An Explanation of Alexander Mayer's Revision of Physics and its Implications

In November of the year before last, an astrophysicist, Alexander F. Mayer, released a completed version of his book, On the Geometry of Time in Physics and Cosmology. His theory ends paradoxes related to the Big Bang and the inflationary picture by revealing a geometrical picture of special relativity, and unifies the strong nuclear force with the force of gravity.
His theory depends on the following premises: that the speed of light is the same in all places throughout the cosmos (invariance), that energy does not change over time in quantity but only in form and location (conservation of energy), and that one can only know so much about a particle's position before its momentum becomes quite uncertain, and vice versa (the uncertainty principle).
Invariance (aka Special Relativity) Reinterpreted
The theory first differs from the conventional theory in its interpretation of special relativity. Special relativity is based on the principle of invariance in the speed of light. No matter how quickly you move as matter, light moves at the speed of light relative to you. This means that time is not something that is universally determined, as though there were a clock or a calendar programmed into the whole universe: instead, time depends on frame of reference. So when someone hops on a spaceship and travels at a speed near the speed of light, to him it seems like the whole universe speeds up, rushing by, while if someone on the planet he left can see into the spaceship, it seems like he is moving very slowly. Additionally, it seems like the spaceship is shorter along the direction it's moving in.
Einstein talked about this phenomenon in terms of clock rates, but Minowski, his mathematics professor, saw a deeper order. He realized that time is orthogonal to all spatial dimensions in the same way that left-right is orthogonal to forwards-backwards or up-down. Pick up a pen, a ruler, or any narrow long object. Hold it out in front of you so that it appears wide (pointing left/right). The left-right dimension represents the direction the object is about to move in. Now, turn the object slightly, so that one of its ends begins to move closer to you. From your frame of reference, the object appears shorter, because you're seeing a cross section of it. But the object isn't shrinking, it's just moving length from one dimension to another. Suppose that the dimension backwards/forwards is the dimension of time for a moment. As you turn the object, its length contracts, while its temporal aspect dilates. When an object moves faster, it is as though it is being turned so that its length is in the observer's time direction, while the dimension of the direction it's moving in contracts. Minowski accomplished this using imaginary numbers, which were not well understood at the time. Unfortunately, Minowski died in 1909, and Einstein dismissed his work as "superfluous erudition." This was particularly unfortunate for Einstein, because if he had taken Minowski seriously and allowed energy to be a complex number (equal to the rest mass of something times the speed of light squared (mc^2, the familiar part of the equation) plus the imaginary component of momentum times the speed of light).
Orthogonally Complex Numbers and their Magnitudes
A word on imaginary numbers: Imaginary numbers are poorly named. They're really just numbers that are perpendicular to the "real" number line. So if you had the complex number 3 + 4i, you could represent it with a point three units to the right of 0, and two units above zero. Complex numbers thus have a "magnitude", which is equal to the hypotenuse of a triangle drawn from 0 to the point of the complex number. So in the case of 3 + 4i, we could represent it using a triangle that goes horizontal for three units, and then has a right angle and goes vertical for four units. By the Pythagorean theorem (A^2 + B^2 = C^2, where C is the hypotenuse length and A and B are the other lengths, perpendicular to each other), the magnitude would be |3 + 4i| = 5, since 9 + 16 = 25.
What we had previously though to be total relativistic energy is actually the magnitude |mc^2 - ipc|. (M is rest mass, c is the speed of light, i is the imaginary unit, the square root of negative one, and p is momentum. Together, mc^2 signifty rest energy and -ipc signify momentum energy) Since you can't have a triangle with a hypotenuse longer than its other sides added together (that is, since |mc^2 - ipc| < |mc^2| + |-ipc|, except when mass (m) or momentum (p) equals zero, where |mc^2 - ipc| = [mc^2| + |-ipc|) there is some leftover energy you notice when you use complex numbers that you do not when using purely real numbers. This remaining energy (equal to the total momentum energy minus relativistic kinetic energy) is completely missed by conventional physics, and it has to go somewhere.
The Momentum Wave: Gravity and Fusion Unified
This energy goes into a standing momentum wave that emanates spherically from the particles involved. These are waves in the geometry of spacetime, and their intensity increases with the momentum of the particles they originate from. P-waves have a central peak with the waves adjacent to it quickly becoming shallower with distance, so that the energy of these waves obeys the inverse square law that applies to gravity. The magnitude |mc^2 - ipc| is the amount of energy in the central peak, and the remaining energy around it is the remainder of (|mc^2| + |-ipc|) - |mc^2 - ipc|.
In all atoms are nucleons (protons and neutrons) which are each composed of three quarks bound in a small area. The Heisenberg Uncertainty Principle states that the more a particle's location can be defined, the more uncertainty there is in its momentum. Quarks, bound in the space of a single nucleon, emit the strongest p-waves, and are responsible for most of gravity, but the theory predicts that gravitation per unit mass varies with the composition of the mass (because the p-waves that gravity emerges from at a large scale depend on mass and internal velocity, not simply on mass). Where there are crests of p-waves, the potential energy of space is lower. This means that matter in the presence of p-waves (and all matter in motion emits p-waves) feels the push of space towards where the energy of momentum waves is highest. P-waves also explains the strong nuclear force. Remember how the energy inside the central peak was equal to the whole magnitude of the complex energy quantity? The wavelength of P-waves is broad enough that three quarks fit together inside the central peak, confining them together with incredible strength.
Testable Prediction: Doppler Shifted Electrons
Providing an experimental testing ground for the theory, Mayer uses p-waves to predict a wavelength in the interference patterns of matter diverging from the wavelength of the accepted de Broglie matter wave as the speed of the matter increases. With the de Broglie wave, there is no variation in wavelength related to the direction of motion, even at relativistic speeds, because the matter wave can have a phase velocity greater than the speed of light (this means that while the matter itself doesn't move faster than light on the whole, its probable locations within that area do). However, with the p-wave, a Doppler shift is predicted.
A Doppler shift is an effect that happens when an object emitting waves moves at a speed near the speed of their propagation. When you're next to the street and a car drives by, as the car approaches you, the sound it makes gets higher in pitch; because the source of the sound waves is catching up to them the wavelength in that direction is decreased increasingly as it approaches, leading to a rising pitch. Then the sound the car makes decreases in pitch, once it has passed the point on the road directly beside you. This is because it is moving away from its waves as it propagates them.
P-waves have a Doppler shift, so when massive particles are fired at a speed around a tenth the speed of light or greater through the double slit setup characteristic of quantum physics, Mayer's theory predicts a divergence in the interference pattern from the de Broglie wavelength (which is inversely proportional to momentum in all directions without regard for relativistic speeds). Indeed, on page 133 of the pdf file (see below), Mayer cites the experiment where matter was found to move as if guided by waves. While x-rays (light) was found to obey the de Broglie wavelength, electron beams did not. In Mayer's theory, light's obedience to the de Broglie wavelength results from the fact that both light and the p-wave move at the speed of light, thus light has no evidence of the Doppler effect in its interference patterns.
A New, Ageless Cosmology
The geometry of time can also explain the redshifting of light from distant galaxies in a way aside from the conventional explanation, the Doppler effect. Influenced by the idea of the Big Bang and the historical cultural resonance it has, Edwin Hubble saw that light from more distant galaxies was more red than it ought to be and took it as evidence that the universe was still expanding from the (presumed) Big Bang. More recently, astrophysicists have been enabled to look further out into the universe, where they found galaxies that were redshifted further still, when they were expecting the rate to decrease at such distances, indicating a slowing on the expansion of the universe since the (still presumed) Big Bang. So they just interpreted the opposite result: the universe is accelerating in its expansion at a rate proportionate to the size of the universe, and thus would within a few trillion years stretch out so much that entropy would dominate and everything would die in a cold sizzle. They called it "Dark Energy," and said it takes up roughly 80% of the universe. Similarly, there was "Dark Matter," invented to account for the fact that according to the laws of general relativity (which was invented with an incomplete understanding of the geometry of time) seem to say that our galaxies should fly apart at their masses. The Big Bang theory was also favored as the answer to another question: if the universe is ageless and uniform, why don't we see star light in every possible direction at night?
Mayer's theory addresses all these problems. Gravity comes from waves of momentum, not purely from mass or through some invented Higgs boson or graviton, and thus by taking the energy of motion into account we can see how the galaxies hold themselves together. The answers to the questions of expansion and Dark Energy, and to why we don't see every star in our apparently ageless universe, are related to the geometry of spacetime.
Spacetime simplified to 3-space
Imagine a sphere whose surface is jeweled with stars as a model of the universe. While you're imagining it, you see its two dimensional surface spread out in three dimensions, but for this model that surface represents space. We're ignoring one dimension of space for now. So, what direction does "up and down" on this globe indicate, if north/south and east/west are spatial? The direction away from the center of the sphere at any point on its surface is the direction of time in that region. Any point in space we can designate as the origin. We put that point at the center of our view of the sphere. Thus we can see everything in the hemisphere whose center is the origin point.
Between any two points a mild distance apart on the sphere is an angle. Using this angle and Mayer's theory, we can expect light from points at an angle to us to be different in time direction from light originating near us. Time becomes space as it changes frames of reference (just like the pen, ruler, or whatever you contracted the length of by turning), and the redshift can be predicted from this angle. Those galaxies we thought were expanding away from us at an accelerating rate are actually just close to the equator that separates us from the other side of the sphere. We can't see stars in all possible directions because we can't see past this cosmic equator.
Extending into 4-space: the Hypersphere
In understanding the shape of the universe predicted by this theory, it is useful to use the model of the Hypersphere as learned from Peter Carroll. Imagine a pair of balls (that is, spheres with space inside as well as on the surface) whose surfaces correspond to one another. Anything that moves through a particular angular coordinate on the surface of one sphere appears at the same coordinate on the other sphere. Thus, from the center of one sphere (defined as the origin), we can move in any direction (at least) twice the distance of the furthest visible star (which is the distance from the center of a sphere to its edge) and arrive at the same point. Traveling twice as far, we'd get back to where we started. Every point in the universe can be defined as the origin, and every point has an antipode, which appears in the center of the "outer" sphere (whose "outer" edge collapses to a point) while the origin is in the center of the "inner" sphere. Regions whose time direction all have the same angle to our time direction are designated in this model by a concentric set of spheres surrounding us with increasing redshift at increasing radius.
A Universe of Dynamic Equilibrium
Another objection to the ageless universe that helped the Big Bang toward favor was the Black Hole. In (real number-only) general relativity, a black hole is a point of infinite spatial curvature which draws everything that's near enough closer towards it, and whose gravitational force is so strong that it compacts anything that gets sucked in down to a tiny volume. Before the reinterpretation, these points were thought perhaps to have virtually infinite temperature as well, being so compressed and bound.
In Mayer's universe, however, black holes aren't represented by points of matter. Instead, a sufficient accumulation of matter develops strong enough p-waves to create an Einstein-Rosen bridge (wormhole). The matter then goes across the bridge, rather than accumulating at its entrance, and emerges at the antipode of the black hole, from a white hole. Gamma ray bursts may be explainable by the other end of matter getting sucked into a black hole. Thus, while the curvature of spacetime can prevent entropy from running down the universe by keeping things from getting too spread out, it also prevents concentrations of matter from eating up the lot of it.

I hope you have found this layman's explanation of Alexander Mayer's new model readable and not too confusing. I'm sure that I made a few errors in explaining and understanding the details of this theory, however, the gist of it is encapsulated here. If the theory seems unpalatable, it may very probably be because I did not explain it effectively enough. If you an understanding of mathematical physics or linear algebra, you will probably do better taking it from the horse's mouth, here: http://jaypritzker.org/pages/book.html . Even if you don't have such a background, if you're curious enough, take it from the horse's mouth. If not, wait until electron doppler shift is either proven or disproven by a set of new experiments, and hope that the theory is either irrelevant or will become relevant enough to be popularized by at least science writers. Thanks for coming with me to look at this new picture of physics.