:**

**and**

**
(Inductive case)**

**then:**

**Then the effective mass related to purely reactive
current wave is given below as:**

** or,
eq. 9**

**Note for a purely reactive current wave, the effective
mass is negative and real. This implies that a powerful enough wave should
be able to reverse the attraction of gravity since the effective field
mass is negative.**

**As an example, let us calculate the force of repulsion
at the surface of the Earth for the above mass. First we establish related
parameters as:**

**Gravitational constant.**

**Mean radius of the Earth.**

**Mass of the Earth.**

**Then the force on the surface of the earth related
to the negative effective mass calculated above is given by the equation
below as:**

**eq. 10**

**or,**

**which is a real and negative force of repulsion by
reason of the standard equation result is normally positive and one of
attraction.**

**If we allow for a 0 or 180 degree (0 or pi) in theta
above, the force will be one of attraction since the effective mass will
be positive. Inserting a theta of (pi/2) or (-pi/2) will yield an effective
negative mass.**

**Then if the top of a UFO style craft had a real component
field while the bottom had a reactive field, the top would attract and
the bottom would repel other normal mass.**

**The following is an analysis of mass related to a standing
wave of current in a transmission line.**

**The voltage and currents along the line with
respect to time are given by the following equations below, which is the
sum of the forward and reverse propagating waves. [1]**

**eq. 11**

**z = any point on line.**

**eq. 12**

**where the Vplusvec and Vnegvec terms are generally
complex numbers as:**

**
Also see ref. [1]**

**Related to the above equations, various other parameters
are defined as:**

**Frequency (Hz)**

**Angular frequency (rad/sec)**

**Propagation velocity of transmission line (m/sec)**

**Actual length of line (m)**

**Characteristic Impedance of transmission line (ohms)**

**Load impedance (ohms)**

**Input source voltage**

**Phase constant**

**where,**

**rad/m**

__Note: Odd multiples of a quarter wavelength are
generally used in the analysis.__

**Line length as fraction of wavelength is given as:**

**eq. 13**

**or,**

**(m)**

**The line length in units of wavelength is:**

**eq. 14**

**The reflection coefficient at the load and the input
is calculated next:**

**eq. 15**

**Next we define z as any point along the line. Then:**

**eq. 16**
**which is the generalized voltage reflection coefficient.**

**Then the reflection coefficient at the input to the
line is:**

** (Input)
eq. 17**

**The voltage standing wave ratio (VSWR) is:**

**eq. 18**

**The nominal line input impedance is calculated to be:**

**eq. 19**

**(ohms)**

**Next, we determine the time domain voltage at the line
input and at the load:**

**First the source end reflection coefficient is calculated
as:**

**eq. 20**

**Then the general voltage equation based on z is presented as:**

**eq. 21**

**Then the input V(z) is:**

** (=
Vin)
eq. 22**

**The input phase is:**

**
eq. 23**

**The load voltage is:**

**(Note that the voltage at multiples of a quarter-wavelength
on the line is equal to the input voltage times the VSWR.)**

**
eq. 24**

**The load phase is:**

**
eq. 25**

**Since we have an expression for the voltage anywhere
on the line, then the current at the load and input may be expressed as:**

**eq. 26**
** (amp)**

**eq. 27**

**The time average power is given below as:**

**
eq. 28**

**The plot of phasor domain voltage and current is presented
below.**

**(Voltage magnitude along the line from start to end)**

** (Voltage
phase along line) eq. 29**

**Voltage magnitude along the transmission line.**

**Voltage phase along the transmission line.**

**Next the current along the transmission line may be
given by:**

**eq. 30**

**Equivalent to:**

**
eq. 31**

**Where again the beginning parameters are:**

**Plot of the current along line**

**The current phase is derived as:**

**eq. 32**

**The current phase plot is provided below as:**

**Based on the line amps calculated above at a given
line length, the effective field mass in the transmission line can be calculated
as:**

**
eq. 33**

**or,**

**If the frequency is increased, the mass calculation
will vary in sine wave fashion, with each wave going through zero and back
to a maximum. Each maximum however will be increasing logarithmically by
the square of the distance along the line, or z2. (This is accompanied
by an increasing frequency.) If the frequency were swept from low to high,
the increasing effective mass nodes and peaks would be pushed along the
line. This suggests a field-mass reaction propulsion system may be possible.**

**Next an animated plot is generated to show how the
mass increases and at the same time travels to the right on the transmission
line. This action would constitute a mass propulsion system, with the reaction
force being to the left.**

**First, we establish new parameters related to the frequency
increasing.**

**Frequency (Hz)**

**Angular frequency (rad/sec)**

**Phase constant**

**The reflection coefficient at the load and the input
is:**

**eq. 34**

**Next we again define z as some arbitrary point along
the line. Then:**

**
eq. 35**

**Then:**

**
eq. 36**

**And:**

**eq. 37**

**Current as a function of z along the line.**

**Next, the line current is animated in quarter wavelength
multiples, (1/4, 3/4, 1 1/4, ---etc.), in terms of current along the length,
z. The input is at the left.**

**Next, the field mass is animated in quarter wavelength
multiples. (1/4, 3/4, 1 1/4, ---etc.)**

**eq. 38**

**The animations are saved as Current.avi
and MassWave.avi
respectively.
To view these from Mathcad, click on the animate feature of Mathcad and
then select playback. Click on the file you wish to view. The animations
may also be viewed with the RealPlayer program (http://www.real.com/) which
is available on the web for free.**

**The MassWave file shows the mass increasing to a limit
slightly below 400 kg. Also, the bulk of the mass is shifting to the right
side of the transmission line. This effectively makes the transmission
line a field mass driver to the right which would cause a recoil
of the line to the left, like firing a rifle.**

**The equation that is used for calculating the mass
above has some interesting properties related to the vector magnetic potential,
force, and energy. The following equations are all derived from and related
to the electric field mass energy equation.**

__Electron Compton Rest Mass Energy Constant:__

**
eq. 39**

**and,**

**(Electron rest mass energy)**

**The above can be restated as:**

**eq. 40**

__Electron Compton Force Constant:__

**eq. 41**

__Electron Compton Momentum Constant:__

**
eq. 42**

__Electron Compton A Vector Constant:__

**
eq. 43**

**(In the same direction as the electron motion.)**

__Electron Compton B Vector Constant:__

**
eq. 44**

**(Circles around electron motion in right-hand fashion)**

**Thus we can see that the mass-energy equation used
above contains the terms for basic force and field parameter constants
which are related to and contained within the electron rest mass energy.**

**Of further interest, the following parameters are also
associated with the equation for the Compton rest mass energy of the electron.**

__The Quantum Inductance of the electron:__

**
eq. 45**

**Note that d ^{2} is related to a torus
as d^{2} = (2pi * r)^{2} = 4 pi^{2} *r^{2}
which = torus area.**

__Rest Mass of the electron:__

**
eq. 46**

__Poynting Power of the electron:__

**
eq. 47**

__Quantum Hall Ohm of the electron:__

**(= Standard SI value.)**

**
eq. 48**

**The fact that the vector magnetic potential (A) is
in the same direction as the direction of the electron is relevant to the
notion of the electron having an associated information wave capable of
action that changes the phase of a distant particle by altering that distant
particles momentum. Further, the (A) vector does not diminish in potential
over distance concerning the inline motion of the electron. The (A) vector
also may exist in a space free of the (B) field that created it and it
has an inline motion with the electron that cannot be shielded against
as conventional shielding is normally understood.**

**The mechanics associated with the inline motion of
the electron and its associated (A) vector lends itself to being adapted
to the Schrodinger wave equation. David Bohm showed that the (A) vector
that is associated with the motion of the electron is connected with a
quantum energy potential Q that has a magnitude dependent on the rate of
change of the phase associated with the electrons wavefunction.
[2]**

**Based on the above information concerning the nature
of the (A) vector passing through all material and its ability to interact
on a quantum level, we have a very strong case for stating that it may
be the gravitational action and also may properly be termed electrogravity,
or electrogravitation.**

**The geometry of the area of a torus of equal circumference
in the major and minor wavelength is suggested by the above equations involving
d ^{2}, (which is equal to d1 x d2 =
d^{2}), which are the major and minor wavelengths associated with
the Compton wave length of the electron multiplied together to form the
area of the surface of the electron torus. (Where d1 = d2 = le of the electron
= h / m_{e}c). See my book, "Electrogravitation As A Unified Field
Theory", pages 8 & 9, equations 14 & 15, where the energy density
of the electron is shown to be related directly to the shape of a torus.
(This book is available on the web for free in Adobe Acrobat format at
http://www.electrogravity.com.) Also is shown how that tremendous energy
is gated through the appropriate circular quantum area and time to yield
the field energy at the surface of the electron. It turns out that the
electron field energy at the Compton radius of the electron is 1/137 that
of the rest mass energy. (Which is also equal to the rest mass energy times
the fine structure constant.) This is an important result that proves the
case for the shape of the electron being a torus.**

**The concept of the electron being a torus shape is
enhanced by the picture of a point spinning around a loop such that the
form generated is like a spring wrapped around to almost meet its beginning
point. This cycle repeats so that space is covered in a given time which
eventually forms a nearly closed spherical shape since the torus is also
precessing due to the spinning point almost meeting at the last starting
point.**

**Since the (A) vector is generated inline to the motion
of the charge, the spinning charge-point eventually vectors (A) in all
possible directions in space which guarantees that the electron will generate
an electrogravitational action in all possible directions. This may also
explain why the assumption of 'spin' seems to have all possible assumed
results in actual measurement conditions.**

**The (A) vector circulates around the axis of motion
of the electron and also the circulation follows the right hand rule where
if the thumb of the right hand points in the direction of the charge motion,
the direction of the (A) vector circulation is in the same direction as
the fingers when closed. Again, the direction of the (A) vector also is
in the same direction as the charge motion for the case of all (A) vector
system analysis. Then the mass also moves in the same direction as the
(A) vector which implies that the (A) vector direction is intimately connected
to the nature of mass as well as charge motion since they all have the
same vector direction.**

**It may be postulated that if a charged mass in circular
motion in a plane parallel to the Earth is directly above a like system
rotating opposite and inline with the upper system, then a force of attraction
may exist between them. This is saying that (A) vectors in nearly parallel
circulation against each other may interweave, (like a screw turning into
threads), thus causing both systems to want to move together. Also, one
of the systems will want to attract the Earth while the other would want
to repel the Earth, depending on the direction of circulation of the respective
system's (A) vector.**

**The (A) vector's interaction with each other suggests
that energy is expended to cause work to be done. How would this energy
be replaced in order that the conservation of energy be maintained? I ask
the reader to consider the case for a singular electron that is located
somewhere in a universe by itself. In this concept, the electron will be
allowed to extend its field energy throughout all of the empty universe.
How much field energy would this take? Or, put another way, how much energy
must be supplied by the electron to fill a nearly infinite volume universe
with its energy field? This is a very important question and it
must be considered as being fundamental to the mechanics of all matter.
The answer is obvious. The energy comes not from the electron itself but
from the same energy space that created the big bang. Then the electron
draws on the energy from energy space whenever it needs to alter its state
or the state of its field. This occurs when its associated wavefunction
is altered, wherever its associated wavefunction is and this action occurs
instantly. This is David Bohm's entangled states of matter.**

**Then, the (A) vector action may be somewhat entropic
in its field action. This will cause a work to be done on another (A) vector
field which will result in a real force of attraction or repulsion. It
is possible that the ordinary photon may not be connected to energy space
since it has a balanced charge aspect which results in zero charge overall.
Then an electrogravitational action may over time and distance cause the
photon to lose energy since a bare photon cannot establish an external
field. This would explain the Hubbell red shift and thus also make the
case for a non-expanding universe. The bottom line is that you must expend
energy to do work and gravitational attraction that moves mass does work
on that mass, period. The energy to do that is supplied from energy space,
which has a nearly infinite amount of energy.**

**It can be further postulated that this is but one of
a myriad of universes, where each one was created in a time apart from
our own by the same huge blast of energy that would be equivalent to a
weighted impulse function. The weighted impulse function has a nearly infinite
energy at time zero and has practically zero energy at time above zero.
Our universe would be likened to part of a huge computer like program where
each universe shared its existence with all of the other universes in time-slice
fashion. This would also allow for a complete hold to be put on any universe
for adjustment purposes or for the elimination, if needed, of any universe
gone wrong. Then since our memories are supported by the action of the
quantum particles in our brain, it would appear to us that our universe
was continuous and there would be no experiment we could devise that would
be able to prove otherwise.**

**The sum total action would resemble a giant spiral
of created universes, each one assigned a specific radial place along the
spiral arm of total creation and a specific angle away from the beginning
of it all. Thus if you knew the correct angular displacement and frequency,
(the displacement code key), you could indeed walk through walls and between
other universes to get to the other side of the wall, where you would simply
pop back into existence. Your matter would take the place of the matter
that had existed where you arrived at and that matter you displaced would
be sent to where you had been. You would not even make a sound leaving
or arriving. These very actions have been reported by stories set down
in print in the Bible as well as eye witnesses in modern times.**

**The above description of the (A) vector interaction
is somewhat similar to the ordinary magnetic force action except the (A)
vector is orthogonal (90 degrees) to the B field magnetic lines of flux
and the (A) vector cannot be shielded against since it can exist apart
from the B field that it would normally be connected with in the same space.**

**Based on the above analysis, if a charge-field mass,
(i. e. high current standing wave node), were to be circulated around the
perimeter of a saucer shaped craft, a corresponding (A) vector would be
generated parallel to and circulate with it. This is the basic action required
to interact with a like field generated by the Earth and the total interaction
would be one of electrogravitational attraction or repulsion. The charge-mass
would best be generated by creating standing waves as outlined previously
in the previous standing wave analysis.**

**The mechanics of hurricanes, tornadoes, cyclones, dust
devils, all mimic the above action. The rotation of planets around the
Sun and the rotation of the planets turning about their axis attest to
the fact that gravity most likely has a circulation action built into its
basic make up. Thus, nature has given us important clues as to the mechanics
of gravity in the motion of things affected by gravity. The (A) vector
carries and imparts a change of momentum since it is born of momentum related
action. Then the (A) vector is not only connected with the B field but
also with the mass energy of the charge that creates the B field. That
was readily demonstrated by the equations of pages 11 and 12 previous.**

**The method of gravitation or antigravitation has been
suggested above but what if we wished to impart a sudden quantum translation
of position that would mimic the electron, but on a macroscopic scale?
We would alter the rate of circulation, changing the 'phase' of our charged
macro particle. Since it looks to space to be an electron, (a BIG
electron), the macro electron saucer would suddenly jump in a direction
inline with the point on its perimeter, (perimeter through center of craft),
that was phase distorted. Then, as with David Bohms quantum Q potential,
it is simply phase that controls energy Q, which then imparts the energy
required from energy space to effect the quantum jump of our craft.**

**The rate of transition and distance covered would occur
in repetitive increments, the faster the increments, the faster and farther
the average translation. This design allows for the craft operator to control
the craft motion directly. The craft could also be controlled via a remote
information wave. This would explain why some UFO craft appear to bobble
around or act erratic, since the control from a distance may be difficult
to maintain if the distance is very great. This also implies that a quantum
information wave, (a controlled and vectored (A) wave), might be used to
initiate an electrogravitational action in what would normally be considered
inanimate material. It may even be used to cause molecular vibration to
heat things up or cool them down. In some cases, it might even be used
to cause so-called spontaneous human combustion. It would do its work from
the inside to the outside, since it cannot be shielded against. This type
of controlled information wave may have been used to build the pyramids.
It could also quite readily undo whatever has been built. Remember, it
is not the power of the wave that causes action, but its ability to cause
sudden energy transition and particle translation/vibration through the
affected particles self energy which David Bohm defined as the Q potential.**

**In the beginning of this paper the formula for the
electromagnetic standing wave was presented as equations 11 and 12 above.
There exist similar formulas for the quantum case involving the motion
of the electron for example. The following quote applies directly to the
concept of particle standing waves and also linear motion. This will be
seen as very similar to the case for a transmission line as presented above.
The following is a quote from the reference [3]
at the end of this paper.**

__Begin quote:__**"A spatial wavefunction is complex if the particle
it describes has a net motion; a spatial wavefunction is real if the particle
has no net motion. For example, the spatial wavefunction (the only component
we consider from here on) for a particle with linear momentum (kh/2pi)
is:**

**
( k = 1/r)
eq. 49**

**The wavefunction is complex, and the particle has a
net momentum (to the right, increasing x). The real and imaginary components
of y are drawn in figure C. 13a, { NOTE: This figure drawing not included
in the quote}, and we see that the imaginary component precedes the
real component in phase (that is, the imaginary component is shifted in
the direction of the particle's motion). The wavefunction of a particle
traveling with the same momentum in the opposite direction is:**

**
eq. 50**

**Now the imaginary component is shifted to the left
of the real component (Fig. C13b), { NOTE: This figure drawing not included
in the quote}, and so once again its relative location marks the direction
of travel.**

**The wavefunction y = cos kx is real and corresponds
to a standing wave with no net motion in either direction. It can be expressed
as a superposition of the wavefunctions for motion to the left and right,
because,**

**
eq. 51**

**and the imaginary, direction-indicating component of
the wavefunction has been canceled."**
**{ End of quote.}**

**Macro electric equation 11 is repeated below for the
sake of comparison to quantum equation 51 above. In the expressions for
eq. 11 and 51 (and in general) i and j are both equal to the square root
of -1. Also, both equations present the standing wave action.**

**eq. 11**

**The point of the discussion in this paper is that mass
is the result of standing waves in the quantum field sense and therefore
that macro standing waves can be said to represent field mass. An
interesting experiment might involve synchronized standing wave lines
placed some distance apart and modulating one of them with a lower frequency
to see if the modulation would show up on the other line. Both lines could
be shielded from each other to decouple any fields present between the
lines. If modulation showed up on the unmodulated line, the case would
be made for standing waves to have a mechanism similar to the action of
gravity since gravity cannot be shielded against by conventional methods.
The same could be tested for with synchronized Tesla coils shielded from
each other. Also, a test of force being present between two shielded standing
wave devices may also be of relevance to the mechanics of gravitation.**

**The similarities of the above equations involving quantum
particles to the equations involving standing waves of a transmission line
are quite apparent. Then, it is suggested that since the quantum and macro-electronic
equations are so similar, it may be possible to cause movement of a macro-quantum
craft simply by altering its phase or wavefunction. It is also suggested
that quantum space is very similar to transmission line geometry as far
as how the particles move through space. Then, if you can see it, it is
real and has a standing wave that is real. This is how the so-called UFO's
may most likely appear and disappear so suddenly.**

**The following is also quoted from source [3]
to further illuminate the nature of the wavefunction and its action on
the particle motion:**

**"All wavefunctions of definite and nonzero energy are
complex if we allow for their time dependence, since a time dependent wavefunction
is the product of a spatial wavefunction y and
a factor e ^{-iEt / (h/2pi)}. The rate at which a time dependent
wavefunction changes from real to imaginary is therefore determined by
its energy: The higher the energy the faster the wavefunction oscillates
between purely real and purely imaginary. In this sense (and perhaps all
the other rich, familiar attributes of energy are consequences of this
sense), 'energy' is the rate of modulation of a wavefunction from real
to imaginary." {End of quote.}**

**Altering the phase of a stable standing wave may induce energy from
energy space to restore the integrity of the standing wave. This energy
can then be released into our normal space via photon action when the phase
is altered again in the reverse direction. See my paper "Quantum
Vehicle Propulsion" which was submitted to the Propellant less Propulsion
Conference at University of Sussex, Brighton England in January 2001.**

**If we allow for the concept of real space being refreshed by gated
in energy from energy space, then the mechanism would be energy space >
real space > photon radiated >energy space > real space > photon radiated,
etc.**

**Also quoted from the book "Quanta" is: "a purely real
(or purely imaginary) time-independent
wavefunction represents a system with no net motion." {End of quote.} [4]**

**NOTE: A purely real or imaginary
time independent wavefunction that represents a system (particle) with
no net motion that would have an infinite uncertainty as to its position
by Heisenberg's uncertainty principle. Thus, a UFO could be traveling
instantly to another part of the universe if its phase were shifted totally
into the imaginary wavefunction mode
at some time in its cycle related to its phase in the Argund diagram.**

**This may also explain why UFO's seem at times to be
translucent and also why they would want to avoid radar. Radar would tend
to interfere with the wavefunction, maybe even cause the UFO to crash.
Just a Roswell type thought.**

**----------------------------------------------------------**

**In summary, the foregoing has established that the
mass related to the electron, (and possibly all other particles), is the
result of quantum electrical standing waves. Based on this analysis, it
is predicted that a large scale system may also be constructed which will
mimic the electron in a quantum sense, that is, tunnel through ordinary
space to pop out somewhere else instantaneously.**

**The energy required to do this 'jump' is not contained
in the particle or structure, but simply gated in from energy space by
controlling the particle or systems wave- function in a suitable fashion
as described above. We may say that in order that the standing wave that
makes up the particle be conserved, the energy is gated in to move the
particle to a new point in space which in effect will conserve the standing
wave and thus the integrity of the particle itself. This also suggests
a method of tapping into energy space using a system of coherently managed
particles where a single wavefunction would control them all and the energy
imparted to the particles in unison from energy space would be converted
by a suitable energy exchange device for use on an ordinary electric power
grid.**

**Finally, we do not need for authorities to admit nor
deny the existence of UFO's. There has been ample evidence presented by
numerous eye-witnesses over an extended period of time that UFO's do exist
and have quite likely been around much longer than the so called authorities.**

**-- Author --**

**Jerry E. Bayles**

**For clarification of space-like verses time-like, non-local verses
local and also how the macro space may be related to quantum space, please
visit LETTERS,
an ongoing discussion concerning such matters.**

**REFERENCES:**

**[1] Introduction To Electromagnetic
Fields; Paul, Clayton R. and Nasar, Syed A.,**

**McGraw-Hill International Editions, 1987, p. 394, eq.
37a & 37b.**

**[2] The Undivided Universe;
Bohm, David and Hiley, Basil j., Routledge Press, 1993, pp. 28-54.**

**[3] Quanta; Atkins, P.
W., Oxford University Press, 1991, pp. 61-62.**

**[4] Quanta; Atkins, P.
W., Oxford University Press, 1991, p. 394.**

**Note: For those who wish an excellent and understandable
companion reference to the book "Quanta" above, I recommend P. W. Atkins
book, Molecular Quantum Mechanics by P. W. Atkins and R. S. Friedman. I
obtained the third edition, (Oxford University Press), 1997, from Barnes
& Noble on the web.**

**W**