The Electric "Field" Modeled By Standing Matter Waves
Copyright Michael Harney
2005-2008
See Experimental Evidence For The Wave Structure of Electric Field
The concept of a field has been ambiguous from its conception. Newtonian mechanics, electromagnetics and quantum field theory use the concept of a field to describe the interaction between two "particles". The particle is considered concrete in definition which therefore makes the field ambiguous by the nature of communication required between particles. It has been shown that the particle can be described by the constructive and destructive interference of two or more standing matter-waves (the particle being referred to as the wave center, or the constructive interference point of two standing matter-waves)[1]. Therefore, we propose in this paper that a field is the interaction between the simultaneous combination of standing matter-waves that make up two wave-centers (or what has traditionally been called the interaction between two particles).
We first look at matter waves from an electron, which has a charge of 1.6 x 10-19 Coulombs and a mass of 9.11 x 10 –31 Kg. The Compton frequency of the electron is found from:
mc2 = hc / l {1},
Where m = 9.11 x 10 –31 Kg, h is Planck’s constant, and c /
l is the Compton frequency. For the electron, c / l = 1.25 x 1020 Hz.This is the frequency of the electron’s matter-wave and is the rate at which energy is propogated in a static electric field. In fact, the power in any wave can be found as:
P = (y2)(
n 2)m v {2},Where
n is the Compton frequency of the standing matter-wave as found from {1}, v is the velocity of the wave which we know to be c from a previous analysis [2], m is the differential mass per unit length, and y is the maximum space-fabric displacement of the wave in the transverse direction. The last two variables, m and y are found by using a formula from elastic space theory [2] as follows,(1/2)ky2 = mc2 {3},
which states that a "particle" is created by the compression or tension in space-fabric, and the energy of this compression or tension is equivalent to the rest-energy of the "particle". The y in equation {3} is the characteristic compression length of space-fabric that creates the particle and is equivalent to y in {2}. By knowing the range of the strong, weak and gravitational forces we can substitute these values in for y and the known mass of the force mediator particles (such as the pi-meson for the strong-nuclear force), we find k = 7.18 x 1017 Newtons/meter. For the mass of the electron from {3}, we find y = 4.78 x 10-16 meters which we use for y in {2}.
We can find
m , the mass per unit length in the compressed space-fabric as,m
= m / y {4},Where m = 9.11 x 10 –31 Kg and y = 4.78 x 10-16 meters, therefore
m = 1.9x10-15 Kg/meter.We now have all the values for the variables in {2} to calculate the power in the standing matter-wave. Assuming that the standing matter-wave power in {2} is the same as that delivered by the electrical field, and knowing that all electromagnetic waves derive energy from the same source of interacting, standing matter-waves, we use the familiar formula for power in an electromagnetic wave per unit area {2},
P = E2 / Re[Z0] {5},
Where E is the electric field intensity and Z0 is the characteristic impedance of free-space, or 376 ohms. Then we equate {5} and {2}, remembering that {2} is for single axis wave while {5} is per unit area and there are 4
p steradians in a sphere:P = (y2)(
n2)m v / 4p = E2 / Z0and solve for E as follows,
E = yn ((Z0)m v)1/2 / 3.54 {6},
and equating {6} to the familiar formula for an electric field,
E = yn ((Z0)m v)1/2 / 3.54 = qe 0 / r2 {7},
Where q is the charge of the electron and r is the radius from the electron to the measured field point.
As we have now found the values for
m , y, v and n from the previous discussion and the remaining variables are electromagnetic constants, we can find r, the distance from an electron that produces the same electric field intensity as the power in the electron’s standing matter-wave:r = ~1 x 10-16 meters which is close to the value of y = 4.78 x 10-16 meters as determined in {3}. Therefore, the closest that we can come to an electron is the maximum amplitude or displacement, y of the electron’s standing matter-wave in the space-fabric. This only makes sense as coming closer than the standing matter-wave’s amplitude implies changing the standing matter-wave itself, which means changing the fundamental nature of the electron. The value y = 4.78 x 10-16 meters is also within the same order of magnitude as the classical electron radius of 2 x 10-15 meters.
We conclude that the traditional equation for an electric field, q
e 0 / r2, although seems to imply a singularity at r = 0, cannot hold because 1) there are no singularities that have actually been measured in nature and the concept is intuitively absurd, and 2) r = 4.78 x 10-16 meters is the closest one can come to an electron without altering the physical characteristics of the electron. This demonstrates the wave nature of the electron in producing an electric field and also indicates that the field is discrete as defined by the Compton frequency of the electron (1.25 x 1020 Hz).
Experimental Evidence (9/06/05)
Equipment used:
The apparatus supplies an electric field (50 KV) between two square (6" x 6") plates and a Cs-137 gamma source is placed on one side of the plates. A digital Geiger counter on the other side of the plates measures the counts from the radiation source. The gamma rays have to pass through the electric field to get the counter, and they do so at a 10 degree angle incident to the electric field vector (- see Figure 1). In it's measurement position on one side of the high-voltage plates, the Geiger counter shows a background radiation (no source present) of 18 counts.
Experimental control: With the electric field off, the counter reads 30 counts after 40 second averaging of measurements. When the electric field is switched on, the Geiger counter shows a decrease in gamma count from 30 to 24 counts (20% decrease) and increases about 4 to 6 counts when the field is turned off ( approximately 20% increase). Next, the Na-22 source (in microcurie level and with gamma ray emission at 512 KeV - the compton wavelength of the electron) is placed on the other side of the electric-field plates, facing the Geiger counter so their path to the counter is intersecting the field vector at a 10 degree angle. Experimental control: With the electric field off, the counter reads 30 counts after 40 second averaging of measurements. When the electric field is switched on, the Geiger counter shows a decrease in gamma count from 30 to 24 counts (20% decrease) and increases about 4 to 6 counts when the field is turned off ( approximately 20% increase).
This test was performed 7 times in the same position with the radiation source and counter giving essentially the same results (although the nominal count with radiation present and no e-field is around 24 counts nominally instead of 30 counts, it shows the same increase/decrease relationship with the electric field). In one time out of the seven tries the field did not change appreciably when the e-field was switched on/off, and this may be due to the timing of when the field was turned on/off with respect to the 40 second measurement. The Geiger counter was shielded with a metal plate to reduce the effects of the E-field on the Geiger-Muller tube.
If the theory is correct, the e-field is really the effect of matter waves at the Compton frequency of the electron (1.25 x 10^20 Hz) which is the same frequency of gamma emission from the Cs-137 and Na-22 sources (corresponds to 512 KeV). When the counter starts out it takes an instantaneous measurement and then it switches to averaging mode and the measurement that is averaged is always less than the instantaneous measurement. The radiation source is added in it's designated location and the counter is turned on.
The count follows the e-field inversely when the radiation is present and when no radiation source is present the e-field works to increase the count value (it causes false activity). The counter never goes down in count with just the e-field present - it only does this when radiation is passing through the electric field to the counter. This agrees with the theory that the E-field is attenuating the radiation source.
References
2. Harney, Michael. "Quantum Foam", Journal of Theoretics Vol. 6-5 Comments Section Oct/Nov. 2004. www.journaloftheoretics.com