Chapter 6

go to page number 1 2 3 4 5 6 7 8 9 10 11 12 13 14

CHAPTER 6

NATURAL SYMMETRIES

INTRODUCTION

The principles upon which modern science is based can be traced back to the original notions of ancient philosophers. The greatest of these early philosophers was Aristotle (384-322 BC). Aristotle developed his ideas from within through a process of introspection. His ideas are based on the concepts of truth, authenticity, and perfection. The conclusions he came to form the basis of western culture and were held as the absolute truth for nearly 2,000 years. Aristotle founded a planetary system and placed the earth at the center of the universe. In the second century A.D. Aristotle's system was revised by Ptolemy. In this system, the stars and planets are attached to nine transparent crystalline spheres, each of which rotates above the earth. The ninth sphere, the primum moblie, is the closest to heaven and is, therefore, the most perfect.

This author made three renderings of the Ptolemaic System so that computer buffs can see the difference between an applet, an animated gif, and Java Script. Some browsers may not be able to execute all three types of programs. IE-4 can.

This JAVA Animation is a compiled computer program. Produced with Sun Microsystems JAVA Workshop. A licensed copy of JAVA Workshop costs approx $150

Java complied program.

This GIF Animation consists of three pictures that are displayed in sequence.
Produced with Alchemy Mindworks Inc.'s Graphics workshop. A licensed copy of Graphics Workshop costs approx $25

Animated GIF

This Java Script Animation is an interpreted
computer program. Java Script can dynamically move images but has no graphics capability.
The best version comes bundled with Internet Explorer.

Java Script interpreted program.

Aristotle's universe is composed of four worldly elements; earth, fire, water, and air and a fifth element which is pure, authentic, and incorruptible. The stars and planets are composed of this fifth element. Due to its proximity to heaven, this fifth element possesses God like properties and is not subject to the ordinary physical laws.

Pg_2 UP

In the seventeenth century, Aristotle's teachings were still considered to be a fundamental truth. In 1600, William Gilbert published his book "The Magnet". Little was known of magnetism in Gilbert's time except that it was a force that emanated from bits of lodestone. Aristotle's influence upon Gilbert is apparent from Gilbert's conclusion that magnetism is a result of the pure, authentic nature of lodestone. Gilbert also claimed that the earth's magnetic field was a direct result of the pure authentic character of the deep earth. In some ways, according to the philosophy of Gilbert, the heavens, the deep earth, and lodestone were close to God.

In 1820, Hans Christian Oersted of the University of Copenhagen was demonstrating an electric circuit before his students. In Oersted's time electrical current could only be produced by crude batteries. His battery consisted of 20 cups, each containing a dilute solution of sulfuric and nitric acid. In each cup he placed a copper and a zinc electrode. During one of the experiments he placed a compass near the apparatus. To the astonishment of his students, the compass deflected when the electric circuit was completed. Oersted had discovered that an electric current produces a magnetic field. In the nineteenth century, experiments and discoveries, like those of Oersted, began to overturn the long-held ideas of Aristotle. Gilbert's idea that magnetism is due to a God like influence was also brought into doubt.

Pg_3 UP

In 1824, Michael Faraday argued that if an electrical current affects a magnet then a magnet should affect an electrical current. In 1831, Faraday wound two coils on a ring of soft iron. He imposed a current on the coil #1 and he knew, from the discovery of Oersted, that the current in coil #1 would produce a magnetic field. He expected that this magnetic field would impose a continuous current in coil #2. The magnetic field did impose a current but not the continuous current that Faraday had expected. Faraday discovered that the imposed current on coil #2 appeared only when the strength of the current in coil #1 was varied.

The work of Oersted and Faraday in the first half of the nineteenth century was taken up by James Clerk Maxwell in the latter half of the same century. In 1865, Maxwell wrote a paper entitled, "The Dynamical Theory of the Electromagnetic Field". In the paper he developed the equations that describe the electromagnetic interaction. These equations, which are based on the concept of symmetry, quantify the symmetrical relationship that exists between the electric and magnetic fields.

Pg_4 UP

Maxwell's equations show that a changing magnetic field induces an electrical field and, conversely, that a changing electrical field (a current) induces a magnetic field. Maxwell's equations are fundamental to the design of all electrical generators and electromagnets. As such, they form the foundation upon which the modern age of electrical power was built. Maxwell was the first to quantify a basic principle of nature. In particular, he showed that nature is constructed around underlying symmetries. The electric and magnetic fields, while different from each other, are manifestations of a single, more fundamental force. The ideas of Aristotle and Gilbert about the pure, the authentic, and the incorruptible, were replaced by the concept of symmetry. Since Maxwell's discovery, the concept that nature is designed around a deep, underlying symmetry has proven to be true time and time again. Today most advanced studies in the field of theoretical physics are based upon the principle of symmetry.

Pg_5 UP

THE SYMMETRY BETWEEN FORCE AND GRAVITY

In 1687, Isaac Newton published his book, "The Principia", in which he spelled out the laws of gravitation and motion. In order to accurately describe gravity, Newton invented the mathematics of calculus. He used his invention of calculus to recount the laws of nature. His equations attribute the gravitational force to the presence of a field. This field is capable of exerting an attractive force. The acceleration produced by this force changes the momentum of a mass.

In 1912, Albert Einstein published his "General Theory of Relativity". The General Theory of Relativity is also a theory of gravity. Einstein's theory, like the theory of Newton, also demonstrates that gravitational effects are capable of exerting an attractive force. This force can change the momentum of a mass. Einstein's theory, however, goes beyond Newton's theory in that it shows that the converse is also true. Any force which results in a change in momentum will generate a gravitational field. Einstein's theory, for the first time, exposed the symmetrical relationship that exists between force and gravity. This concept of a gravitational symmetry was not, as in the case of the electromagnetic symmetry, universally applied. In the twentieth century, it was applied in a limited fashion by physicists in the study of gravitational waves.

Pick the icon to view the symmetrical relationship between the original and induced fields.

Pg_6 UP

In 1989, this author wrote his first book "Elementary Antigravity". In this book he revealed a modified model of matter. This model is based on the idea that unbalanced forces exist within matter and that these forces are the source of the gravitational field of matter. In this present work, the symmetrical relationship that exists between the forces is fully developed. The exposure of these relationships will lead to technical developments in the fields of antigravity and energy production. These developments will parallel the developments in electrical technology that occurred following Maxwell's discovery of the symmetrical electromagnetic relationship. In review, a changing electric field (a current) induces a magnetic field and, conversely, a changing magnetic field induces an electric field. Likewise, a gravitational field induces a force and, conversely, a force induces a gravitational field.

The relationship between force, gravity, and the gravitomagnetic field has been known for 100 years. This author was the first to place force in a model of matter. This author's work is fundamental to the development of zero point technologies. This author's work on the force/gravity symmetry was published in INFINITE ENERGY Vol. #4, Issue #22, November 1998.

To get an idea of the magnitude of the force required to produce a gravitational field, consider the gravitational field produced by one gram of matter. The amount of gravity produced by one gram of matter is indeed tiny. Now assume that this one gram of matter is converted into energy. A vigorous nuclear explosion will result. If this explosion is contained within a vessel, the outward force on the vessel would be tremendous. This is the amount of force necessary to produce the gravitational field of one gram of matter. This force is produced naturally by the mechanisms that contain the energy of mass within matter.

Pg_7 UP

THE STRONG NUCLEAR FORCE AND THE NUCLEAR SPIN ORBIT SYMMETRY

A third symmetrical relationship exists between the strong nuclear force and the nuclear spin-orbit interaction. A moving nucleon induces a nuclear-magnetic field. The nuclear-magnetic field is not electromagnetic in origin. It is much stronger than the electromagnetic spin orbit interaction found within atoms. The nuclear-magnetic field tends to couple like nucleons pair wise into stable configurations. The nuclear spin orbit interaction favors nucleons with equal and even numbers of protons and neutrons. The nuclear spin-orbit interaction accounts for the fact that nucleons tend to contain the equal numbers of protons and neutrons (Z = A/2). It also accounts for the fact that nucleons with even numbers of protons and neutrons tend to be stable. The formulation of the nuclear spin orbit interaction has the same structure as electromagnetic and force-gravity interaction, however, the constants of the motion are different.

Pg_8 UP

THE MATHEMATICAL RELATIONSHIPS

The next portion of this chapter is devoted to developing the mathematical relationship that exists between the forces. The reader, who is not interested in mathematical details, may skip forward to the conclusion without missing any of the chapter's essential concepts. Following Maxwell's laws, the known electromagnetic relationship will be derived. Then, by following the same procedure, the unknown gravitational force relationship will be found. The interaction between the strong nuclear force and the nuclear spin orbit interaction will also be explored.

Pg_9 UP

THE ELECTROMAGNETIC INTERACTION

The magnetic field produced by a changing electrical field (a current) is described by Maxwell's electromagnetic relationship. This particular formulation, given in Equation #1, is known as Gauss' Law. In words, Equation #1 states that the change in the number of electric flux lines passing through a closed surface is equivalent to the amount of charge that passes through the surface. The product of this charge and the electrical permittivity of free space is the current associated with the moving charge.

I = e_o (d/dt)E•ds

Equation #1 The current produced by an electron passing through a closed surface.

e_o = the electrical permittivity of free space

I = the current in amps

E = The electrical potential in newtons/coulomb. Note the italic bold script means that E is a vector having a magnitude and a direction.

The product of this current and the magnetic permeability of free space "u_o" , yields, Equation #2, the magnetic flux through any closed loop around the flow of current.

F = (u_oe_o) d/dtE•ds

Equation #2 The magnetic flux surrounding an electrical current.

F = the magnetic flux in Webbers

u_o = the magnetic permeability of free space

Substituting charge "q/e_o" for the electrical potential yields, Equation #3.

Pg_10 UP

F = (u_oe_o ) d(q/e_o) / dt

Equation #3 The magnetic flux surrounding an electrical current.

Simplifying equation #3 yields equation #4. ( Equation #3 was simplified by taking the derivative using a mathematical operation called the chain rule. In this process e_o comes out as a constant.)

F = u_o (dq / dt)

Equation #4 The magnetic flux surrounding a current carrying conductor.

Equation #4 states that the magnetic flux around a conductor equals the product of the current flow ( in coulombs per second dq/dt ) and the permeability of free space.

i = (dq / dt) = (qv / L)

Equation #5 The current flow through a closed surface.

Equation #5 states that the current flow "I" in coulombs per second (dq/dt) is the product of the charge "q", velocity "v", and the length "L" of the current carrying conductor. Substituting Equation #5 into Equation #4 yields Equation #6.

F = u_o i

Equation #6 the magnetic flux around a current carrying conductor

Equation #6 gives the total magnetic flux around a conductor carrying a constant current. The flux carries the momentum ( inductive reactance ) of the moving electrical charges. Its magnitude is proportional to the product of the current "i" carried in the conductor and the permeability of free space.

The derivative of Equation #6 was taken to introduce an acceleration into the system. This acceleration manifests itself as a change in the strength or direction of the current flow. This acceleration generates a second electrical field. This second electrical field contributes a force to the system. This force opposes the acceleration of the electrical charges. The electrical field described by Equation #7 expresses itself as a voltage ( joules / coulomb ) across an inductor L.

E₂ = u_o (di / dt)

E₂ = L (di/dt) volts

Equation #7 The voltage produced by accelerating charges.

Pg_11 UP

THE GRAVITATIONAL FORCE INTERACTION

A second analysis was done. This analysis derives the relationship between gravity and a changing momentum. The analysis employs the same procedure that was used to derive the electromagnetic relationship. Disturbances in the gravitational field propagate at the speed of light. _1,2,3,4,5 During the propagation interval induced fields conserve the momentum of the system. Disturbances in a gravitational system induce a gravitomagnetic field. Equation #8 is the gravitational equivalent of equation #2. Equation #8 states that the momentum of a moving mass is carried by a gravitomagnetic field. The strength of the gravitomagnetic field is proportional to the number of gravitational flux lines that pass through an infinite surface.

F_g = (u_ge_g) (d/dt)E_g•ds

Equation #8 The gravito-magnetic flux surrounding moving mass

E_g The vector, gravitational potential in (newtons / kg)

F_g = The gravitomagnetic flux

Substituting mass "m" for gravitational potential yields equation #9, is the gravitational equivalent of equation #3.

F_g = (u_ge_g) d (Gm) / dt

Equation #9 The gravitomagnetic flux surrounding a moving mass.

m = The mass in kg

G = The gravitational constant

Maxwell discovered a relationship between light speed and electrical permittivity, and permeability. This relationship is given by equation #10.

u_oe_o = (1 / c²)

Equation #10 Maxwell's relationship.

This author does not know the magnitude of the gravitational constants u_g and e_g , however, he has concluded that they share the same realtionship with the speed of light as u_oe_o. Substituting light speed squared for gravitational permittivity and permeability yields equation #11. Equation #11 is the gravitational equivalent of Equation #4.

F_g = (G / c²) dm / dt

Equation #11 The gravitomagnetic flux surrounding a moving mass.

Equation #12 states that the mass flow "I" in kilograms per second (dm/dt) is the product of mass "m", velocity "v", and the length "L" of a uniform body. Equation #12 is the gravitational equivalent of Equation #5. It is the gravitational mass flow.

Pg_12 UP

I_g = dm / dt = mv / L

Equation #12 The mass flow through a closed surface.

Substituting #12 into Equation #11 yields Equation #13. Equation #13 is the gravitational equivalent of equation #6.

F_g = (G/c²) (mv / L)

Equation #13 The gravitomagnetic flux around a moving mass.

F_g = The gravitomagnetic field

Equation #13, the gravitomagnetic field, carries the momentum "mv" of a mass moving at a constant velocity. The magnitude of this field is proportional to the product of mass flow in kilograms per second times the ratio of the gravitation constant "G" and light speed "c" squared.

Momentum "p" is substituted for the product "mv". Taking the derivative of the result introduces acceleration into the system. This acceleration generates a second gravitational field.

This field is given by Equation #14. This second gravitational field contributes a force to the system which opposes the acceleration of the mass.

E_2g = (G / c²)( dp / dt ) / L

Equation #14

"L" is the length of the moving mass. The induced gravitational field drops off past the end of the mass at a rate of 1/L. If L is short, the gravitational radius r may be substituted for L. The result gives the intensity of the induced inertial force beyond the ends of the accelerating mass. The field described by equation #15 expresses itself as an applied force ( newtons / kilogram ).

Induced inertial force = [G / c² r ] (dp / dt)

Equation #15 is the general formula of gravitational induction. This formula will be extensively applied in upcoming chapters.

G (the gravitational constant) = 6.67 x10¹¹ Nm² / kg²

c (light speed) = 3 x 10⁸ meters / second

(dp / dt) = the applied force in newtons

r = the gravitational radius

Pg_13 UP

THE STRONG NUCLEAR AND NUCLEAR SPIN ORBIT INTERACTION

A third analysis was attempted . This analysis derives the relationship between the strong nuclear force and the nuclear spin-orbit interaction. This analysis employs the same procedure that was used in deriving the electromagnetic and gravitational relationships. The principle of symmetry requires a nuclear-magnetic field to be produced by the movement of nucleon. Equation #15 is the nuclear equivalent of equation #2. Equation #15 states that a change in the strong nuclear force induces a nuclear-magnetic field. The strength of this field is proportional to the number of strong nuclear flux lines that pass through an infinite surface.

F_n = (u_n e_n)(d/dt)E_n•ds

Equation #15 The nuclear-magnetic (spin orbit) field

The strong nuclear force is nonlinear. The analysis cannot be fully developed. An estimate of R at the surface of a nucleon may obtained empirically.

R = 23 MeV

The nuclear field described by the equation below expresses itself as a potential ( MeV / nucleon ) associated with the spin of a nucleon.

Nuclear-magnetic energy = R d ( spin ) / dt

Pg_14 UP

CONCLUSION

Nature is constructed around underlying symmetries. The idea that nature is constructed around underlying symmetries has proven to be correct time and time again. The electro-weak theory, for example, is based on the principle of symmetry. The first natural symmetry to be discovered was the relationship between the electric and magnetic field. A second symmetrical relationship exists between force and gravity. A third symmetrical relationship exists between the strong nuclear force and the nuclear spin orbit interaction. The nature of these symmetries was explored. The mathematics used to describe the electromagnetic relationship were applied to the gravitational / force relationship. This analysis yielded (Equation #15) the general formula of gravitational induction. The mathematical analysis performed shows that gravity produces a force and conversely that a force produces gravity. Each relationship has a similar formulation and involves the element of time. The relationships differ, in that electromagnetism involves a change in the magnetic field while the gravitational/force involves a change in momentum. The nuclear spin-orbit interaction was also explored. In light of what was learned from the study of electromagnetism and gravity, it was determined that the nuclear spin-orbit interaction involves a change in the strong nuclear force.

The formulation of the each relationship is the same, however, the constants of the motion (L, G/c², and R) are radically different. Some very profound conclusions have been obtained through the application of the simple concept of symmetry. The remainder of this text will explore, expand, and develop these constructs into a synthesis that will become the foundation of many new futuristic technologies.

A main point. Pick to view a chart that shows how the constants of the motion, discussed in this chapter, changes in a vibrationally reinforced condensate.

Pg_15 UP

NOTES

1. S. Kopeikin (2001), "Testing the relativistic effect of the propagation of gravity by very long baseline interferometry", Astrophys.J. 556, L1-L5.

2. T. Van Flandern (2002),
.

3. H. Asada (2002), Astrophys.J. 574, L69-L70.

4. S. Kopeikin (2002), .

5. T. Van Flandern (1998) , The speed of gravity What the experiments say², Phys.Lett.A 250, 1-11.

// end of chapter 6 .............................................................................