Abstract. This paper presents my solution of what gravity is and a method of building a vehicle that uses quantum principles to cause that vehicle to jump through space much as an electron jumps through space.
While this is not a new idea, the methodology to achieve this has not been forthcoming until now. The formulas presented in this paper are based on a new science created by this author wherein the gravitational action is defined both in quantum mechanical and electrodynamic terms.
It has long been established that the electron, (as well as other basic quantum particles), can somehow move from one point in space to another instantaneously. They can also tunnel through matter to show up on the other side, also instantaneously. This is observed for instance in the jumps to higher or lower energy levels inside the atom when stimulated by external electromagnetic energy and when electrons "tunnel" through an energy barrier to suddenly show up on the other side. Einstein labeled this as "spooky action at a distance" since it did not fit into his idea that space time had to be everywhere continuous and differentiable.
The late Professor Emeritus David Bohm of Birbeck College, London England, solved Schrodinger's wave equation for a quantum energy potential, Q, that represents the self energy of the electron that is determined by the interaction with the phase of it's associated pilot wave. This quantum self energy potential is theoretically infinite and is capable of instantly placing the electron at a point anywhere in normal space. The formulas I have developed not only define the actual structure of the electron but parallel David Bohm's concept of infinite potential energy being controlled by a phase shift of the parameters that make up the electron. For the sake of comparison, David Bohm's equations are presented below and will be compared to my own below that.
David Bohm has defined the electron as, "never being separate from a new type of quantum field that fundamentally affects it."
The field is defined by David Bohm as:
where R is the amplitude and S is the phase of the wave function.
And his quantum energy potential is given by:
His equation that satisfies a system of particles is:
According to the last equation, the quantum energy potential Q, (in the absence of any atomic potential energy V), is controlled solely by the phase parameter S, (the momentum times the radius). This is the foundation for David Bohm's equation of motion:
(Note that del is equivalent to 1/r.)
Along with his famous quantum potential equation and equation of motion, the idea was presented by him that there existed a vector magnetic potential apart from the field of magnetic flux that created it. This was demonstrated by the famous Aharonov-Bohm experiment. David Bohm's equation that relates the vector magnetic potential to the quantum potential Q is given by the below equation.
(Note that del cross A = B, the magnetic flux.)
The fact that the vector magnetic potential can exist apart from the B field that creates it means that the vector magnetic potential cannot be shielded against. Thus it implies that it has a connection to the mechanics of gravitation which seems to penetrate all material and interacts with everything.
The physics related to David Bohm's quantum potential and the Aharonov-Bohm effect have been presented to introduce my concept of energy potential and the mechanics of gravitation which I call electrogravitation. The energy that created the big bang is likely still there and I call this energy space. This is equivalent to David Bohm's quantum potential Q.
Below is presented my equation of electrogravitation which yields the same absolute magnitudes of force and is proportional to 1/r^2 as in the standard gravitational equation.
System 1 System 2
In the above equation, each system may be an individual particle such as an electron. I propose that the rest mass energy of the electron's basic structure is the result of standing wave energy so that it does not radiate its energy as in a normal electromagnetic wave. Thus it is stable if not acted on by an incoming electromagnetic action such as photon energy. Each system is represented as the standing wave action resulting from a phase difference of 90 degrees between two parameters, the inductive (Ø') and the other capacitive (Ø''). Below is a plot of the force output from the FG equation above when the capacitive parameter is allowed to change over 180 degrees. Note that the force goes from one of attraction to one of repulsion.
The parameter on the left of the chart, F'''''(Ø''), is equivalent to FG. It is readily seen that the force variation is extremely large with only a phase change being the controlling factor. This is equivalent to the quantum potential Q action. It is obvious that a UFO shaped craft having standing waves oriented such that the top and bottom are the voltage nodes and the perimeter the current nodes, changing the phase of the standing waves would cause the craft to duplicate what the quantum electron does. Take in energy from energy space and jump to a new position in normal space. I present the mechanics of this in detail in the main paper. Also presented in the main paper is the reason why the first orbital occurs in the Bohr Hydrogen atom as well as how the quantum jump space impedance is connected directly to energy space and from that connection, how all electromagnetic quanta are derived.
Main Paper Beginning: Let the following constants be stated for the purpose of computations regarding the analysis of the electrogravitational formulas presented below. Note that these are in SI units. The boldface constants are derived from my theory. This document prepared with Mathcad 6.0+ software and all results are units checked.
Electron rest mass.
Quantum Hall Ohm.
Classic electron radius.
Electrical permittivity of free space.
Magnetic permeability of free space.
Bohr n1 radius
Velocity of light in free space.
Variable rx preset to Bohr n1 orbital radius.
Basic electron charge.
Quantum Electrogravitational Inductance.
Quantum Electrogravitational Capacitance.
Quantum Electrogravitational radius.
Quantum electrogravitational frequency.
Quantum electrogravitational time.
Quantum electrogravitational velocity.
Quantum electrogravitational current unit.
For the sake of comparing the absolute magnitude results during the following analysis, the forces derived will be considered as the gravitational equivalent force between the mass of two electrons at the Rn1 radius of the n1 orbital of the Bohr atom of Hydrogen. Then the force calculated by means of the standard gravitational equation is given as:
Established below is the new equation for mass that relates charge, magnetic permeability, and the classic electron radius to the standard rest mass of the electron.
where the standard SI value for the electron rest mass is given as:
The new electrogravitational action equation is now stated below as:
System 1 System 2 Note the equality exists below as:
(at rx = Rn1.)
The above formula may be stated in terms of LQ and CQ and the quantum current iLM as is shown next.
(Force polarity is not corrected yet.)
The result above is by reason of transmission path (line) impedance is given by:
The above may be expressed in terms of inductive and capacitive reactances in the following:
Then also arranging the above expressions for CQ and LQ;
Inserting the above expressions for the quantum inductive and capacitive reactances into the above equation with the proper phasor form of XL and XC we arrive at the next equation:
or the quantum electrogravitational force in terms of the proper reactive sign is:
Note that multiplying the source side of the equation above by XL and dividing the receptor side by XL, the equation below is obtained.
The receptor side of the above equation now contains two cotangent forms of RQ/XL and RQ/XC that represent two interaction angles that can be made independent of the angular frequency of the interaction. The cotangent ratios are:
where the arctan of the inverse ratio will yield the phase angles;
This has the effect of rotating the first quadrant clockwise by Ø'' degrees which is in a negative time direction. (Counterclockwise is always in the positive and increasing time direction.) This represents a definite power loss and an increase in total system entropy. The previous equation may now be put in the form of the below equation where the cotangent ratios may be expressed as angles.
It must be emphasized that now the electrogravitational force expression contains the cotangent functions that can be made independent of frequency so that any L, C, or R may be utilized so long as the reactive ratios are preserved for a given angular frequency of consideration. In other words, the electrogravitational interaction force is controlled in the receptor by the phase angles Ø' and Ø'' which may be altered by means of suitable phase shifting techniques.
More specifically, Ø'' can be most easily altered to reverse the polarity of the total interaction force sign by altering the capacitive reactance, (through planar varactor diode action), where the planar surface is a capacitive plate layered with an insulating surface. The planar surface has a series of conductive dots etched upon an insulating surface which then forms a transmission line capable of emulating a coil that has a variable capacitor action to its ground plane surface. These dots would be charged in rapid sequence to emulate an actual circular-moving current if desired.
For the purpose of symmetry of action, It is possible to use the right side of the electrogravitational action equation in the left side also such that both sides have the same terms. (See below.) Now both systems have the same parameters. In general this should apply to all systems of electrogravitational interaction.
Then for an interaction distance at the n1 Bohr orbital of Hydrogen:
System 1 System 2
Please note that the sign of the equation is now one of attraction.
A very interesting aspect of the above equation is the possibility of the capacitive related cot(Ø'' ) of both system 1 and 2 being coherently connected, or many systems being coherently connected, as in a star. If all systems in a star were to suddenly shift their phase angle (Ø'') in the same direction, the result may be the sudden creation of a supernova.
For example, let
System 1 System 2
The above equation yields the plot:
The above plot shows 0 gravitational force attraction at -90 degrees. This would be disastrous for a star. The nuclear explosions that are held together by the gravitational force would cause an immediate supernova. Then a pulsar would be a star that is bordering on coherent loss of gravitational action.
If just one side or the other of the two system interaction were to have a variable phase related to the capacitive phase parameter, we can plot the result below. (This would be for the purpose of electrogravitational propulsion.)
The next equation will present the case for both electrogravitational attraction and repulsion.
System 1 System 2, variable phase
Note that only the right side of the above equation is changing related to capacitive phase.
The force goes from one of attraction to one of repulsion as the phase goes from near 0 to near -180 degrees (right to left) with zero force being at -90 degrees. Again, it is not the magnitude of the parameters, but the system number 2 phase of the interaction that controls the polarity and magnitude of the total system interaction. This is in agreement with what one would expect for a quantum interaction where the time related parameters control the energy.
Since the above equations have the quantum inductance LQ and the quantum capacitance CQ parameters, we can see that there is a definite phase difference relationship between the angle related to the inductive properties and that angle related to the associated transmission line capacitive properties. This angle difference is 90 degrees in the normal mode of interaction. For a transmission line, this is a situation of maximum standing wave ratio. We will have a condition of maximum and minimum potential, (as well as maximum and minimum current), separated 90 degrees timewise. I propose that this condition is equivalent to rest mass energy. In otherwords, particle rest mass is standing wave energy that does not radiate. (Electrical standing waves do not radiate through normal space). However, the associated scalar electric and vector magnetic potentials do convey the nature of the particle, perhaps at superluminal velocities. The nature of the particle (such as its velocity) may then also be related to the Schrodinger wave equation. David Bohm's quantum potential and his equation of motion in relationship to the vector potential was presented above.
My FG electrogravitational equation presented above can be restated in terms of the vector magnetic potential and is presented below. First we define the electrogravitational wavelength:
(A) Fconstant (A)
variable |-------constant newton-------| variable
weber/meter (amp) (amp) weber/meter
Which can also be expressed as:
which is the same absolute magnitude as the previous electrogravitational results for the force at the Rn1 radius of Hydrogen between two electrons. The force constant implies a power constant if multiplied by c, the velocity of light. Then the electrogravitational equation as presented above also has the mechanics of the vector magnetic potential which cannot be shielded against.
How the ratio of the electrons free space impedance to its inner quantum space impedance determines the first atomic level, (as well as the photon coupling constant), is presented next. First, the electron rest mass energy will be derived. For the purpose of the following analysis let the following new parameters be stated:
Then the quantum electron time is:
The current related to charge is:
The frequency fe is:
Compare this with the actual electron rest mass energy:
Now it is possible to state the case for the electron having a quantum potential energy, (via changing Ø''), that could be very large. Large enough to have the self energy required as in David Bohm's quantum potential Q. Note that this energy is standing wave energy. This is also the type of energy required for a quantum jump.
It is of interest that by carefully adjusting the phase angle, we can obtain the field energy in the first orbital n1 of the Hydrogen atom This is equivalent to the rest mass energy multiplied by the square of the fine structure constant.
Let the free space electromagnetic impedance be defined as:
Comparing the above result with the computed energy of the n1 orbital of hydrogen we first state the value of the fine structure constant as:
(This is the standard SI value.)
which is the pure ratio of the field energy to the rest mass energy at the Compton radius of the electron. It is also known in general as the photon coupling constant.
Then the absolute results are very nearly exact in agreement. Note that the negative energy result in the phase parameter energy equation above suggests an energy well that the electron would want to stay in. It also has the imaginary operator i which implies a standing wave associated with the electron Rn1 energy level..
This is a most exciting result since it implies that the mass equivalent standing wave energy supplies the field energy of the electron. Since the field energy of the electron may extend to nearly infinity then theoretically, the electron is capable of supplying nearly an infinite amount of self energy simply by adjusting its inductive and capacitve phase parameters. This energy may be said to be supplied from the zero point energy field adjacent to our normal space which is likely connected to the same energy space that created the big bang. This further implies that all matter is thus connected to the same point in energy space that again connects to all of normal space. Then an electron's self energy is also aware of all of the other electrons position and energy in our normal space through the information obtained from its energy space connection.
Below is a pictorial that suggests a construct for building a craft that would represent a macro quantum particle having the above described mechanics of the electron.
The sketch represents only the right hand portion. Also, looking down from the top, there would be at least three feed lines spaced 120 degrees apart around the perimeter. This would allow for balance and horizontal offset jumps.
The derivation of the parameters related to electrogravitation are presented below.
The quantum electrogravitational energy was derived as follows:
First we obtain the rest mass by dividing Eequiv by c2 below to obtain the rest mass of the electron.
Note that the imaginary form suggests a standing wave situation. Now the electron must have its companion electric potential charge-field. The way to establish the field not related to its rest mass energy, E equiv, is to tap into its connection to energy space via the conversion geometry of the ratio of the free space impedance ZS to the internal quantum Hall ohm impedance RQ as mentioned previously. This is equivalent to the fine structure constant and represents a transformer action which allows just enough energy to be established so that the quantum electrogravitational energy derived is equivalent to the following:
where the SI standard is:
(A unit multiplier of one is used to introduce the velocity squared units.)
ELM is the least quantum electrogravitational energy and the 1 m2/sec2 is a dimensional constant which allows for a velocity component to be associated with the generation of the least quantum electrogravitational energy, like Einstein's E = m c2 rest mass energy equation. Also, the transform coupling from energy space to normal space via transmission line parameter RS/RQ suggests a velocity associated with the least quantum field must exist. The next page shows further justification for the least quantum velocity dimensional constant being used above.
The least quantum velocity VLM is derived below by dividing the energy ELM by m electron and taking the square root of the result.
Compare with the beginning constant parameter stated value of:
The fact that the frequency is imaginary suggests that it cannot be detected in our normal space. Further, the fact that it has a minus sign suggests that it is entropic. That is, it causes a loss of energy when interacting with energy in normal space. This was because ELM was also negative in sign.
In the most elemental form, the concept of electrogravitation is based on the interaction of two systems (particles) where the energy per unit distance in system 1 is coupled through the permeability of free space to the energy per unit distance of system 2. This can be stated as:
Comparing this to the standard gravitational equation:
In order for the absolute magnitudes to agree, a least quantum velocity must be employed. The very close agreement in absolute magnitude suggests very strongly that this must be so. Note that the gravitational constant G may now be defined in new terms.
It is all about energy. Field energy to be exact. It is only the type of field energy that determines wheather a particle with rest mass or photon is present for observation. A photon is real energy and a particle with rest mass is imaginary (reactive) energy, (having the i operator.) Also, it is not a feature in my theory that higher dimensions need to be invoked to unify the strong, weak and electromagnetic forces to the gravitational force. All dimensions start with a single point. A line has theoretically an infinite number of points. Finally, all points have a common connection through imaginary energy space.
In summary, it is postulated that there exists an energy, apart from normal space, that may be tapped by the electron structure to allow it to transfer instantly through jump space. It is therefore possible that a macro particle (or vehicle) using the same standing wave field mechanics as used by the electron can achieve the same results. Further, the direct transformation of energy from energy space to our normal space is also shown as a possibility in the preceding equations. The ability to travel to the stars in a very short time is now possible according to the equation results. (After seeing my equations, one fellow put it this way, " you could leave the solar system on a flashlight battery!"). Considering what the payoff would be if the above analysis is correct, someone should be willing to put the idea presented above to an immediate test.<>In conclusion, Man achieved flight by imitating the mechanics connected with the flight of birds. We can do the same concerning interstellar flight, by learning about and then duplicating electron mechanics on a larger scale. This could be a technology available for the betterment of all humanity. --- Jerry E. Bayles