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A paper on Gravity, Resonance, and Electronics
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Title : Gravity Paper
Keywords: GRAVITY ELECTRONICS RESONANCE
This is an ASCII file of an unpublished paper. The paper presents a
hypothesis that gravity is the result of a distortion in space-time This
paper does not present basic information and an understanding of
college/university level physics and electronics is required. Comments are
requested and should be addressed to the address of the person posting this
A DIFFERENT POINT OF VIEW
by John R. Majka
Edited by Francis J. Ernest
Let us assume that there is a charged particle in free space. There
is an observer which is at rest with respect to the charged particle.
This observer "sees" the gravitational field and the electric field of
Let us now add a second observer. The second observer is exactly like
the first observer except that it is travelling at some constant
speed, v, which is less than the speed of light, with respect to the
first observer and the charged particle. This second observer also
"sees" the gravitational field and the electric field of the charged
particle. However, this second observer also "sees" a magnetic field
surrounding the charged particle.
Now, we will add a third observer which is identical to the first two
observers except that this observer is travelling at the speed of
light relative to the first observer and to the charged particle.
According to the Theory of Relativity, the third observer must "see"
an electromagnetic wave at the location of the charged particle since
their relative speed is the speed of light.
At the same time, the three observers see the charged particle
At a relative speed of zero, the observer "sees" a mass and an
electric field. At a relative speed other than zero but less than
that of light, the second observer "sees" a mass, an electric field
and a magnetic field. At a relative speed of light, the third
observer "sees" an electromagnetic wave with no gravitational field
and no electric field other than that associated with the
electromagnetic wave itself.
The hypothesis is that as the relative speed of a charged particle
increases from zero to that of light, the particle appears to change
to an electromagnetic wave because of the expansion of the magnetic
field. This magnetic field combines with some of the static electric
field, in proportion to the energy of the magnetic field, to form an
electromagnetic wave. At the speed of light, the electric field is
entirely combined with the magnetic field and the particle appears as
an electromagnetic wave.
At speeds less than that of light, the magnetic field of the
electromagnetic wave collapses. The collapsing field distorts or
twists space-time which appears to us as a gravitational field. Thus,
it is the distortion of space-time which appears to us as "mass"
rather than "mass" causing the distortion.
This hypothesis seems to be justified by equations from classical
physics. The equation describing the energy density of the particle's
magnetic field, Um , is:
Um = B2 / ( 2uo )
where uo is the magnetic permeability of free space
The equation describing the energy density of the particle's electric
field, Ue , is:
Ue = eo E2
where eo is the electric permittivity of free space
The total energy, Ut , of the electric and magnetic field of a
particle travelling at some speed, v, is the sum of these two
equations. Converting to like terms and combining terms, the total
energy equation is:
Ut = ( eo E2 / 2) ( 1 + v2 /c2 )
If we now let V = C, the equation becomes:
Ut = eo E2
which is also the energy density equation of an electromagnetic wave.
Classical physics equations also show that the direction of the
magnetic field of a charged particle, travelling at some speed, is
such that the Poynting Vector cross product is satisfied. That is, E
x H = I.
The hypothesis is also supported by experiments which have shown that
charged particles travelling at a high speed exhibit duality. That
is, when travelling at high speeds, charged particles exhibit particle
characteristics and electromagnetic wave characteristics. If, as is
hypothesized, the magnetic field combines with a portion of the static
electric field to create an electromagnetic wave, duality is expected.
Since the particle is only partially an electromagnetic wave, it
should exhibit duality at speeds less than light.
The accepted theory is that mass increases as speed increases. The
finding by Bucherer in 1908, that the electric field to mass (e/m)
ratio is less for high speed particles, has been accepted as proof of
an increase in mass. The hypothesis proposes that the reason for this
finding is not that the mass has increased but rather that the
electric field and the mass have decreased. That part of the electric
field which combines with the magnetic field to create an
electromagnetic field can not participate in static charge
measurements. Therefore, those experiments measuring e/m will show a
lower value for high speed particles than for slower particles.
Experiments with particle accelerators seem to show an increase in
mass with an increase in the speed of a particle. After being
accelerated, charged particles are passed through a velocity selector
which passes only those particles which are travelling at a
predetermined speed. Immediately, the particles are passed through a
momentum selector which is a uniform magnetic field. This magnetic
field produces a constant acceleration on the particle which causes
the particle to travel in a circular path. The radius of the path is
proportional to the linear momentum of the particle. Since momentum
is proportional to the mass of the particle, it is assumed that the
radius of the path is then proportional to the mass of the particle.
Experiments have shown that the higher the speed of the particle, the
greater the radius through the momentum selector. It has been assumed
from these experiments that the greater radius is due to a greater
The hypothesis states that the apparent mass of the particle decreases
with relative speed and that the magnetic field combines with a
portion of the electric field to produce an electromagnetic wave. A
decrease in apparent mass should be observed in particle accelerator
experiments by a decrease in the radius of the path of the particle if
mass were the determining factor.
However, electromagnetic waves also have a linear momentum and this
momentum is not affected by an external magnetic field. When passed
through a momentum selector, an electromagnetic wave would pass
straight through and not describe a circular path. Since the
electromagnetic wave is characteristic of the particle, it's path is
the same as the particle's path. The linear momentum of the
electromagnetic wave adds to that of the particle and increases the
radius of the path.
CHARACTERISTIC VELOCITY OF SPACE
It has been assumed that electromagnetic waves can travel only at the
speed of light. The hypothesis proposes that there is an
electromagnetic wave which is a characteristic of any charged particle
travelling at any relative speed greater than zero and less than the
speed of light.
Since electromagnetic waves travel through transmission lines and
through space, it is possible to model their propagation through space
by a transmission line analogy. Transmission lines and space share
common parameters. The most notable are the parameters of distributed
inductance (or magnetic permeability) in henries per meter,
distributed capacitance (or electric permittivity) in farads per
meter, characteristic impedance in Ohms and characteristic velocity
in meters per second.
Models of transmission lines are basic in the study of electricity and
electronics. A model circuit diagram describing a typical, real
transmission line is shown in Figure 1. The inductance, L, is in
terms of henries per meter. The capacitance , C, is in terms of
farads per meter and the resistance, R, is in terms of Ohms per meter.
Note that the circuit diagram basically consists of one RLC circuit
repeated for the length of the transmission line. The resistance, R,
is responsible for losses in transmission lines. In an "ideal"
transmission line, without losses, the resistance is ignored. Since
it seems that an electromagnetic wave travels through space without
losses, we may assume that the model for an ideal transmission line is
adequate for an analysis of free space. Also, since the circuit
segment is repeated for the length of the transmission line, the
analysis of one segment is sufficient. Figure 2 shows the circuit
diagram for an ideal transmission line.
Circuit modeling involves determining the voltages and currents
through the circuit. By Ohms Law (E = I x Z), the voltages and
currents are related through impedances. (Note: Impedance is
mathematically treated as a resistance. It differs from a resistance
in that there are no energy losses through an impedance.) Figure 3
shows the same circuit with the impedances of the circuit elements.
The values of the impedances are shown in typical electrical analysis
notation. Since the impedance of an inductor varies directly with the
frequency of the current through it or voltage applied to it, the
impedance is in terms of the frequency, jw. Since the impedance of a
capacitor varies inversely with the frequency of the current through
it or voltage applied to it, the impedance is in terms of the inverse
frequency, 1/jw. (In electrical analysis, since the symbol "i" is
used to represent current flow, the symbol "j" is used to represent
the square root of -1 and the symbol, w or omega, is used to represent
frequency where w = 2 pi f.)
It can be seen that this circuit is also the circuit of a series L-C
circuit. To go from a transmission line model to a series L-C circuit
model all we need do is change the terms of the parameters from
henries/meter and farads/meter to henries and farads. The normalized
transfer function, H(jw), of such a circuit is:
H(jw) = 1/( w2 - wo2)
The symbol w represents the frequency of the signal applied to the
circuit. The symbol wo represents the resonant frequency of the
circuit and it is numerically equal to the square root of (1/LC).
The resonant frequency is the frequency preferred by the circuit. If
a signal was applied to the circuit and it was not at the resonant
frequency, the circuit would
offer an impedance to the signal. If a signal at the resonant
frequency was applied to the circuit, the circuit would offer no
impedance. The reason for this is that the impedance of the inductor
(jw) varies directly with the frequency of the applied signal. The
impedance of the capacitor (1/jw) varies inversely with the frequency
of the applied signal. At the resonant frequency, the magnitude of
the impedance offered by the inductor and the capacitor are equal.
Impedances due to inductors and capacitors are vector quantities. The
direction of the inductor's impedance vector varies directly with the
frequency of the applied signal in the positive direction. The
direction of the capacitor's impedance vector also varies directly
with the frequency of the applied signal but in the negative
direction. At resonance, the magnitudes of the impedances are equal
but the vectors are 180 degrees out of phase with each other and thus
cancel. At resonance, the circuit offers no impedance.
The values for L and C in a series L-C circuit are in terms of henries
and farads. The resonant frequency, wo, is equal to the square root
of (1/LC). The resonant frequency, then, is in terms of 1/second or
Hertz. If we were to substitute henries per meter and farads per
meter for the values of the circuit elements, then resonance would be
in terms of meters per second. Instead of a resonant frequency we
would have a resonant velocity. Indeed, for transmission lines, the
velocity of propagation is the square root of (1/LC).
The speed of light is the square root of (1/uoeo) which are the
magnetic permeability and electric permittivity of free space.
Therefore, we may assume that the speed of light is the resonant
velocity of free space.
The series L-C circuit does not forbid frequencies other than the
resonant frequency but it does provide an impedance to them.
Similarly, we may assume that the universe does not forbid speeds
other than the speed of light but would provide an impedance to them.
Electromagnetic waves, which are characteristic of charged particles,
can travel at speeds other than the speed of light.
We should note that the series L-C circuit does not prohibit
frequencies greater than the resonant frequency. Since the analogy
between series L-C circuits and free space has held in other
circumstances we may assume that space also does not prohibit speeds
greater than resonant speed but will provide an impedance to them.
The hypothesis predicts that electromagnetic waves can travel at
speeds other than at the speed of light. At light speed, the universe
offers no impedance to the propagation of electromagnetic waves. At
other than light speeds, it is expected that the universe will provide
an impedance to these waves.
We are familiar with speeds less than light. At a zero relative
speed, the "stopped" electromagnetic wave appears as a "particle" and
exhibits a gravitational field and an electric field. In the series
L-C circuit, the impedance encountered by a signal with a frequency of
zero Hertz is provided entirely by the capacitance. As the frequency
of the signal is increased, the impedance of the capacitor is reduced.
Similarly, as the speed of a particle increases, the effects of the
static electric field are decreased.
Similarly, we may compare the impedance of the inductor to the
magnetic field of a particle in relative motion. At zero Hertz, there
is no impedance offered by the inductor and a "particle" at zero
relative speed has no magnetic field. As the frequency of the applied
signal to the circuit is increased, the impedance provided by the
inductor is increased. As the speed of the particle increases, the
effects of the magnetic field are increased.
At frequencies less than the resonant frequency, the impedance of the
circuit is due primaily to the capacitor. At speeds less than that of
light, the electric field is dominant and the magnetic field is a
function of the electric charge.
At frequencies greater than the resonant frequency, the impedance of
the circuit is due primarily to the inductor. We may then assume
that, by analogy, at speeds greater than the speed of light, the
magnetic field will dominate and will appear to be as constant as the
electric field at sub-light speeds. At these speeds, it may appear
that the electric field is a function of the magnetic field.
To repeat for clarity: The impedance offered by the capacitor is
analogous to the electric field of a charged particle and the
impedance offered by the inductor is analogous to the magnetic field
of a charged particle in motion.
Let us assume a series L-C circuit, as described above, with no
applied signal. The inductor does not have an initial magnetic field
nor does the capacitor have an initial electric field. Now let us
apply a signal of zero Hertz and the circuit will oscillate at its
resonant frequency. In a real circuit, resistances cause the
oscillation to dampen. In an ideal circuit, the oscillation does not
die out and continues forever. If we assume the creation of a
particle, we would see that this particle causes a disturbance which
propagates as an electromagnetic wave.
Now we change the frequency of the applied signal. Again the circuit
will respond with an oscillation at it's resonant frequency.
Similarly, if we accelerate a charged particle, an electromagnetic
wave is generated. Indeed, any change in the frequency of the applied
signal to a series L-C circuit will generate transient oscillations
just as acceleration of a charged particle will generate
The electric and magnetic fields of a particle have been associated
with the impedances offered by the capacitor and inductor of an
analogous series L-C circuit. The hypothesis proposes that the mass
of a particle is due to the collapse of the magnetic field of the
Mass is not recognized directly but a gravitational field is. A
gravitational field is probably not a different form of a magnetic
field. The gravitational field is, most likely, a result of the
collapsed magnetic field. It is possible that the collapsed magnetic
field pulls or twists the fabric of space-time in such a way as to
form what we call a gravitational field.
As the speed of the charged particle increases, the magnetic field
expands and decreases its pull or twist which causes a decrease in the
gravitational field. At speeds greater than light, the hypothesis
predicts that the effects of the electric and magnetic fields will be
reversed. At these speeds, it is likely that the magnetic fields will
become polar and the electric fields will become circular, that is, a
magnetic monopole will result.
At speeds much greater than that of light, the electric field may be
expected to collapse. This collapsed electric field may also pull or
twist the fabric of space-time and form a type of field not now known.
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