Chapter 5 - THE UNIFIED FIELD THEORY

 The Shape of Time

To define time, the perfect shape must be explained. This shape is by all accounts, the most beautiful shape ever conceived and is used to define all particles. In this analysis of time, infinity is defined as a factor of Plank's Constant.

The hypothetical Wave motion gives a pictorial analysis of time based on spherical harmonics and the 99% probability curves of quantum mechanical atomic orbital theory. An Archimedean spiral groove (or path) of infinitesimal separation creates area in an otherwise circular record album (upper left). Time Normalization shows how these spirals are generated by the equations r = aƟ + ke.

To create volume in matter, first this continuous spiral groove of change (upper left) is extended to a spiral toroid forming a cylindrical groove (upper right). This cylindrical toroid is composed by infinitely wrapping the spiral to the left around a hollow space.

Secondly, the spiral toroid forms a spiral cone. This seashell logarithmic spiral differs in shape depending on frequency and direction depending on polarity. It must be clearly understood that the sine wave has a period based on π and not 2π. This cuts the sine wave in half-tones corresponding to the action(0-π) and reaction (π-2π) principle of physics. This seashell only depicts 1/2 of the sine wave (0-π). The second half is the inverse or reaction to the first half.

To understand the polarity, picture a reversible fan. The fan can be reversed by either changing the direction of spin or changing the slope of the blades themselves. By combining these alternatives, 4 possibilities of wave combinations exist, which can effectively define all matter and light via constructive or destructive interferrence.

Thirdly, the seashell of time (above) is the center of a hollowed sphere created by a Rhumb line (left) - which externally spirals to the top in a spherical toroidal path of time (Loxodrome). (NOTE: The rotation about the x-axis is shown so that the spiral shape can easily be seen, the actual rotation is about the y-axis).

It can easily be seen that one of these spheres, representing only 1/2 of the sine wave can equally explain contraction or expansion depending upon direction of spin. However, the ingenious beauty is in the fact that the paths creating these spheres are not actually lines but connected beads of these spheres.

Thus, go back to the first figures, and replace the lines with beads composed of the spheres depicted in the Loxodrome figure. And not only this, but when the beads composing the lines are analyzed, their lines are created in the same Loxodromic way - ad infinitum. The Shape of Time is herewith defined as an infinitely spiraled fractal, conical loxodrome.

The perfect shape is composed of infinitely many perfect shapes. Imagine a circle composed of circles or a sphere composed of spheres with an infinite regression. The equations depicting this configuration will be fractally composed and discontinuous by nature. Yet, by the nature of the logarithmic spiral an infinite regression exists in its very definition of continuity.

Not only is the shape unaltered as the size of logarithmic spirals increase they are also self-similar in that they are self-congruent under all similarity transformations (scaling them gives the same result as rotating them). They are also congruent to their own involutes, evolutes, and the pedal curves based on their centers.

The most amazing fact is that: Starting at a point P and moving inward along the spiral, one can circle the origin an unbounded number of times without reaching it; yet, the total distance covered on this path is finite; that is, the limit as ϑ goes toward -∞ is finite.

In a flat spiral or circle, only x and y coordinates change in time (with the angle Ɵ) and are related to the sine and cosine functions, but in the conical and spherical spirals (x,y,z) change with the angle Ɵ allowing the angular velocity, angular acceleration, and frequency to be expressed in terms of dx/dƟ, dy/dƟ and dz/dƟ (a dampened sine spiral).

An analysis of the polarization of time is shown in the figures to the left and right. The figure on the left depicts the overall motion of a photon (levels are spiraled and rotation is uni-directional about the y-axis).

Although light must compressed and expanded to form a wave, the rotational direction of compression and expansion are the same. This uni-directional nature of light creates ever increasing conical loxodromes and light is propagated by following this path of time in ever increasing logarithmic spirals. Light, therefore, can not have a density because it is ever propagating in an unimpeded fashion.

However, when The Light is analyzed, the gamma-ray frequency range of light will be shown to be equivalent to matter (minus the bi-directional collisions) and eventually will be shown to be ultimately responsible for gamma-decay in nuclear physics.

The figure on the right depicts the overall motion of a graviton. The seashell paths collide because of the alternate spins in the vortices giving rise to matter and density - by compression.

By viewing the cone in the center of the Loxodrome, it will be explained how a compression from a large volume, low density to a low volume, high density can be achieved - while still keeping the compressing forces united.

At the point where maximum density is reached (where the cone turns into the Loxodrome), the wave disperses or expands going back up to the top of the cone via the Loxodrome. Thus, 2 opposing compression forces are centered by the cones of compression and held together by the spheres of expansion.

The opposing motion of the gravity vortices can been seen in the Coriolis effect showing that hurricanes, tornadoes, and under perfect conditions even water down a drain will spin in alternated directions depending on hemisphere - counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

Although the direction of spin differentiates light from matter (at c3), in either configuration, the wave has wavelength, wavewidth, and wavedepth depicting 3 dimensions of change multiplying space by spiraling it to form volume and density in matter and energy and frequency in light.

 Dimension Concept Description 0  Nothing The MIND Stillness, Absolute ZERO 1- Length Roll = x-axis rotation Spin Clockwise or CounterClockwise, Wavelength 2  Width (Area) Yaw = y-axis rotation Spin left or right, Wavewidth 3  Depth (Volume) Pitch = z-axis rotation Spin Forward or Backward, wavedepth 4  Change linear, duration, motion itself (1/s) Spiral Wave propagation, velocity (m/s) 5  Variance (Activity - 1/s2) change in motion Wave Peak/trough, Acceleration (m/s) 6  Frequency (Field - 1/s3) recurrence in motion Wave Frequency/Transmission, repetition (m/s) ₯ - ALL Infinity The Speed of Light (c)

The advancement of science is limited by mathematics. It is impossible to define the shape of time without introducing the concept of Harmonic Quantum Fractalization. This process will explain many phenomena of the linear wave equation such as: why waves have fundamental frequencies and resonance based on Mass per unit length.

Any traditional wave form of arbitrary complexity can be described as a Fourier Series. Also, any traditional wave form can be fractally defined. However, some fractally defined waves can NOT be described as a Fourier Series. So what is a fractally defined wave?

A fractally defined wave is a wave in which various segments of the wave are defined using the wave definition with a integral scaling and rotation factor. Imagine the sine wave being defined differently between 0 and .01 with each .01 interval defined with the same equation (multiplied by a resolution factor and rotated by an angle).

Then imagine the points between 0 and .001 defined using another equation with each .001 interval defined with the same equation rotated by an angle. Although mathematically this process can be continued indefinitely, physically it is continued down to the size of the quantum.

Thus, the interval between 0 and quantum becomes the base frequency and equation. Not only is the scaling factor logarithmic in nature, but the progression of integral points are periodic in nature. And only specific integral values will accurately define wave nature. The resolution factors correspond to quantum, atomic, molecular and classical levels of perception.

For a smooth sine wave, each resolution would seemingly be defined by the sine wave itself. This exists at the classical level, but at the atomic and molecular levels, each particle undergoes an additional minimal rotation in a direction at an angle to the wave propagation.

If a water wave were viewed, the water itself would rise and fall according to a wave function, but the actual water molecules rotate in an oval or circular motion 180 degrees to the wave propagation. Thus, at the molecular resolution, the fractal wave function has a different definition.

However, it can be shown that each wave has a quantum origin defining the basic quantum fluctuations, which are fractally expanded to the atomic, molecular and classical levels of resolution to generate the overall motion.

And these quantum fluctuations are specifically definable in an equation that relates mass to light and equates to a harmony of the mass per unit length correlating wave velocity to resonance.

As a note: the fractalization of time is being worked out. A fractal has the unique properties of being continuous everywhere yet differentiable nowhere.

To totally normalize time, motion must be defined differently. The derivative is viewed as a small change in position with a corresponding small change in time (each change approaching 0). However, by using time as a constant and providing recurrence relations or equations, time in deed becomes normalized.

To picture this, view a 30 frames per second movie camera. Time is constant. Assuming a quantum displacement, called Δh; a recurrence equation defining constant velocity will be: Δh -> Δh + k where k is a constant. This is merely stating that with each frame, the distance traveled is constant.

Now, picture an acceleration - with each frame the distance traveled will increase resulting in a recurrence relation: Δh -> nΔh + k where n is an interger factor greater than 1 for acceleration. NOTE: since nΔh is the quantum, only interger factors of nΔh are possible.

The mathematics of this must be worked out. However, something very exciting is happening with recurrence relations that will undoubtedly prove Fermat's Last Theorem. I.e. the square root fuction will have a recurrence relation based on integer values and the values must explode beyond the exponent of 2!

By toying with the Δh recurrence equations using a circle; concentric compression and expansion diffraction rings can be factorially defined. And by using linear or parabolic relations acceleration and frequency become definable.