We know the relationship between matter and energy and it's described by Einstein's famous mass-energy equation. One way to differentiate the two as alternate manifestations of the same underlying principle is that particles of matter exist in space and propagate through time while EM energy exists in time and propagates through space. Together, matter and energy coexist in a manifold known as space-time, where the space and time components, and hence, matter and energy, are inextricably linked through the speed of light, which leads us to the famous equation, E = mc**2.
EM energy propagates through space at the speed of light, and can be described by well known physics and mathematics. It's perfectly described by Maxwell's equations which have been known for well over a hundred years.
Matter appears to propagate through space through another well known mechanism called orbital mechanics, which is governed by gravity, and which has been studied since Issaic Newton's encounter with an apple.
During the last century, space and time were linked through Einstein's Theory of General Relativity. This led to a dramatic re-understanding of gravity when it was concluded that space-time, in the vicinity of matter, tends to become warped and demonstrates a verifiable curvature. Furthermore, we know that EM energy, by virtue of its tendency to want travel along the shortest path through space-time, is affected by this curvature. The crux of General relativity is a very simple equation with profound implications. It states that the curvature tensor, G and the stress energy tensor, T are equivalent. In simplified terms, it's just G = T, where G is a measure of how space-time is curved and T is a measure of the energy passing through it.
The linkage to gravity results from considering orbital mechanics as matter following the path of least resistance through space-time. The curvature of space-time associated with the matter in the Sun warps space in such a way that the path of least resistance for any nearby matter in the same inertial reference frame as the Sun is an orbit around it. The fact that this orbit circles around back on itself means that the net propagation of matter through space is zero, resulting in a intrinsic propagation only through time. Another way to consider matter as propagating through time is to consider each particles history back to time zero. Each particle can trace its existence, all the way back to when matter first condensed out of the primordial soup resulting from the Big Bang. Most particles have changed very little since then.
The periodic nature of orbits is directly related to the periodic nature of EM energy in that they are both described as simple harmonic motion with periodic behavior in both the spatial dimensions and the time dimension. One difference is which dimension is involved with propagation. In the case of energy, propagation is through space (the Poynting vector), while for matter, propagation is through time (the Arrow of Time). Another difference is the frequencies involved. The frequencies of EM energy are generally considered to start at a few hundred KHZ. Considering the gravity perturbations of an orbit will result in frequencies on the order of cycles per year rather than millions to trillions of cycles per second of EM energy.
While our understanding of gravity has changed significantly, it's important to remember that all of the old mechanics still apply and in fact can be derived from the newer theories. Being able to derive old theories from new ones is one of the most important tools for validating new theories.
The biggest single problem with General Relativity is that it doesn't mesh very well with Quantum Mechanics. Conversely, the biggest problem with Quantum Mechanics is that it doesn't mesh very well with General Relativity. Both are supported with many compelling arguments and experimental data and both are generally accepted as validated theories. We have been conditioned to believe that General Relativity describes the cosmos while Quantum Mechanics describes its constituent parts (protons, neutrons etc.).
One thing that General Relativity theory does not specificly address is whether matter is a consequence of curvature or if curvature is a consequence of matter. Either interpretation is equally valid since the relationship between matter and energy is a strictly causal one. The general consensus is that curvature is a result of matter. This is largely a result of our being able to directly perceive matter. Curvature is harder to see, and even harder to think about, even though it's something that can be measured. CTE requires thinking about matter as a consequence of curvature, but to get there, we can start from a more traditional perspective.
If matter curves space, then even the tiniest components of matter, sub-atomic particles, must curve space as well. The net curvature of a large collection of particles is the sum of the curvature contributed by each individual one. Since curvature is associated with sub-atomic particles and we know that packets of EM energy can be both absorbed and emitted by collections of such particles, there must be a more fundamental connection between curvature and EM energy. Since EM energy is associated with charge and electric fields, there must also be a relationship between curvature and charge. Identifying these relationships is what a Unification Theory is all about.
The biggest single thing that's missing is the identification of the basic building block from which everything is constructed. Since charge, matter and energy are so intimately intertwined, there must be something at the core of their existence that they share. The most compelling reason for this is the annihilation of matter with its anti-matter twin, which results in 2 photons, each with the energy given by E = mc**2, where m is the mass of one of the particles. This alone is a compelling argument that charge, matter and energy are made out of the same stuff.
The basis of CTE is that everything is comprised of the same stuff. This stuff is curvature and two new concepts are required in order for this representation to work. Individually, each concept is quite compelling in its own right. Fully integrated with existing theories, they will usher in a new understanding of the universe and could lead to the development of some far reaching future technologies.
The first new concept is the notion that space-time opposes curvature. This is not all that difficult to accept and is supported by circumstantial evidence. First, we know for sure that curving space-time is a difficult and energy intensive task. The relation E = mc**2 clearly illustrates that the magnitude of the energy required to curve space is very large. The curvature associated with just a gram of matter is equivalent to 6E15 joules, or about 25 million kilowatt hours. What makes this easier to accept is that it can be shown that a resistance of the Universe to curvature manifests itself in the same way as gravity. This idea is nothing really new, just an reinterpretation of something old.
The second new concept is that curvature must be conserved. That is, for all positive curvature that exists, there must be an equal and opposite amount of negative curvature. This arises from the fact that space-time is so difficult to curve. About the only thing with sufficient energy density to sustain a region of curved space, the magnitude of that associated with a sub-atomic particle, is another region of equal and oppositely curved space for it to push against. Given the magnitude of the energies involved, particles would otherwise squash themselves out of existence or spread away to nothing unless something keeps the curvature in check.
The implication of these two concepts combined is that if a region of curved space were spontaneously created, an equal and opposite amount of oppositely curved space would result as space-time squashes the original curved space out of existence. This would in turn create more curved space as this oppositely curved space is subsequently squashed out of existence. The speed at which this propagation occurs is the speed of light. Again, this is nothing new and is indirectly described as electric and magnetic fields obeying Maxwell's equations.
What would a particle comprised of both positive and negative curvature look like? Consider a spherical region of negatively curved space comprising the inside of a particle which is equal and opposite to the curvature imposed on space-time on the outside of the particle. For a collection of particles, only the positive curvature on the outside will be apparent. The negatively curved space-time on the inside of any particle will never be coincident with the negatively curved space-time of any other particle as those 2 particles will never occupy the same point in space-time. In effect, this 'inside' curvature is shielded by the boundary of zero curvature separating the inside and outside curvature. However, the positively curved component on the outside of each individual particle will overlap with the components contributed by all of the other particles and additively contribute to the net curvature of the system. This is exactly what we observe.
A photon, and EM energy in general, consists of equal and opposite amounts of positive and negative curvature propagating through space. This is also consistent with what we observe. Photons exhibit zero mass and hence have no net curvature or gravitational field. Yet, photons are still influenced by the ambient curvature. This is a result of local, time varying, non-zero curvature fields within the photonic packet of energy. This also results in a valid conservation theory for the photons resulting from the annihilation of matter and anti-matter.
This description of a photon is consistent with the conclusion that the intrinsic rate at which curvature can propagate through space-time is the speed of light. This is also consistent with the general description of all EM radiation, including planer RF energy, as being organizations of curvature.
Attempts to quantize space-time all suffer from the same problems. Such attempts include mechanical representations of the Universe and any representation which requires energy independently locked up in the fabric of space-time.
These problems fall into 2 classes. First, the quantum can not be made small enough and second, the expansion of space-time dictates that new energy arises as space-time expands.
Quantization limitations are very apparent when it comes to gravity. While we observe gravitational effects as a macroscopic phenomenon, it's really just the sum of the effects from all the individual particles in a system of interacting particles. This is crucial since each particle is independent of each other and the effects of relative positions between them must be propagated. This means that at the particle level, the effect of each must be independently transferable, even at intergalactic distances.
By way of example, consider the interaction of a pair of Hydrogen molecules in a weather balloon whose diameter is just 1 meter. The gravitational attraction between 2 molecules a meter apart can be computed as about 10E-63 newtons. If one molecule changes its position by 10E-10 meters (about an atomic diameter), the change in force is about 10E-83 newtons. Already, this is too small to be adequately transferred as a basic quanta. If quantization doesn't make sense here, how can it possibly make sense at galactic or intergalactic scale distances?
Energy arguments are also not easily explained. If tremendous amounts of energy are locked up in the fabric of the Universe, either by virtue of a mechanical aether, zero point energy, or other mechanism, where does the energy come from to create new space-time as the Universe expands? Even arguments that claim space-time doesn't really expand can be discounted as it can be easily shown that it is for no other reason than the progression of time, space-time is expanding.
Space-time is quantized, but not spatially or temporally. Its quantization is more virtual and simply a consequence of the quantization of the particles and photons within it. There is no need to impose a additional level of quantization to the fabric of space-time. Considering the quantum of space-time to be a unit of curvature, which acts over all space time, provides for particle scale quantization while still maintaining galactic scale continuous behaviors. The CTE notion of space-time is that it's a consequence of curvature and the passage of time, and not a container of curvature as is often considered.
If everything is made of of equal and opposite amounts of positive and negative curvature, anti-matter would have all of its negative curvature on the outside and positive curvature on the inside. This would imply that anti-matter will have negative gravitational mass. However, this doesn't violate any current physics since from an inertia point of view, CTE based matter and anti-matter are identical.
Inertial mass and momentum are strictly properties of the interaction of the boundary between the opposite curvatures on the inside and outside of a particle and the ambient curvature along this boundary. This boundary is called the Surface Of Equilibrium, or the SOE, and has other important properties as well. All of the motion of a particle can be described as interactions between the SOE of a particle and the ambient curvature along it.
The curvature function associated with an uncharged particle of matter would be sphericly symmetric and could be described as a simple magnitude as a function of radius. This magnitude would have its maximum negative value at the center of the particle and its maximum positive value at a point away from the SOE at a distance on the order of magnitude as the distance from the SOE back to the center of the particle. At the SOE, the curvature would be zero and as you get infinitely far away from the particle, the curvature will fall off to zero.
Treating a particle as a surface has other useful consequences. It makes the singularity associated with particles and General Relativity disappear. Many of the problems relating General Relativity with Quantum Mechanics arise from the curvature becoming infinite in the immediate vicinity of a particle. With CTE, the curvature function and its derivative are well behaved in this critical region. CTE brings the 2 theories into agreement by considering the surface of space associated with an SOE as occupying only a single point in time.
Consider an SOE with time varying components. For example, consider a particle whose SOE pulsates like an expanding and contracting balloon. Such a motion could be set up as a result of the constant fight between the positive and negative curvature as they strive to establish equilibrium combined with the finite speed of light which bounds the delay between when one side of a particle notices an external change and when the opposite side does. This gives charged particle attributes found in both matter and energy. That is, its curvature function contains both a static component and a dynamic component.
As a result of a vibrating SOE, there will be a dynamic component of curvature emanating away from the particle superimposed on the static curvature associated with its mass. If this vibration is asymmetric in time, for example, the curvature is increasing for 1/3 of the time and decreasing for 2/3 of the time, opposing forces will arise between particles with the same asymmetric behavior and attractive forces will arise between particles with opposing asymmetric behavior. This is consistent with the fact that like charges repel and unlike charges attract and is consistent with the notion that like masses attract. The nature of a dynamicly varying SOE is also consistent with the concept of isospin which is a crucial component of Quantum Mechanics and the Standard Model.
Note how that when an SOE is vibrating asymmetrically like this, in one case, it will end up on average a little more in the future and in the other, a little more into the past, than it would be if it were static. This is also related to the phase of the curvature which is a measure of where an SOE is in time, relative to where it should be. The force of charge can be thought of as the force that keeps the arrow of time in sync.
The force of charge is much greater than the force of gravity for 2 reasons. First is because of the relatively high local slope of the curvature at the SOE. This acts in the much same way that a linear amplifier acts to turn a small signal into a much larger one. Second is the periodic nature of the time varying curvature function and its high frequency. Since forces are a result of changes in curvature, each cycle of the periodic component contributes independently towards the total force attributed to it. The greater this slope is, and the higher the frequency of the periodic function, the larger the difference between the force of charge and the force of gravity will be. Quantifying this slope leads the charge to mass ratio of an electron. The asymmetries in the dynamic component of curvature are due to the non linear nature of the slope at the SOE, that is, the difference in the slope at the SOE, between the SOE and the center of the particle and the SOE and a point away from the particle.
First, consider how the apparent force of gravity arises in the first place. Lets start with a sphericly symmetric curvature function and associated SOE with no time varying component (an uncharged particle). In the presence of an external curvature field, one side of the SOE will experience a higher ambient curvature then the opposite side. At the SOE, the slope of the curvature function resulting in the particle will be much greater than the slope of the ambient curvature (unless we are near a black hole) and will be greater towards the inside of the particle than away from the particle.
Assuming space-time opposes curvature, we can analyze what would happen across the SOE as a result of space-time wanting to squash out any curvature. Since the particle has equal amounts of positive and negative curvature, there is nothing that space-time by itself can do which will make the curvature associated with the particle go away. Instead, the net result will be an apparent force affecting motion of the particle through space.
particle
center /
b .. V /
-------------+------/-------- line of zero curvature
./. a (relative to the particle)
/
The ambient curvature can be considered linear, but the curvature
resulting from the particle is not, at least in the vicinity of the SOE.
The larger curvature towards the inside of the particle at point 'a' will
drive the particle towards the left (the direction of greater ambient
curvature) by an amount greater than the curvature at point 'b' will drive
it to the right. The result is an apparent force pushing the particle
towards the source of greater curvature. The leading edge of matter is not
pulled by gratity, as is commonly believed. What really happens is the
trailing edge is pushed towards the center of the particle by an amount
greater than the leading edge is pushed towards the center, resulting in an
apparent pull. CTE describes all apparent forces as differences in the
push along the SOE towards the center of the particle.
The strong nuclear force is also a result of the high local slope of the curvature at the SOE interacting with the high local slope of the SOE of a different particle and the magnitude of this force is relatively large for the same reason that the force of charge is so much greater than the force of gravity. It's ironic that the strongest and weakest forces, the strong force and gravity, are a result of the same static component of the curvature function. Similarly, the weak force can be described as the complementary behavior of the dynamic component of the curvature associated with charge in the vicinity of the SOE.
Electrons can be considered photons in orbit around themselves. The difference is that this 'photon' has more curvature than anticurvature. It's this curvature imbalance that influences the geodesic this photon follows. In effect, it's affecting its own path into an orbit around itself.
For a photon, the curvature and anticurvature cancel and there is no inertial mass. In contrast, the electron has unequal amounts which results in an effective inertial mass proportional to the difference between the two. The close connection between photons and electrons provides a convenient basis for photons to act as carriers of kinetic energy acting on the effective inertial mass into and out of orbiting electrons.
This also illustrates how charge can be thought of as a local violation of Conservation of Curvature. Globally, conservation of charge insures that curvature is ultimately conserved.
Since antimatter has negative gravitational mass, the first inclination is to consider that it would be repelled from matter just as like charges repel each other. However, the reversal of the arrow of time, with respect to antimatter, results in an apparent attraction between matter and antimatter, at least from our observational reference frame.
The Theory of Dimensional Evolution provides the second explanation which is in the way the Universe evolved. It describes how it ping-ponged between a matter Universe and an anti-matter Universe, and ended up as a matter Universe. All the anti-matter in existence was created by mechanisms other than the Big Bang.
Organizations of curvature are not limited to spherically symmetric particles and cylindrically symmetric photons. Other organizations are possible included ones with inertial mass but no gravitational mass and classes of differently symmetric organizations associated with quarks and the ring like organization of neutrinos. A neutrino has the same SOE as a photon, but has a different organization of curvature around it. Of course, in all cases, some kind of circular symmetry is expected to be present. Perfect symmetry is not required in order for everything to fit within the model and exotic combinations with directional mass and other bizarre combinations are possible.
Organizations of time varying curvature are not limited to have sinusoidal time varying components either. Thermal energy, the Cosmic Background Radiation would be associated with random, asynchronous time varying curvature components.
Curvature functions need not be monotonic. This includes both static and dynamic components. A bimodal curvature function offers an answer to the nature of Dark Matter. For example, if the curvature presented by the galactic central black hole had a second, smaller peak in the space surrounding the galaxy, the galaxy can be described as being contained within a gravitational potential well associated with its central black hole. Such an organization of curvature could arise if galaxies started out as galactic mass balls of primordial gas, whose gravitational influence was preloaded into the Universe after inflation. If these balls of gas collapsed very quickly to form the central black hole, they would leave a gravitational potential well in the wake of its collapse. Quasars are observations of this collapse whose ejecta comprises the galaxies star systems.
If the time varying components of curvature for a system of particles are phase synchronous with each other, interesting behaviors can arise. Ordinarily, the frequency of the dynamic curvature component associated with charge is a constant, so in virtually all cases, the dynamic components will be period synchronous. However, the phase will be completely random.
If the phase of all of the time varying components of curvature in a system becomes the same, portions of the SOE's of different components can start to be shared. This would give rise to apparent 'single particle effects' arising from a collection of particles. This is something that happens to a limited extent within crystal lattices and to a larger extent in superconductors, superfluids and other 'quantum' states of matter.
The SOE is something that can be seen in higher order collections of particles. At the most primitive level, a particle has a SOE. The next level up, an atomic nuclei has an SOE of its own. The next level of SOE is that associated with an atom. While an atomic nucleus and an electron have their own SOE's associated with them, the combination of the 2 results in an SOE for the atom as a whole. The diameter of the SOE for an atom is on the order of the diameter of the electron shells of an atom. The next level above this is the SOE for a molecule. This is the combined SOE of the atoms comprising the molecule. The atoms in a crystal lattice share an SOE with each other as well.
The most important force in driving the development of this hierarchy of SOE's is the propensity for an SOE to seek the most perfectly spherically symmetric shape. Another way to look at this is that the area of the SOE will want to be minimized. For particles and atomic nuclei, both of these driving forces are quite clear. For atoms, where the SOE is significantly larger than that of the constituent components, the minimum area concept is harder to realize until you consider that the area that's minimized is the composite SOE, which includes the effect of the electrons, and not just the SOE of the nucleus. The actual SOE of an atom lies somewhere between the last orbit of electrons and the nucleus. For atoms with multiple shells of electrons, there are several local SOE's, one per electron shell. From outside the atom, all that we can see is the outermost one since it effectively hides the inner ones. This is consistent with observed chemical behavior where all interactions take place at the outermost shell of electrons.
For molecules, we need to think a little differently. If the SOE of a noble gas can be considered a perfect sphere, the SOE of a +1 valence atom can be considered a perfect sphere with 2 lumps, oppositely opposed along its surface. The SOE of a -1 valence atom would be a sphere with 2 depressions, also oppositely positioned on the surface. When analyzed in terms of 'surface area' and enclosing volume, the depressions are equal and opposite to the bumps. The combination will be 2 intersecting spheres which has less surface area than the 2 original atomic SOE's. Note that the SOE still occupies the regions within the molecule and not just the outside of the composite molecule.
For crystal structures, the SOE is shared among all of the elements in the lattice. For doped crystals (i.e. semiconductors), an N-type semiconductor has a composite SOE with little bumps, similar in principle to that of a +1 valence element. Similarly, P-type semiconductor material have little depressions in the composite SOE.
One potential consequence of this theory is that there should be a lower energy way to initiate fusion. Normally, fusion is initiated by bringing ionic forms of atoms close enough together to overcome the electrostatic repulsion and get the nuclei to fuse together. This requires tremendous energy and is compounded by the fact that the SOE of an isolated nucleus is quite small. It should be possible to initiate a fusion reaction by bringing an ionic form of an atom in close proximity with a non ionic form. When an atom is surrounded by electrons, its SOE is larger, this making it an easier target than an ion. Bringing ions close to non ionic forms is easier since there is no electrostatic repulsion between the 2 organizations of curvature.
Another consequence is that, based on the relationship between static and dynamic curvature, it should be possible to construct static curvature fields with specifically crafted EM energy. If a specific collection of standing waves were assembled, it should be possible to increase the local curvature in one direction while decreasing it in the opposite direction, thus maintaining the same total curvature. If you could 'fall' in this local curvature field, and carry the field generator with you, a non chemically based propulsion system would result.
(C) 1997-2004 George White, All Rights ReservedCTE Home, Doc map