Gravitation 101

Gravitation 101 and the Holy Grail of Physics






First things first... You have been a resilient reader and have been seen the trademark HyperGeometrical Universe Expanding Hyperspherical picture above time after time... It is about time for me to explain the exact meaning of each line.

The first thing you notice is a green circle - this is the cross-section of what we know as our 3-D Universe. X is any direction. Notice that the model defines that the radius of curvature is equal to the dimensional age of the Universe (c - lightspeed times the age of the Universe - circa 15 billion years). Also notice that even though the curvature is defined by the motion along the fourth-coordinate, this is not the curvature that is referred to in General Relativity. That curvature is measure between the 3-D Universe and time (or spacetime). That curvature is influence by velocity and mass here and in the General Relativity.

The curvature in the figure relates to the Hubble expansion process. Simple geometric considerations indicate that the average receding speed between two points of the Universe is c*Fi , where Fi is the Cosmological Angle. For a π radian angle (opposing points in the shock wave Universe) would result in a receding velocity of π*c. Notice that Universe expansion in this model does not requires any Dark Energy or Antigravitational Force although we do have Antigravitation in it. Antigravity will be covered in the HyperGeometrical Universe Standard Model.

The receding speed for two points separated by one radian is c, that is, at one radian the average Hubble speed will be c and any radiation from that region will appear in the microwave region due to Doppler effect. This means also that one can never reach any point after one radian from where you are, the further you travel, the further the one radian point recedes. One can never observe any event that is moving away from you faster than the speed of light, one cannot see any point further from you by one Cosmological Radian.

The initial space fluctuation was a little Hypersphere prior to breaking apart into all the particles of the Universe. Due to symmetry (perfect Hypersphere), the initial decomposition occurred in all places of the Universe. This means that wherever you are is where the Big Bang occurred. It also means that if you look far away (with a telescope), you will see the beginning of times or thereabouts. I will digress about the meaning of time later. These inital fluctuations will be covered in the Hypergeometrical Universe Cosmogenesis.

The second fine point in the figure above are the time projections:
1. Radial Time (Absolute)
2. Dimensional Time τ (Relative)
3. Cosmological Absolute Time Φ

Follow the Yellow Brick Road to learn about time projections and a simple way of thinking in five dimensions. You will also learn why τ is called Dimensional Time when it is clearly a direction in the Four-Dimensional space. If you didn't go to the Yellow Brick Road, I will like to tell you that along that direction lies actually two directions (one direction and one projection) because linear motion is equivalent to two rotations. One around the axis perpendiculat to XΦ and another around the axis perpendicular to XR. One angle is imaginary and the other is real, respectively.

Now it starts to become clear that the motion of the particle is actually in a five dimensional space (four physical dimensions and a time) and at the speed of light, being the three dimension motion just a drift. If you need to review supporting arguments about the last statement click here.

Rotations imaginary or otherwise will reproduce nice relationships between waves. The imaginary angle rotation will produce Relativity, since it is a Lorentz transform. Here the directions are proper time and X.

The real angle rotation will reproduce a nice visual relationship between the wave decomposition components (τ Direction propagating wave and the X direction propagating wave).

Now that you know what the figure means, you can see the Holy Grail of Physics (of course, if this is correct - you have my word on it... after all, I've never lied to you before ...:)

I couldn't resist and reproduced the Grand Unification Equation below...
The total waveform is given by:






The Gradient of this waveform should be set to zero and the closest maxima to each particle found. Notice that there is a k-vector in the equation. The k-vector has to be modified for particles in motion (magnetism from DC currents and electromagnetism from AC-currents). The modification is the appropriate Lorentz transformation and it is how I derived the Biot-Savart equation. The derivation will be presented later.

This equation shows a body with N dilators (X Particles) interacting with another with just one.

Notice that the first has a cosine on the denominator while the other doesn't. The reason for that is the usage of a "Short Wavelength Approximation". The large mass wave contribution is thought to have a small wavelength, thus the cosine oscillation is extremely fast. This means that maxima due to that contribution are bound to be extremely closely together. The oscillatory cosine is approximated by a constant.

Notice that there is a P factor that relates to the dimensionality of the decay. Notice that the "field" equations are two dimensional (cross-sections) and that the decay happens in terms of the increasing circular perimeter. The perimeter increases in terms of the number of spatial dimensions (3) plus spin*(fourth-dimension). For example, for a particle of spin half P would be 3.5. For a particle of spin zero (neutral matter) P would be 3.

It is slight complicated to understand that a body (collection of dilators) is perfectly lined up with the space in which it is embedded.

THE HOLY GRAIL OF PHYSICS









This work makes a huge claim: to be the source of the Holy Grail of Physics.

It is or maybe it isn't the Grand Unification Theory. This model changes paradigm to do so, based on a solid argument of an expanding 4-Dimensional Hyperspherical Shock-Wave Universe.

This is, of course, unexpected and to some degree some might argue that it has a lower level of sophistication (mathematical sophistication). The theory, on the other hand, is laden with physical insight guiding each and every hypotheses and simplifications.

This theory was created during a period of six months, while riding the subway in New York City during my commuting. It was never intended to be complete and to rewrite all physics. It was meant to be just my opinion and something for people to build upon.

It turned out that Holy Grail is a very appropriate description of any work in this area. I bothered to review the Science Status Quo throughout my life. After my initial insight, it became clear to me that these ideas should be investigated further and that drove my subsequent efforts in communicating them.

Raiders of the Lost Ark

In the Raiders of the Lost Ark, people also find the Holy Grail and discover that just its sight is enough to explode their Brains while melting face, eyeballs etc...:) A really horrendous sight..:)

It turned out that this is a good explanation why I cannot find feedback on this theory. Anyone who has any competing ideas, will peddle theirs and never read anything else seriously. The simple sight of a competitor's theory would be enough to make one's thoughts impure and thus make their theory fraudulent to some degree. I don't think that this is the case, myself. I believe many of us were able to create half-baked ideas and those half-baked ideas could be great contributions if they were the subject of strong intellectual scrutiny. By defending one's ideas, one make them more solid (better baked).

I believe that this is the explanation for the lack of any serious scrutiny, which would be welcome...

Of course, I speak a different language, but the basic claim of this model should scream OBVIOUSLY CORRECT or OBVIOUSLY INCORRECT... One cannot have an indifferent position about an Universe flying at the speed of light...:)

This is a departure from anything that is SANE IN SCIENCE (although I believe it is the correct paradigm.:).

Come to the Light and let me know your thoughts. I place a CONTACTME button on purpose to get any one of your opinions...:) Preferably knowledgeable opinions, but I will be glad to see anything relevant on my mailbox...:)

May The Force be With You, Not

May The Force be With You, Not







This is the most important installment of the theory. You have been told that you are strong, can pull up big weights, big biceps etc... Luke Skywalker was told that the Force should be with him....etc...

The only thing I can tell you is to Forget The Force.... It will not do anything to help you with The Grand Unification... By the way, Forget The Field... It doesn't help either... at least at this stage... Later, you can come back and redefine everything in your own words....

Now that you forgot, Force... Forget Mass... Forget Charge... One cannot Unify anything with those constructs...

Now, think about what is the goal of mechanics (Gravitation), electrostatics, electromagnetism... The goal is to explain why things move by action at distance...:)

The HU Theory describes the Universe as a Four-Dimensional Lightspeed Expanding Hyperspherical Surface. You might imagine what I was thinking... Dilatons are spacewaves... What waves do?... During my thoughts, I remembered the tropical storms that stranded me in the room in the backward of my childhood home... Mini lakes separated me from the main house and there was nothing to do other than to look at the hypnotical waves ...

Many years passed by and I had to face waves again...This time they were four-dimensional and my little pond was actually the whole Universe hurling through the four-dimensional space at the speed of light... (four-dimensional space equal five-dimensional spacetime).

The first challenge is what property or symmetry to pay attention?.... The second problem is how to think in four-dimensions, that is, how to simplify the problem such as to be able to fit inside my Brain...

The solution to the first problem are Lorentz transforms... The solution to the second problem is the usage of cross-sections... The Solution to the third problem is 42 or the Pendulum of Brahma...

The Pendulum of Brahma is an allegory that states that the Pendulum swings and every time is passes again, it is at a different place (different four-dimensional spacetime coordinate in Relativity or different fifth-dimensional spacetime coordinate in HU). The Universe is never the same, it moves forward every time the Pendulum of Brahma Passes By.

de Broglie proposed that matter has an equivalent wavelength (de Broglie wavelength) that identifies the equivalent wave in the particle-wave duality. The Pendulum of Brahma corresponds to each de Broglie wavelength expansion of the whole Universe. This will become clearer later...

The theory does not need the definition of Mass, Charge etc.. to predict action at distance. It needs those definitions for calibration with what we know.

Let's start with the easy "Force", Gravitation. - to be continued tomorrow...:)

Hope Springs Eternal

Hope Springs Eternal









When I decided to blog this theory, I hoped that it would generate enough interest and bring more scrutiny to it. While creating it, I tried to get people to read it without success.

I am not from this field and learned that outsiders are outcasts in any situation. This theory was created by an outsider and I believe that is why it is so different, creative and probably correct...:)

Many people following the same idea, repeating the same Mantras, Higgs Bosons, Conjecture This etc... will never be able to think outside that vocabulary.

It has been said, that the theory of everything would require a new vocabulary, meaning a new set of mathematical constructs, new theorems etc...

It was never said, the theory of everything would require a fresh perspective...:) Before scalating complexities for complexity sake, one should see if one can find simplifying assumptions. I looked around and found a few.

Well, let's not be too involved with one's own ideas and restate this as, there should be a place in the literature for ideas which are not the one's which are the mainstream, giving that they have a rational support. I believe my ideas fall into that category.

"Can't we all get along???? (hypergeometricists, string theorists, conjecturists...:)

I failed to get through their spam-killer software last time I tried to contact the leaders in this field (positive thinking).

I decided to take a new try now that the theory is nicely presented in a blog...:) and I will be contact a few scientists in hopes to make the theory more widely available...:)

In the next few blogs I will make public the results of my efforts.

Hope Springs Eternal..:)

Why do things move?

Why do things move?








Mostly likely you never asked yourself this question? In fact this is actually two questions:

1. Why things move when they are subjected to a force?
2. Why they keep moving afterwards (after the force is not in place any longer)?

The answer to the first question is due to the fact that constraint forces do no do any work. They are perpendicular to motion and thus cannot do work even if they wanted..:) They are not lazy...:)

The theories before mine were bult on the base of Classical Mechanics and use Lagrangians and minimization principles. Those principles have built-in concepts of Potentials, momentum, mass etc... Using them one could not create my theory. The reason being is that one has to go one step below. One has to use the reasoning of lazy constraining forces not doing any work and avoid introducing the concept of force.

Instead of thinking about Force, I thought about de Broglie (or Compton if you so prefer) stepwise hyperspherical expansion of the 4-Dimensional Universe Shock Wave. Minimization of the contraint forces means in this perspective having the dilators to be in phase with surrounding dilations caused by other dilators. Notice that this means that all dilators are in phase with each other dilations at each swing of the Pendulum of Bhrama or de Broglie step.

This in synch stepwise motion is the source of Quantum Mechanics and allows for the addition of wave amplitudes as opposed to their squares. I call this a Cosmological Coherence. It is the reason why radiation (spacetime dilatons) generated from each and every atom of your body to add up to form an extensive property, that is, the field amplitude is proportional to the number of dilators.

This simplifies the theory and makes it a simple theory of everything.

Now returning to the problem of why things move (inertially). Inertia can be thougth as the resistence spacetime generates when subject to deformation. The space has a spring constant (which I used to calculate the natural frequency of spacetime waves or gravitational waves and the number is 42!!!!)..... Just kidding...but it is not that far from 42...:)

Thinking along those lines, a body that is traveling has all its dilators siting on a shock wave that has a local distortion. This figure shows that local deformation of the spacetime as arrow 1, which is not perpendicular to the hyperspherical shell any longer. Motion happens as the hyperspherical Universe expands. Notice that moving from the situation 1 to the situation 3 resulted in the elimination of spacetime stress. The k-vector on situation 3 is perpendicular to the hyperspherical shell and will move away from the original point with the same velocity as always, its Hubble velocity...:) albeit remained fixed onto the Fabric of Space...:)

That space distortion will travel to the point in the Universe where the distortion is relaxed. When it reaches that point it will stop and site onto the relaxed Fabric of Space. Surprisingly, due to the expansional character of the Shock Wave Universe, it will be seem as moving at constant speed (its local Hubble speed) forever.

This is the reason for motion and this is the logical complement to Newton's First Law!

Next, I will explain why things move when subjected to a "Force".

Superstrings

SuperStrings








First I have to say that the research in SuperStrings or any other tremendously mathematical theory is valuable and has been set forth by brilliant minds. In addition, the theories might really being brought back from the 23rd Century and be totally correct.

Secondly, I have to say something that might help you see other perspectives with an open mind.

Here is what I have to say:

There is a bothering aspect in the present search for the theory of everything.
There are precepts on how the theory should look like.

Unseeming comments like the claim that String Theory is a theory from the 23rd Century (thus should be correct) are not scientific. It delegates all other
attempts to second best just by using that empty statement.

I see the big picture although I might fail to see the details. The big picture is that superstrings are supposed to replicate energy levels (mass) of particles and the different types of bosons that convey the so called Forces. The problem is that SuperSring boundary conditions create evenly spaced energy levels (the length of the string is a multiple of the wavelength associated with an specific state). All the contortions of creation of Tori, folding the space in membranes etc are used to try to compresses those strings into submission to yield the observed particles and bosons.

The fact that the superstring is supposed to be extremely small means that there will be a lot of trouble to make matter out of them (to find states that are low enough to accommodate the observed particles' masses).

The fact that the strings are floppy also means that they do not have nice moments of inertia and thus are not good to be modeled for quantized rotational energy levels. In my theory, I used the rotations to replicate the intrinsic quantized quantum numbers. Superstring, Kaluza-Klein theories use compact curved spaces to replicate the same property. That results in dimensional inflation, that is, the inflation in required the number of dimensions. I believe that it is more likely the existence of a soliton that has a well defined moment of inertia tensor embedded in a simpler space than to have a utterly complicated space membrane that sometimes foams..>:)

I think it is too much work for a simple string. In this theory, I divided the problem into many:

1. First, find out how many forces are out there... I found only one "force" that reproduces Gravitation and Electromagnetism. Light speed expanding Universe means that E=mc^2 is kinetic in origin, thus there shouldn't be any potential energy stored.
2. I proposed a particle X (four-dimensional ellipsoid of revolution) that can provide all the structure associated with experimental nuclear scattering.
3. Particle X axes are modeled after the Quark Composition of matter and thus provide anisotropic collisional cross-sections.
4. The dilatons decay in a quantized manner as a function of the number of waves and not spatial distance. This is certainly new. Asymptotic freedom or spherical symmetric collisions are recovered if one managed to get the particles close enough (high energy collisions).
5. Another problem to be solved is the nature of the solitonic state of these four-dimensional dilators (X Particles). For this, I believe it is just necessary to create a simple potential for space deformation and derive the dilator states (particles masses).
6. Another problem that HU Models solves is the explanation for the intrinsic quantum states. Charm, Spin etc are modeled as rotations (tumbling) of these four-dimensional dilators.
7. Weak force is modeled as a Relativistic Hadronic Nonlinear Wave Scattering problem and it naturally lead to hadronic lasers.
8. Next to last, I have to mention that this is a first viewing (nobody wanted to read it) of this theory and thus it is in the same level (perhap's better) than the first research papers on Quantum Mechanics, when people were discussing if Schrodinger equation should be linear or non-linear, etc. I am proposing a framework with well defined hypotheses and some initial results (Grand Unification). I don't have access to particle physics data and thus there is work left to be done all over the place. This means that if you are interested and have the appropriate background, I would certainly welcome collaborators.

Last but not least, the theory not only proposes that the Universe is traveling at the speed of light but tells you that you are composed of four-dimensional particles (tumbling 5-D spacetime solitons). I tell you, this has to be a difficult pill to swallow...:)

How Science is Done These Days

How Science is Done These Days








This is a preemptive strike against people who thinks that the language of the theory lacks mathematics...:)

If you are a theoretician in this area, you will know what I mean. This field has tremendous difficulties. The field has become more and more mathematical and abstract, to the point that many theoreticians work in Universes that have nothing to do with this one.

Some people talk about how to create an Universe or if there are many Universes around... It is easy to come up with an infinite number of Universes. Say, let's pick up a Pagelike Universe (a 3-D sheet of Paper or Universe) immersed in an infinite Fourth Dimension. It is clear that one could stack Universes one over the other and jump from page to page... Maybe we could do that just by concentrating in front of a mirror as we did in the early science fiction...:)

The fact is that Science has been detached from reality. Papers oftentimes start with a given metric from nowhere to be used in the construction of geodesic using a Lagrangian from nowhere... There are no physical considerations... Of course, the complexity of the math makes it difficult to see the implicit hypotheses. I believe Wesson was very close to propose a hyperspherical shock wave Universe, he should have. But there is a dogma that precludes matter to travel at the speed of light and the questions or reasoning displayed prior in this blog were never asked or proposed.

Many people, including myself when I was 12 years old, considered that the Universe could be somehow traveling at the speed of light in some way. I believe that was a half-thought, that is, it did not have a reason of being, didn't answer or asked the pertinent questions (what happens when mass disappears from this Universe - that would lead to a suitable explanation for the famous E=mc^2 equation and to a genuine insight). I had that half-thought at early age and did not try to defend it to anybody because it did not pass my own scrutiny on why, how, what are the consequences, what is the topology etc...

Just to clarify, the Dogma is alright in traveling within the 3-Dimensional LightSpeed Expanding Hyperspherical Universe or Shell. Motion within our simple 3-D Universe is governed by interaction among dilators and dilatons and cannot ever go above c. This should be seem as a lateral motion while Universe progresses onward (radially outwards) at the speed of light and thus it is just a change in direction or the original radial velocity vector. The amplitude of this velocity vector can never be changed since it is the speed of dilaton (spacetime wave) propagation.

There are implicit hypotheses in this theory which might not have been fully declared or perceived. I consider that the ones I brought forth are worthwhile to think about. I will try to bring the others about as I blog my theory into existence...:)

The Cosmic Microwave Background

The Cosmic Microwave Background








Anisotropic Universe is what I would expect from a 3-D Big Bang or from any other Big Bang Model with which I am familiar.

What does Anisotropy means? Well, if you look into the sky we should be seen a hole (lack of galaxies) in a given direction and that would be where the Big Bang should had occurred.

I am not familiar with Inflation and other schemes to make the Universe Uniform but I felt bothered by that Uniformity. Einstein hoped, as many others, for a Static Universe that has always being here and forever will be. He even included the Cosmological Constant to make the Universe static, non-expanding nor imploding. It hurts one's feeling to see everything go up in smoke.... :)

The Microwave Cosmic Background has been proposed to be the remnants of the Big Bang. It bothered me that the thing is called Background and presents no or little anisotropy. Why it bothers me? It bothers because it would indicate that there was some thermalization of the radiation followed by an adiabatic expansion of the Universe. Thermalization means that radiation has to bounce back and forth within reflective boundary (or non-absorbing) conditions. I have a hard time finding how one creates those conditions in the early Universe. Let's say that the thermalization occurred while the Universe was small and opaque. As soon as it becomes transparent light will fly away at the speed of light leaving matter behind and thus escaping any further thermalization. I cannot see how one could cool down the original radiation into a Black Body radiation that is 2 or 3 Kelvin degrees cold.

Forget about the fact that the background is called a background because it is the same in any direction...:) This is absolutely insane and would indicate that the original radiation is being diffused back by the scarcely populated Universe that somehow found itself ahead of the original radiation... It doesn't make any sense to me.... By the way, I know how to make a Black Body...

HU Theory proposes that the Big Bang occurred in each and every poing of the Universe at the same time. This is an obvious although may be not self-evident result of the topology of the Hyperspherical Explosion. This means that from each and every point, energy and matter would flow away. The Big Bang Occurred in All Places At The Same Time.....

Radiation created at that time from a point one radian away from you, would arrive now and it would be Doppler shifted and go through multiple scaterings in the dense and early Universe. Doppler shifting would explain quite well the microwave nature of the radiation seen today. The fact that microwave radiation emanating from one radian in any direction (homogeneity) would arrive today (or any day) perfectly Homogeneity and Lack of Anisotropy...HU is intellectually gratifying.

Universe as a Higher Dimension Shock Wave

Universe as a Higher Dimension Shock Wave

Many people might have a knee-jerk reaction to the premises of the HyperGeometrical Universe Theory of Everything (HU for simplicity)...

There are undoubtedly new ideas which are tough to digest. We are all used to think the same thoughts and new concepts are supposed to receive higher scrutiny. I will try to clarify some of the most likely contentious points of the theory:

1. The first that comes to mind is the iconoclastic idea that we are traveling at the speed of light from the focal point of a four-dimensional space (or five dimensional spacetime) Big Bang.

The Big Bang has been proposed to be the result of a four-dimensional Big Bang in the past. Li and Wesson proposed this in his paper "The Big Bang as a higher-dimensional shock wave". In this paper the three dimensional Universe is presented as a hypersurface immersed on the fifth dimension. Solution for Einstein field equations without sources are provided including Wave-Like solutions of RAB=0. The topology is a one of a matter filed thus curved 3-D space in a flat 4-dimensional space. This means that the curvature is mass derived and the Universe resembles more an sphere inside a swimming pool. The Big Bang shock wave can be thought as 3-D shock wave crossing a page-like (flat) Universe. The crossing of the shock-wave creates what I consider an unpalatable anisotropy. Just a matter of taste.

In my theory, the shock wave creates not a flat Universe curved by its mass, but a 3-D shell-like expanding at the speed of light. It is difficult to be precise when speaking about curvature along a dimension we are not used to think about. I will only mention that there might be differences when I speak of curvature and when Relativity speaks of curvature. The other point is that the 3-D shell is defined based on the figure above, that is, X, Y and Z are perfect circles. As we travel around the Universe, we are always in the hyperspherical shock wave and if it were possible to propel oneself at speeds higher than the speed of light we would be able to go around the Universe. In fact, we would be able to get out of the Universe into the Void.

One might ask why the speed of light? The answer is simple and based on the following points:

1. Black Holes are considered to be very curved spacetime created by accretion of mass.
2. If we fall in a Black Hole we will be one with it, thus we will be a deformation of spacetime.
3. If item 2 is correct, we should be a deformation of spacetime since the beginning.
4. Light is due to alternate motion of matter (electrons), thus it should be a propagating deformation of spacetime.
5. Light propagates at the speed of light.
6. We are a non-constrained deformation of spacetime and thus we also should propagate at the speed of light.
7. If we are not traveling at the speed of light, that should mean that we are traveling perpendicularly to the directions we are able to see, thus we should be traveling perpendicular to our 3-D Universe.
8. The fact that we don't see anything from outside this Universe means that there shouldn't be any dilator (generator of spacetime oscillations) outside our 3-D shell.
9. The topology should be hyperspherical or whatever one would call this 4-dimensional object I proposed in my papers...:)
10. The space is naturally curved and has a radius of curvature equal to the dimensional age of the Universe (c * the age of the Universe).

It is important to notice that prior 4-Dimensional proposals of Big Bang as a Higher Dimensional Shock Wave missed the possibility that the Universe itself would be the shock wave.

Hypergeometrical Cosmology

HyperGeometrical Cosmology







The HyperGeometrical Universe theory is a simple Theory of Everything that based on clues from Relativity and Quantum Mechanics proposes that the Universe is actually an expanding shell on a light-speed expanding hyperspherical space disturbance. That shell where our Universe lies is a three dimensional hyperspherical shell that travels outwards at the speed of light.

Simple inspection of the above figure allows for many conclusions.

1. The first one is the Hubble expansion and why the Hubble constant is not a constant.
   
2. The Big Bang occurred in all points of the Universe at the same time. This explains why wherever you look, if you look far enough, you will see the beginning of the Universe.
   
3. In a three dimensional Big Bang a tremendous amount of anisotropy would ensue. One does not expect to find pieces of a bomb where the bomb exploded. Many "explanations" were proposed but as far as I can tell, they were not palatable.
   
4. The Four-Dimensional Big Bang is the only model that allows for a smooth microwave cosmic background. It is my believe that the background is actually the Doppler shifted gamma radiation from the early few seconds after the Universe was set in motion.
   
5. The reason for 2) is that at the time the Universe was set in motion (point of supersymmetry of the hyperforce), energy flew from each and every point of the early Universe. As the Universe expanded, energy that traveled the dimensional age of the Universe (circa 15 Billion Light years) will be reaching you by now no matter where you look.
   
6. There is a funny corollary: Everyone is the center of the Universe (at least of the three-dimensional shell where we live).
   
7. Newton proposed that a body under the influence of no force will travel in straight line with constant velocity. This model explains why it will continue moving and inspection of the figure above shows that is is never a straight line.
8. The HyperGeometrical Universe Theory shows that non-inertial motion takes place through the change in propagation vector. Two radial trajectories (outgoing along the Radial fourth-dimension or k-vector along the Radial direction) at positions separated by alpha radians (see figure above) will run away (Hubble expansion) from each other at speed alpha * c (velocity of light). If a body starts moving from Point A with speed alpha*c, it will continue moving until it reaches a point alpha radians from Point A (Point B). Reaching that Point B the body will simply move outwards while its Hubble speed from Point A will remain alpha*C. In this model , motion is due to a change in k-vector which has a dual equivalent as a local spacetime deformation. The motion from point A to point B relaxes spacetime and make it naturally curved again. This means that the HyperGeometrical Universe Theory provides the reason for free motion and complements Newton's Law...:)
   
9. Of course, inspection of the figure also indicates that opposing point in the Universe will travel apart at speed equal to Pi*C (greater than the speed of light). Of course, this is immaterial since it is impossible to cross more than a radian in any direction (at the speed of light through the duration of the Universe).
   
10. Two regions of the shell separated by one radian will run away from each other at the speed of light...
    
11. If you look into the sky at positions distant from you the dimensional age of the Universe, you will be looking at your very next neighboring point when the Universe was just a few millimeters wide.
    
12. In summary, the Universe has a radius of curvature equal to the dimensional age of the Universe, is finite and circular and cannot ever be traversed.
    
13. The answer to the Age Old question of what do we have after the end of the Universe is more Universe (you just cannot go there ever..:)
    
14. The Universe is in expansion and that doesn't depend upon the Universe mass content nor Dark Energy or anything slightly shadowy... This is an expanding four-dimensional Universe. Einstein could only see three dimensions and thus was concerned with the mass content of the Universe and the mass induced curvature. In this model, these kind of considerations might have a meaning locally.
15. The average curvature is defined by HyperGeometry (or Geometry)...
16. Please review the attached paper HyperGeometrical Universe - Cosmology and the original HyperGeometrical Universe -Grand Unification and feel free to ask any questions or to provide any comments.

HyperGeometrical Universe Topology

HyperGeometrical Universe







From the name of the theory one can conjure up that the Universe topology I am proposing is of a LightSpeed Expanding Hyperspherical Universe, that is, the three dimensional Universe is located in a very thin space disturbance that propagates outwards (radially) at the speed of light in four-dimensional spatial Universe. The fifth dimension is the Cosmological Time.

Since the spacetime itself is a non-compact five dimensional manifold, there is a need for the three-dimensional spatial Universe, we are so used to, to be thin along the radial dimension.

The thinness is consistent with a localized event (Four-Dimensional Big Bang) that set the Universe in Motion fifteen billion years ago. A thin travelling shell is clearly the remnants of an above dimensional threshold event (Big Bang) that generated the Universe.

This is also consistent with the lack of aberration we see in our Universe. If the Universe were set in motion by a longer lived event, there would be aberration, which is difficult to visualize.

All forces we see are actually projections of the interactions that takes place in the five dimensional space. All forces including the ones associated with the most violent events in the Cosmos are just the result of interference patterns on a Four-Dimensional Hypersphere. In the papers contained in the Yahoo Groups site, you will find how using simple intereference patterns one can replicate Gravitation and Electromagnetism interactions.

That said, it is time to introduce X Particles This is actually a solitonic normal mode of space oscillations. The soliton aspect is mentioned to emphasize its traveling and localized nature. Different particles would correspond to different modes of oscillation and rotation of the X particles.

The fact that these are four-dimensional particles allow for three axis of revolution. The particle is a four-dimensional ellipsoid of revolution. Three axis of revolutions means also that spin, which is an intrinsic motion under current Science, becomes an extrinsic tumbling.

The axes of this ellipsoid of revolution maps to the quark content of a particle. Negative quark (down quark) is mapped to a negative phase (180 degrees out of phase with the oscillations of positive axes) in spacetime oscillations.

Now it should be clear that X particles are spacetime oscillators that thumble (spin <>0) while traveling at the speed of light with the rest of the Universe (also composed ot X particles) along the Radial direction. Particles with spin zero do not thumble and correspond to surface modes generators of the traveling hypersphere.

This theory revises the Standard Model with some interesting results, which will be review later, if there is interest.

Now let's investigate the first assumptions of the HyperGeometrical Universe Theory.

Are we actually traveling at the speed of light?

The most obvious indication that we are traveling at the speed of light is the famous Einstein Equation E=mc^2

Relativity states that the energy of a particle with rest mass m0 and momentum p is given by:


(A.1)

where m is the mass in motion.

This equation has implicit assumptions which can be brought into light by considering it a momentum conservation equation instead:

(A.2)

This is obviously the Pitagoras Equation for moments in two perpendicular directions adding into an hypothenusa aligned resulting momentum. The p momentum is our 3-dimensional linear momentum, while the m0C is the momentum perpendicular to our three dimensional space and it has a c-speed (the speed of light).

This indicates that we can consistently travel at the speed of light perpendicular to our three dimensional space and that will explain the E=mc2 energy.

Einstein did not realize the possibility of a hyperspherical expansion. Without that insight, the E=mc2 formula has no underlying reason for being.The energy has to be stored somehow, either as kinetic or potential energy and the storage mode has no connection to Relativity, that is, Relativity provide no guidance to how Nature store the famous nuclear energy. Without guidance, Science followed the potential energy paradigm, but missed the infinitely simpler and more elegant kinetic explanation. This theory tries to correct that misdirection.

This means that the nuclear energy is explained as being of kinetic nature and that precludes any potential energy stored in the form of strong or weak forces.

Needless to say, this is a great simplification and that is why it is a good idea to take one step back before moving forward in this area. In fact, the projection paradigm presently used, can be stretched further using the guidance of the hyperspherical topology, although that doesn't seem to be the best usage of it.

TIME THE FINAL FRONTIER

Talking about the meaning of time will require a Thought Experiment and that will address only what I called the PROXY OF TIME. c.t1 and c.t2 are proxies of time in the Lorentz transformation. They are proxies because they do not reflect time flow itself but are a artifact of multidimensional wave decomposition. I call them dimensional time in my papers.

Consider yourself as Being an Amoeba Stuck to the Surface of an Upwards Traveling Air Bubble (Traveling from the bottom of the sea to its surface) to understand it...:) ... You will also have to understand the concept of Proxy....

Remember that Chemical reactions will increase their rate as the temperature increases (in general, just go along and don't sweat the fine stuff). This means that the Amoeba will speed up as the temperature increase and temperature is increasing function of height from the bottom of the sea. This means that the PROXY OF TIME will speed up as it travels upwards.

Let's say that the Amoeba knows its biological clock (rate of replication) and can measure the passage of time by measuring how its colony grows.

This Amoeba, looking on a telescope, will see another bubble with other Amoebas and conjure up some theory of how time passes as you distances from each other (vertically). A very complex theory will be derived. The theory would be simple if the Amoeba knew it was traveling upwards and the temperature profile and the rate of acceleration of their biochemistry with temperature. Notice that chemistry is what controls their sense of time. In our case, velocity (local spacetime distortion) controls the speed of all forces, which in a Grand Unification Theory as this one, is just one.

Fortunately we have a simpler problem.

We are also dealing with relative speed, height and its influence on the PROXY OF TIME passage. Similarly to the Thought Experiment, there is a height (distance traveled by the HyperSpherical LightSpeed Expanding Universe) since the Big Bang (circa 15 Billion light years) and there is a relative measurement to be made. In the Amoeba case, it was the relative distance (PROXY OF TEMPERATURE DIFFERENCE). In our case it is a relative imaginary angle difference.

Lorentz transforms are equivalent to a rotational in a four-dimensional space, but they can easily be understood as a rotation in a five dimensional space, where the new direction (dimension) reflects the existence of an absolute time and a Radial direction (c.t1). Any inertial reference frame corresponds to a rotational of an imaginary angle around the Cosmological Time Direction. Since we don't have any reference to be able to see what lies outside our thin Universe crust, we can't never see the Radial propagation or have an idea of where is this preferential direction pointing towards. We can measure only the angle difference between two bodies in this 3-dimensional crust. This means that we are in the same boat as the Amoebas Stuck Inside Raising Bubbles and can only measure relative time passage.

The other conclusion is that Lorentz transformation corresponds to a rotation by an imaginary angle between the reference frame and a Radial Direction and that any system in this Universe would be traveling at the speed of light radially.

This means that the cross section of the Expanding Hyperspherical Universe can be thought according to the figure below:



Figure 1. Shows the cross-section XTau for the expanding Universe. The Universe length along X is represented by the band. X (or Y or Z) is displayed along the perimeter of the circle. Also shown in the diagram is PSI (Cosmological Time) and Radial Time R.


It is clear that space is curved in this model and that the radius of curvature is the dimensional age of the Universe (age of the Universe times the speed of light).

From Wikipedia

Wikipedia description of a Lorentz transformation. It relates coordinates (x1,y1,z1,ct1) to (x2,y2,z2,ct2)

Notice that it corresponds to a rotation of an imaginary angle around a direction that is perperndicular to x2 and t2, not unlike a rotation around F the Cosmological Time coordinate.

Notice that the concept of time flow depends upon the angle between c.t1 and c.t2, which are represented by tau and tauPrime in the diagram.