Biefield-Brown, electric field, gravitational field, electro-gravitation, Unified Field, acceleration, electric-acceleration, Force Plate, gravitation, Newtonian Field, Reissner-Nordström, metric.

This paper examines the similarities between a prediction made by a recent Unified Field Solution and the Biefield-Brown Effect. This prediction describes the conversion of an electric field into a gravitational field. The equations are distilled down to describe the optimum configuration for a capacitive type of Force Plate. A Newtonian metric variant is derived and experimental data is presented to test the prediction.

The Biefield-Brown Effect Revisited

The solution to Einstein's Unified Field Equations predicts the existence of a force very similar to the Biefield-Brown Effect. This paper will examine this prediction because it details the direct conversion of an electric field into a gravitational field.

The Biefield-Brown Effect, as found by Thomas Townsend Brown in the late 1920's, produced a slight weight change in a specially constructed capacitor when it was subjected to an extremely high DC voltage^[1]. Others have verified the effect and several patents have been granted over the years^[2], but no one has been able to explain what the effect is or its source.

Prior attempts attribute the effect to: stress in crystals, gravitational forces, electrostatic wind/forces, etc. Because no one could explain it, plus the fact that it required such very high voltages to produce the effect it has fallen into obscurity.

This paper will derive the weak field generating equation for this effect and explain what the force is, and examine commercially available materials suitable for producing the force.

Most of the predictions from the Unified Field Solution were derived from the Finsler solution metric by the author. However, the essentials of the Biefield-Brown Effect can easily be derived from the older classical Reissner-Nordström metric. This metric can be shown to have the following form^[3].

          g₄₄ = e^2v = 1 - 2 M/r + Q²/r²                    (1)

Where g_ij is the metric tensor, and M can be shown to be equal to G m/c^{2 [4]}. For a dominate matter field equation (1) reduces to

          g₄₄ = D = 1 - 2 G m/(c² r)                    (2)

Here D is the metric component in Dingle notation^[5]. This equation is seen to be the classical Schwarzschild solution.

     For a dominate electric field there follows a similar equation (notice the sign difference).

          D = 1 + Q²/r²                               (3)

Unlike the matter solution no one has been able to find a verifiable Newtonian definition for Q. A method defining Q using Newtonian gravitational and electrical equations was set out in a recent paper^[6]. Using this method, with modifications, will be shown to produce a simplified Newtonian definition for Q, less a correction factor also predicted by the Unified Field Solution.

     We start by equating the electrical acceleration metric component to the Newtonian electric field^[7].

          a_e = ½ c² D_r (3 D - 2)/%(D - 1) = E = -k q/r²     (4)

Here D_r is the partial of equation (3) with respect to r, c is the speed of light in a vacuum, and E is the Newtonian electric field. Rewriting this equation substituting a new lumped term X₁.

          a_e = ½ c² D_r/X₁  = -k q/r²                     (5)

Where X₁ is a manifold constant. From equations (3) and (5) a definition of Q² readily follows.

          Q² = X₁ k q r/c²                          (6)

Here k is the electric field constant, q is the Newtonian charge, and r is the radial distance the electric field propagates across. Substituting this result into equation (3) yields a metric definition with Newtonian terms.

          D = 1 + X₁ k q/(c² r)                      (7)

Next we will make the substitution for Newtonian charge to capacitance.

          D = 1 + X₁ k C V/(c² r)                      (8)

From equations (4), and (8) it can be seen that X₁ will be a very small number.

     Because this last equation is describing the charge on the plates of a capacitor we can break X₁ into smaller components consistent with this geometry.

          X₁ /2 = ,_o /(x N)                            (9)

Here ,_o is the permitivity of free space, N is the near field correction term used to adjust the general electric field equation for field orientation and for distances much less than infinity, and x is a constant yet to be determined. It should be noted that while equation (6) holds for other combinations of systems and types of charge equation (9) does not.

     Taking equations (8) and (9) and substituting into the radial acceleration metric^[8], we find a new relationship for radial acceleration within a dominate electric field.

          a = ½ c² D_r = -,_o k C V/(x N s²)               (10)

Here   a   is the general radial acceleration for weak fields, and s is the radial distance the electric field operates across - which in this geometry is the separation between the capacitor plates. For a circular plate capacitor N = r_c/s, where r_c is the radius of the capacitor plate (for a shape other than circular r_c can be found by taking the square root of the plate area divided by B; this would then be called the effective radius).

     Substituting for N and using the basic equation for a circular plate capacitor (C = k₁ ,_o B r_c²/s) we can rewrite the above equation.

          a = -,_o/(4 x) @  V k₁ r_c/s²                    (11)

As k = 1/(4 B ,_o). Where k₁ is the dielectric constant of the material between the plates of the capacitor. All that is left is to evaluate x.

     I obtained several thin capacitor disks of different sizes and materials from several manufacturers. I then applied a DC voltage to each of them, while they were on a sensitive scale, and recorded their weight change versus voltage.

     Before each test 50 Volts/mil (a mil is 1/1000 of an inch) was slowly applied to the sample. Then the sample was slowly discharged. This sequence was repeated twice before starting a test. This relieved any residual stress from any previous voltage reversal. If this relieving wasn't done, when the polarity was reversed from the previous test, the weight change seen was an order of magnitude greater than the steady state measurements presented here. This wild fluxuation only lasted for one cycle if the final voltage exceeded 50 V/mil.

     Each test was conducted by first discharging the sample then slowly increasing the voltage incrementally across the sample while recording any weight change. Then the voltage was slowly decreased and the retrace weight change versus voltage was also recorded. This was done twice. Then the polarity was reversed and the test repeated; after the stress was relieved as set out above. This process produced a steady state condition that was reliable and produced repeatable results.

     The samples were measured while resting on an insulated plate on a Mettler A100 digital scale. This scale had a repeatable accuracy of 0.0001 grams. In order to eliminate the twisting torsion effect of the disk when it was stressed two small #26 copper wire was soldered to the electrodes on the disks. The other end of these wires were placed in two small Styrofoam cups filled with mercury. There was an additional wire in each cup that connected to the high voltage supply. This way as the disk twisted it didn’t pull on either of the wires and induce a false mass change.

     A sample's weight change was converted to an acceleration by dividing the weight change by that sample's dielectric mass and then multiplying by 9.82 to convert the result to units of  meters/sec². The characteristics of the sample disks are listed in Table I.

TABLE I - Sample Characteristics

* effective radius

   Column Definitions

Initial     =     Capacitance as received

Tested     =     Capacitance as tested (wires, insulation, etc.)

r_c        =     Radius of electrode surface

s         =     Dielectric thickness

k₁        =     Dielectric Constant

mass      =     Dielectric mass in grams

Poled     =     Polarized when manufactured

Mfg.      =     Manufacturer of the sample

Rewriting equation (11) yields the generating equation.

          a = -V k₁ r_c/s²    C  x 10^-14                   (12)

     Equation (12) predicts that a charged plate capacitor will produce a unidirectional acceleration field normal to the electrodes, as it will follow s (here, C is a constant relating to the system of units chosen). This acceleration will produce a force that is equal to the dielectric mass times the acceleration. If the capacitor shape is designed to be a flat plate the acceleration produced will move the plate along an axis that is normal to the plate.

          F = m a                                     (13)

Combining this with equation (12) and rewriting m for the defined geometry describes the components of the force produced.

          F = V k₁ r_c³ D/s   C₁  x 10^-13                   (14)

Here D is the density of the dielectric material between the plates. This equation predicts a force effect, like the Biefield-Brown Effect, that is unidirectional and originates within the dielectric material of a specially designed capacitor. As above C₁ is a constant that depends on the units chosen.

     Equations (12) and (14) describe a condition where a thin flat plate capacitor will operate as a Force Plate. Using sinter technology and available exotic materials a properly designed capacitor can produce a very substantial force. The samples used in this experiment were not optimized for this effect and consequently were quite inefficient in producing much force. One of the major drawbacks of T. Brown's devices were that they required hundreds of thousands to millions of volts to produce a weight change of only a few percent. From the test data and equations (12) and (14) it can be seen that an optimized device would require well under a thousand volts to operate efficiently.

     Once one of these devices is charged up it will continue to produce the same force after the voltage has been disconnected, unless it has been discharged. The force will slowly diminish with time after the voltage has been disconnected. If the voltage is held constant only a few microamps of current are required to sustain the force produced, even if the physical loading on the device is changed.

     In addition to the weight measurements presented here I also performed free swinging tests, using a laser and mirrors to give increased resolution. Unfortunately, these tests showed that the disks deformed when voltage was applied. These deformations produced motions greater than the motion produced by the acceleration. The amount of deformation varied with the sample and the load attached to the sample. This only complicated the problem. This forced me to resort to the weight test described above, as it responded only to the acceleration component. The down side of the weight test was loss of sensitivity over the optical method.

     The acceleration characteristics within one cycle of a voltage reversal did not follow equation (12). For voltages between 4 V/mil and 15 V/mil the acceleration followed a cubic relation, and between 15 V/mil and 30 V/mil it followed a square relation. Between 30 V/mil and 35 V/mil it followed a linear relation. Above this voltage limit the acceleration reversed direction and decreased rapidly mainly due to disk deterioration. While some of the samples survived at stress levels exceeding 55 V/mil most were damaged at levels over 35 V/mils.

     Equation (12) predicts that the effect will be linear with respect to the applied voltage. The tests indicated that below 30 V/mil the effect was greater than expected. Between 30 V/mil and 35 V/mil it was as predicted.

The effects measured under 30 V/mil were extremely small and at the resolution of this test setup. It is thought that the low voltage results were mainly comprised of the effect measurement plus an error reading due to the electrostatic effect between the two wires causing 0.1 mg fluctuations. Above 35 V/mil some of the samples broke apart ending their testing.

While very thin plates lend themselves to small and convenient voltage levels the stress levels make thin plates less reliable. Thick plates on the other hand tend to handle the higher voltage densities far better with the inconvenience of requiring much higher voltages.

Cingular