Center 4 CM

The Unified Field Theory

The conceptual foundations of the research presented here were favorably evaluated by NASA and senior editors at Tab Books (a division of McGraw-Hill), in 1982. "Your concepts about the Unified Field Theory [link to the letter NASA sent me] appear to be so profound as to be years ahead of the current scientific thinking in the areas in which you delved." All aspects of the theory have since then been subjected to exhaustive analysis, most of it computer based, and the original theory - now restated in terms of celestial mechanics - has held up 100%. (The original theory is reproduced in the "star ship" paper.) The papers are in PDF format. You can download a free PDF reader from Adobe.

The original theory suggested two distinct gravitational regimes within the Solar System; for the inner and outer planets, respectively. In dynamical theory a shock wave is created whenever two distinctly different wavefronts meet. Presumably this would happen where these two gravitational anomalies collide, creating a shock - e.g. a THIRD wave front, moving faster than either. This could theoretically form the basis for a "jump gate" to accelerate spacecraft beyond our Solar System. In order to investigate this phenomenon, I created a computer model of the Earth to Mars trajectory. You can download the program itself at my Bar X Software website. The simulation was, in fact, successful in finding this super fast mission profile. Subsequent research has been to find an underlying physical and mathematical basis for this phenomenon. Again, this endeavor has been fairly successful - as you shall see.

The Four Body Problem

An example of the Four Body Problem is the Earth to Mars trajectory: the Sun, Earth, and Mars are the three large bodies and the spacecraft is the small fourth body. The purpose of the "orbital mechanics" section is to study the problem numerically by modeling the problem in a computer simulation . This optimization program found a faster, more efficient trajectory. The papers on "celestial mechanics" are devoted to an analytical solution of the Four body Problem (4BP), in an attempt to find a theoretical basis for this faster, more efficient flight path from Earth to Mars. The "solid state physics" papers show how the 4BP can be used as a model for the transistor junction.

The computer simulation is unique in that it optimizes the Earth to Mars trajectory without the use of a nonlinear optimization program. The problem has twenty five unknowns, plus several more parameters set by the user. Typically a nonlinear optimization routine is needed for anything more than four unknowns in a problem of this nature. The source code is also compact and efficient, taking less than 30 seconds on a low speed PC. On the other hand, a problem of the same order of magnitude with as many unknowns typically takes several minutes to solve on an institutional quality mainframe. The routine finds a trajectory to Mars that uses 20% less fuel and arrives 40 days faster than any comparable NASA mission.

A new coordinate system is found which eliminates one of the six variables (plus time) normally required to represent a body in an elliptical orbit. Such a coordinate system is suggested by an investigation of the planets in our Solar System, described in The Invariant Plane.

When the motion of the planets is transformed into this new coordinate system it is possible to eliminate one of the variables. This property is described here. In order for this hypothesis to be valid, it is now necessary to show that an Invariant Plane is not a unique characteristic of our Solar System but is a property of dynamical systems in general. That is done heuristically in the following series of papers.

A transformation of the data coordinates of the planets with respect to this Invariant Plane shows the ten bodies actually behaving as only three: the sun, the prograde planets, and the retrograde planets. This implies that these ten bodies can modeled as three bodies; and the very complex 10BP becomes the familiar and well known 3BP. A mathematical proof of this is shown in The Regularized Ten Body Problem.

The Inverse Problem

It is customary in Celestial Mechanics, once a problem has been regularized, to then investigate the problem from within the transformed coordinates. What should be expected? Just as the Trojan Asteroids are situated at a stable equilibrium point on the Sun-Jupiter 3PB, the planets should be at stable equilibrium points in the 10BP. The exact nature of these equilibrium points should be more complicated than a single point at the apex of an equilateral triangle. They are suggested to be segments of a helical curve in the 10BP.

The solution of the Inverse Problem of Celestial Mechanics is derived graphically. It is supported by astronomical data on all the planets and the asteroids. The result sheds light upon many heretofore unexplained phenomena in the solar system. That's a good sign - it means the theory developed thus far is robust.

To make it a comprehensive theory, the graphical solution just derived must be consistent with existing theory, in particular as a dynamical model of the solar system. This is shown to be the case in The Gravity Ellipsoid . The curve derived from the graphical solution is shown to be the unstable axis of a three dimensional ellipsoid. Similar ellipsoids exist in other dynamical systems - for angular momentum and inertia. It's logical to expect an ellipsoid exists in the gravitational sense.

All together, these technical papers present strong support for the existence of an Invariant Plane, sufficient to allow it to be used to characterize the Four Body Problem as noted.

Solid State Physics

Everything we know about semiconductor transistor devices is statistical. Yet, statistics has its limitations. Transistors are now on the order of only ten atoms thick. Statistical models with so few random bodies are not as dependable. A discrete model of the transistor junction is needed if the computer revolution is to continue. Research on the 4BP shows it can be used as a discrete model for the transistor junction.

The model presented here is based on the Earth to Mars trajectory. The structure of this problem in orbital mechanics is shown to be very similar to the processes that happen in the transistor junction. That is, a spacecraft goes from a stable orbit around Earth to a stable orbit around Mars; versus an electron going from a stable regime in the emitter to a stable regime in a collector. The thrusts necessary to accomplish this task are exact corollaries to the voltages applied at specific points in the transistor; the thrusts give energy to a spacecraft, and the voltages increase the energy of an electron. The optimal Earth to Mars trajectory is one in which the largest thrust is at conjunction, about half way; the most efficient transistors have a large bias (or voltage) applied in the middle of the device. Many more corollaries are noted. The first paper describes how the 4BP fits the transistor junction model, in a conceptual sense. The second paper goes into great detail. The correspondence of the 4BP to the transistor junction is shown conceptually, graphically, and then mathematically.

A theory is not complete without a way to test and develop it further. The last two papers fulfill this purpose. The first gives a mathematical proof for anti gravity. The second gives a physical proof, in the behavior of our own Solar System. The idea is not difficult: (1) gravity is known to be a wave; (2) all waves exhibit constructive and destructive interference; (3) anti-gravity is by definition destructive interference. Hence, gravity would have to defy all known laws of physics NOT to exhibit the property of destructive interference. I don't show how it can be achieved, only propose a mathematical structure that seems to have the potential of furthering our understanding of gravity in the context of Celestial Mechanics.

Finally, all of the above papers (except the Earth to Mars Trajectory optimization) paper are assembled into one formal paper, called The Inverse Problem of Celestial Mechanics in PDF format.





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© 2002 bill h. clark ii