Next, conforming C function solutions are identified which represent various forms of existence and through the application of the Equivalence Principle, are shown to be valid models of this existence. From this, C can be shown in the limit as distances get large, to look and behave exactly like classical curvature as described by GTR, hence the designation of 'C'. The generalized C functions are more complex than ordinary curvature and are comprised of static and/or dynamic components with a magnitude and a phase.
These three properties, restated as laws, comprise a theory called CTE, or the Curved Theory of Existence (aka. Curvature Theory of Everything). The only 'new' physics required is the reinterpretation of space-time curvature as the core of existence and not an independent consequence of it. The most remarkable thing about this theory is how it can change everything without breaking anything. Unlike other guesses about the nature of unification, this one can be proven mathematically, starting with the energy equation for a photon.
CTE suggests that dark energy may be quantified as a consequence of time and is the complementary reaction to the space-time created as the Universe expands. Imagine a line, extending back to the beginning of time, through the history we observe when looking out into the Universe. Bisect this line to divide the apparent history into 2 pieces, representing equal amounts of elapsed time since the Big Bang. For the first half, more time has elapsed since the observed events have occurred, so we would expect photons from more possible places to have caught up to our viewport into the Universe (the imaginary history line). The first half will appear to have more history recorded in it than the second half, giving the illusion that more time has elapsed during the first half than during the second half. When reconciled against red shift, the expansion of the Universe would appear to be slowing down during the first half (more recorded history is evident) and speeding up during the second half (less recorded history is evident). This is exactly what we observe and attribute to Dark Energy.
Yes and no. While the fabric of space-time doesn't appear to have any dimensions beyond the 4 that we know of, it certainly may be modeled as having more. One possibility, consistent with CTE, is that the 'extra' dimensions represent the future while ordinary 4-dimensional space-time represents the past. For particles, the extra dimensions only exist on the 'inside' of the particle and are complementary to the dimensions of space-time on the 'outside'. Owing to the perfect symmetries of particles, only 2 'inside' dimensions are needed, one which is the complement of past time and another which is the complement to the radius of the SOE. CTE defines the relationship between space and time as being dynamic and that space lags time in the past and time lags space in the future. In other words, all of the time that is yet to come is contained within a particle and all of the time that has already passed is on the outside and the boundary between the two defines the present. However, it doesn't appear that the math required to describe CTE actually requires extra dimensions, in fact CTE appears to work all the way down to a one dimensional Universe, which has inspired a unique description of the early Universe.
There is a multitude of other ways to model the fundamental stuff that comprises existence and the inverse of the Equivalence principle would seem to imply that if there were a unifying mechanism, it could be described in many different ways, each of which converged to similar results at various limits. It's easy to see that as dimensions are added to a specific mathematical representation of a unifying concept, the extra degrees of freedom will provide better correspondence and even an exact correspondence if the model is sufficiently close to reality. However, this doesn't necessarily mean that those dimensions actually exist and the correct unifying approach would be the one which requires the fewest number of dimensions.
CTE suggests that all forces can be described as the interaction of C functions with the underlying 'force' mechanism being the property that the Universe is fundamentally opposed to C. We can show that this fundamental opposition to C, acting on conforming C functions, has an effect which is identical to gravity, so in a way, all forces can be considered as different manifestations of gravity. This introduces some additional symmetries where gravity and the strong force are complementary effects of the static components of C functions and charge and the weak force are complementary effects of the dynamic components of C functions. Unification that starts with gravity, as opposed to ending at gravity, represents a significantly different approach to unify the forces. A feature of this approach is that it doesn't require the high energies, temperatures and densities associated with quantum unification while at the same time, it doesn't preclude quantum unification, or even the quantification of forces as the interactions of real or virtual particles.
The fundamental opposition to C, combined with the finite speed of light at which this opposition acts, results in a natural resonance in the fabric of the Universe. This resonant frequency, which is one of several echos of the Big Bang, is the Compton frequency and the myriad of particles are various combinations of harmonicly related solutions that fit within this resonance condition. These harmonic relationships also relate to why seemingly different particles share so many attributes. This is well known when applied to the energy states of an electron, but isn't as obvious when applied to general particles, photons and other forms of existence.
The C functions that describe the CBR are similar to those that describe other forms of EM energy except that they have a non zero average value, which represents a CP violation which the Universe attempts to correct. It's possible that this non zero average value of curvature that manifests itself as the mass of Dark Matter. We could create this in the laboratory through the generation of random, or pseudo random EM-energy, although the amount of Dark Matter created would be relatively small, making the results difficult to measure and the process would require the generation of very high power, non periodic EM-energy which is easier said than done. However, this is theoreticly possible and would be far cheaper than Tev particle accelerators. Note that Dark Matter like this isn't really a particle, but the consequence of a wave. However, it may be modeled as a collection of small, random mass particles.
There are potentially other organizations of curvature which could manifest the effects of gravitational mass. These may correspond to WIMP's and need to be investigated a little further.
A more interesting possibility is to consider what would happen if our Galaxy started out as a galactic size ball of uniformly dense, primordial gas. Gravity would quickly collapse this ball of gas into a massive, stellar like object and eventually to a black hole. We see such things in the very early Universe and call them Quasars and we see very large black holes at the centers of galaxies. From a gravitational point of view, a massive wave would form as the difference between a mostly uniform initial matter distribution and the concentrated, post collapse matter distribution. If the speed of this collapse was sufficiently fast, a massive standing wave of space-time curvature would be created as the result of the collapse. The consequence would be that the gravity (curvature) associated with the central black hole that eventually arose would have a bimodal distribution, by virtue of the standing wave, across a much larger region than the physical black hole itself. The effects we attribute as Dark Matter are really an effect of the bifurcated gravitational influence of the black hole at the center of our Galaxy. The evidence of this that we can observe today is the apparent correlations between the velocities of stars in the outer arms of galaxies and the size of the central black hole. The stars in our galaxy are essentially trapped in a gravitational well created by the rapid formation of the central black hole. This could not be reproduced in the laboratory.
Don't really know yet. One possible model suggests that the neutrino has inertial mass, but no gravitational mass. Another suggests that it may have directional mass, that is, its mass is different, depending on how you look at it. None of these has been deeply investigated at this time.
The Theory of Dimensional Evolution (TDE) is a theory suggested by CTE for the early Universe. TDE suggests that the Universe started out as an initial 1-dimensional, timeless, proto Universe with an ordinate of space-time, an intrinsic opposition to C and containing randomly fluctuating C. In its initial equilibrium state, any C that appeared was quickly snuffed out by complementary anti-C as a consequence of the intrinsic opposition to C. While the arrow of time hasn't been established yet, time can be considered as randomly fluctuating around zero as the random C and anti-C perturbations come and go. When the amount of C exceeds a threshold determined by the finite resistance to C, this Universe curved in on itself and a new Curvature Universe arose as the original single space-time dimension split into independent space and time dimensions. As an analogy of how new dimensions arise from a Universe curving in on itself, consider a one dimensional line, which when sufficiently curved such that its ends meet, forms a 2-dimensional circle. Notice how the timelessness of the original proto Universe means that in the presence of random C fluctuations, the critical curvature threshold is destined to eventually be exceeded. As time is now independent of space, the C and anti-C can no longer exactly cancel each other out. The result is a geometric expansion of curvature, where the total amount of curvature oscillated between geometricly increasing values of C and anti-C, which eventually caused this new 2-dimensional Universe to be so highly curved that it curved in upon itself, resulting in yet another new dimension and a new Energy Universe. This process continued, adding more and more curvature in the form of energy, until it again curved in on itself, spawning yet another dimension, after which, a stable, Matter Universe came into existence.
The inflationary period of this Universe is the entire existence of the Curvature and Energy Universes and lasted only a tiny fraction of a second. A new equilibrium state was reached as the C and anti-C became isolated from each other by spherical boundaries of zero curvature which arose at the instant of the last dimensional split. In effect, the anti-C became shielded from the Universe by this boundary and was able to act to exactly offset the C on the other side which resulted in a new stable equilibrium. We know that curvature is hard to maintain based on E=mc**2 and it turns out that anticurvature is just what we need in order to maintain curvature in the presence of an intrinsic opposition to it. From a mathematical point of view, this is conveniently modeled as real C and imaginary anti-C.
CTE models particles as being comprised of equal and opposite parts of C and anti-C, where the C is on the outside and the anti-C is on the inside. The evolution of the Universe could not have stopped in a state where this was reversed. That is, where the anti-C was on the outside and the C was on the inside. Due to the reversal in the arrow of time related to anti-C, an anticurved Universe would uncurve from itself, thus subtracting a dimension and doesn't lead to a stable alternate equilibrium state and ends up back where it started. An interesting attribute of this model is that a Universe consisting of any ratio of matter to antimatter does not pose a CP violation. Parity is maintained by virtue of the C and anti-C pushing against each other, to maintain the stability of either particles or antiparticles.
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