The First Law of CTE describes this property as the opposition of the Universe to curvature. Part of the proof of CTE shows how this manifests itself in a way that is indistinguishable from gravity. In addition to converging to classical theories, including General Relativity, CTE provides a different context in which to view other theories and processes without breaking them. One unique divergence is the chain of events suggested for the very early Universe.
The Second Law of CTE states that curvature is the most fundamental form of existence and that all charge, matter, forces and energy can be described by mathematical functions describing this curvature. Such representations of curvature are far more complex than would be required to satisfy just the considerations of gravity. They have a magnitude, a phase as well as static and dynamic components. The static components are responsible for gravity and the strong force, while the phase relationships of time varying components are responsible for charge and the weak force. Mathematically, this curvature can be represented as a vector with real and imaginary parts and manipulated with ordinary complex arithmetic. As the distances get large, relative to the size of particles, this quantification of curvature becomes the same as that suggested by General Relativity Theory.
The consequence of these two laws is that all forms of existence can be completely quantified as wiggles of space-time and how the Universe reacts to those wiggles. These wiggles can be expressed as functions of space-time called 'C functions', whose value at any point in space-time is related to the curvature presented to the Universe by the source of the wiggles.
Ordinarily, curvature is quantified through the application of non-Euclidean geometry where forces act along straight lines in curved space-time as opposed to curved lines in conventional flat space-time. Even with CTE, this is perfectly adequate as long as the distances involved are significantly larger than elementary particles. The complication of CTE is that curvature also has a phase, which is a representation of the phase difference between time and space. In positively curved space like the observable Universe, space is lagging time, while in negatively curved space, i.e. the future, time is lagging space. The speed of light sets the relationship between time and space and the absolute reference of this phase relationship is time zero when the Universe first arose. With CTE analysis, C functions describing some form of existence act on other C functions and the effect of curvature is embodied in the C functions themselves and not the 'fabric'. In CTE theory, the fabric of space-time is a consequence of curvature and not a container of curvature as is usually considered. However, this only matters at dimensions on the order of the size of elementary particles and perhaps around black holes.
Equipotential surfaces of C functions, or the contours where the value of the function is the same, exist and are continuous functions of space and/or time. The equipotential surface whose value is 0 has a special name, the Surface of Existence or SOE. The SOE separates existence into 2 components, one where space is ahead of time and another where time is ahead of space.
From the perspective of the arrow of time, the SOE defines the present and separates the past from the future. Each particle, or other manifestation of existence, has a unique arrow of time, which when combined into a system of gravitationally related, uncharged matter, are all more or less in sync. Macroscopic time is the average of time for all particles. An implication of the future being on the inside of a SOE and the past on the outside is that red-shift and the observed expansion of the Universe originates from within the Universe itself, is not the result of a kinetic expansion, but simply a consequence of the passage of time observed across large distances.
Even though space-time originates from particles, particles in a gravitationally related group of particles do not just fly away from each other as the space between them expands. The reason for this is that all of the SOE's in a group of related particles are in exact time sync thus their relationships to each other remain constant. Its only when time gets out of sync that particles start moving to or from each other. When time is ahead of space, a positive charge results and when space gets ahead of time and a negative charge results when time gets ahead of space. CTE describes Conservation of Charge as the mechanism which keeps the time arrows of gravitationally related particles in step with each other.
A property of an SOE is that it's the attribute of a particle, photon or other form of energy that can trace its ancestry all the way back to the instant of time when the Universe first arose. At time zero, the Universe was flat and the zero curvature at time zero linearly maps to all of the SOE's that currently exist. In a way, the SOE can be thought of as a projection of this pre-Universe nothingness into existence in our observable 4-dimensional space-time. From an equilibrium point of view, the present and the pre time nothingness that preceded the Universe are the same. The present is represented by the net effect of all SOE's that exist, where each is an echo of the nothingness from which the Universe arose.
One significant implication of the properties of an SOE is that all forces acting on a particle can be describe as the effect of relative changes in the ambient curvature integrated across an SOE. This gives rise to a mechanism which can describe all forces uniformly.
The Third Law of CTE states that curvature must be conserved and that this is the number one constraint which must be applied to all C functions and systems of C functions. A C function can then be quantified as an amount of curvature and an equal and opposite amount of anticurvature, separated by an SOE. Mathematically, the magnitude of curvature is positive and the magnitude of anticurvature is negative, such that the sum is zero. The difference between them is that curvature only exists only in the past and anticurvature exists only in the future. Existence itself is the sum of the past, the future and the present. Anticurvature doesn't actually exist very far into the future. For example, in a photon, it never needs to be more than about 1/2 of a Compton period ahead.
Conservation of Curvature is the fundamental principle which forms the basis for all other conservation laws. Conservation of Curvature also prevents the First Law from simply snuffing out the existence quantified by the Second Law and is what drove the inflationary period of the early Universe. The nature of curvature and anticurvature is that the attempted cancellation of one with another is what results in the arrow of time.
To fully understand CTE, a small change in the thinking about the nature of space-time must be made. CTE considers space-time a consequence of existence (curvature), rather than a container of existence. Consider that space-time is just the recorded history of all existence in the Universe. The entire EM history of our star system exists somewhere out there in the fabric of space-time, as does that of every other star system in every other galaxy. CTE shows how EM energy is congruent to curvature wiggles, thus the entire curvature history of the Universe exists somewhere in the fabric of space-time. Another way to think about this is to consider that our perception at the scale of a foot, represents 1 light nanosecond away, but as a record of history, is no different than being 1 light year away, except for how far back the recorded events occurred.
Macroscopicly, C functions often exhibit perfect spherical symmetry. At the scale of individual particles and photons, C functions always exhibit some sort of perfect radial symmetry. These radial symmetries can be taken advantage of to further simplify the math. Perfectly spherical functions of space can be represented with just a single spatial dimension, the radius, and represents an equipotential surface. Most C functions can be represented with only 2 dimensions, one corresponding to space and the other to space-time with an origin at some arbitrary point in space-time.
A photon can be represented by a C function comprised of equal and opposite amounts of curvature and anticurvature where the dimensions of the curvature fields are on the order of the photons wavelength. At a specific instant in time, the SOE of a photon is a spiral line in space. As time progresses, the SOE traces out a spiral path along a perfect cylinder in space-time, whose diameter and pitch is a wavelength. This can also be represented as a 2-dimensional function, only instead of radius as the spatial ordinate, the angle of Poynting vector, or direction, is used. Notice how photons represented as an SOE have characteristics in common with radio frequency transmission lines. Planar EM energy and other forms of energy also have corresponding curvature representations.
Particles of matter are organizations of curvature where the curvature is on the outside and the anticurvature is on the inside. The SOE is a sphere whose radius is on the order of the size of the particle. More precisely, this radius is the distance at which the strong force crosses through zero.
An important property of the SOE is that it occupies a single point in time, but a surface in space. Ordinarily, a point in space corresponds to a point in time. Another point in space, dx away, corresponds to another point in time, dt away, where dx/dt is the speed of light. An SOE can be thought of to arise as an organization of curvature stretches a point in space-time to one where a surface in space corresponds to a point in time. As a result, dt for points along an SOE goes to zero. This is what manifests itself as the singularity often associated with particles and provides a foundation for deriving QCD from curvature considerations. Specificly, the Heisenberg Uncertainty Principle is a direct consequence of this property.
The enclosing nature of the SOE of a particle (as opposed to that of a photon), is what results in inertial mass. The anticurvature associated with matter is isolated from the rest of the Universe by its SOE. The curvature on the outside of the SOE overlaps with that from all other particles resulting in the much larger net curvature that we can observe and measure. This overlapping curvature on the outside of all SOE's is the curvature associated with gravitational mass. The isolation of the anticurvature, which effectively must push curvature out of the way when it moves through space, is responsible for inertial mass. This also predicts that antimatter (where the curvature is on the inside and the anticurvature is on the outside) will have negative gravitational mass but will have the same positive inertial mass as its matter counterpoint.
Charge is a result of dynamic component of C functions resulting in a net phase difference between space and time. This time varying function is asymmetric and a complementary asymmetric function is the basis for an opposite charge. The time varying function and its asymmetry is a consequence of a local violation of Conservation of Curvature which is what the force of charge attempts to overcome. The combined C functions of a positive charge and an equal negative charge restores Conservation of Curvature. From an SOE perspective, charge can be thought of as an SOE which asymmetricly is varying between being ahead and behind relative time. The frequency of the time varying component is the Compton frequency. This frequency is a resonance point in the Universe, left over from the Big Bang, where the intrinsic opposition to curvature is in equilibrium with the speed of light.
An electron can be considered as a photon with 2 parts curvature and 1 part anticurvature. Whereas in a photon, the SOE traces out a cylinder, in an electron, it traces out a sphere. This is a result of the curvature orbiting itself owing to the asymmetry. An electron is really a photon which violates Conservation of Curvature, and instead of following a straight line in space-time, follows an orbit enclosing a volume of space-time. The asymmetry results in ripples of curvature originating from the electron which manifest themselves as charge in much the same way as static curvature manifests itself as gravity. This relationship between photons and electrons is why it is so easy for photons to transfer energy in and out of organizations of electrons.
A positron would have 2 parts anticurvature and one part curvature. This would have the same inertial mass as an electron, but would have negative gravitational mass. This is why a positive charges must be superimposed on particles with mass. Note that the implication is that antimatter has negative gravitational mass, but has positive inertial mass. The definitive experiment to prove this theory would be to measure the gravitational mass of antimatter, however, this is easier said than done since when antimatter is created, it generally has large amounts of kinetic energy which is a function of its inertial mass and hard to separate from gravitational effects. However, there is circumstantial evidence that antimatter in a trap will fall towards earth, which owing to the reversal of time for antimatter, is what we would expect to see.
A proton can be described as a particle whose SOE also has both a static component and a time varying component. This SOE can be conceptualized as the surface of an inflated balloon whose temperature is varying very quickly. It will appear to inflate and deflate, as the temperature rises and falls, but will always contain the same amount of air. This would result high frequency ripples in the curvature superimposed on the static curvature associated with the protons mass. These ripples are complementary to those of the electron.
The SOE of a neutron is more like a balloon in a constant temperature environment. While the SOE of a proton is relatively rigid, the SOE of a neutron is more like a soap bubble. The only constraint on a neutron is that the volume enclosed by it must be constant. If poked on one side, the shape will deform such that the volume enclosed remains unchanged. This provides a C function which flows to fill in the gaps when multiple protons are brought together within an atomic nuclei.
Within an atomic nuclei, the time varying components of all of the protons are phase synchronized with each other and the neutrons flow into the spaces between the protons as they pulsate in sync. The net result is a single, larger C function representing the nucleus, which has the same dynamic characteristic as a single proton, except that its magnitude is proportional to the number of protons contained within it. Within an atom, the time varying components of the nucleus and the electron cloud are also perfectly synchronized.
Macroscopicly synchronized dynamic components of C functions, combined with the representation of an SOE as being a single point in space-time, provides a convenient mechanism to explain things like superconductors, superfluids, tunneling and other quantum effects.
An important property of an SOE is that all forces acting on its C function can be quantified by differences in the rate of change in the Local Ambient Curvature, or LAC, across its SOE. The LAC is the sum of all other curvature functions outside of the SOE, that is, the curvature presented by the rest of the Universe. If the LAC is greater on one side of the SOE than it is on the other, the SOE will fall towards the side with the higher LAC resulting in movement through space-time and apparent forces. All forces can be thought of as manifestations of the Universes intrinsic opposition to curvature. Note that even though the SOE represents only one point in time, it occupies space and that the curvature presented by the rest of the Universe will be different across the SOE in both time and space.
Charge is a more powerful force than gravity largely because each cycle of the periodic curvature function responsible for it contributes independently to the total force, thus the force of charge is proportional to the frequency of this periodic function. In macroscopic systems of units, like MKS, greater apparent differences in force arise owing to the arbitrary nature of the units of charge, mass, space and time with respect to each other. A third possible factor is that the effective resistance to the phase of the curvature deviating from zero may be larger (by a factor of 1/a) than the the effective resistance to changes in its magnitude. Gravity can be considered weaker as its computation involves particles being pushed from both sides towards the center, with the net result arising from one side pushing a little harder than the other owing to a slightly different LAC.
The three laws of CTE are summarized below.
The First Law:
The Universe presents an intrinsic opposition to curvature.
The Second Law:
Curvature is the most fundamental form of existence.
The Third Law:
Curvature is conserved.
When taken together, the First and Second Laws would imply that the nature of the Universe is to oppose its own existence. Only when the Third Law is introduced is there a basis to keep the Universe from snuffing itself out. The notion that there is a counterbalance to curvature allows an alternative equilibrium to exist, other than the original equilibrium of nonexistence. Of course, the initial state of nonexistence must also fit within the laws. The most significant difference between these two equilibrium states is the nature of time. In the initial equilibrium state, time randomly fluctuates around zero while in the final state, time marches on. The transition between these 2 states is described by the Theory of Dimensional Evolution.
(C) 1997-2004 George White, All Rights ReservedCTE Home, Doc map