L4Y3R C4K3 TH30RY

Proposal for the Unification of Quantum Mechanics and Relativity.

Accelerating a massive object to the speed of light, if it were possible, would be equivalent to sending said object through a type of inter-dimensional Young's slit experiment, in which all of its de Broglie wavelengths would interfere with one another to create a holographic image that extends throughout time as well as space.

The wave-function would be vibrating in phase with time and would therefore appear completely static in this dimension - a proposal which conforms to the Relativistic Principle of time contraction. This theory, which I have dubbed Layer Cake Theory, attempts to unify the concepts of quantum weirdness and relativistic principles in an intuitive and lateral kind of way.

LAYER CAKE THEORY

Experiments involving the passing of a single photon through a double-slit grating, and the interference patterns that resulted from this, were influential in the formulation of the particle-wave duality theory of matter. Matter, like that which composes your body, is said to be made out of waves of probability. On a small scale the position/velocity of a particle becomes uncertain. But when enough of these particles are combined together, renormalisation occurs leading to the collapse of the wave-functions into a stable amount of what we call 'matter'.

In one of his lectures, the famous physicist Richard Feynman made reference to an experiment in which a stream of photons were fired at a detector behind a solid steel plate. Every now and then the detector would register a hit. The researchers concluded that the photon had taken a trajectory allowing it to swerve around the metal plate and hit the detector. This means that when looking at a single sub-atomic particle that comprises your body, for instance, we may find that its probability wave-function is looping out towards the stars... Such is the weirdness of quantum mechanics.

When an amount of matter begins to accelerate, I propose that some of its particles accelerate out from it at speeds which are, in a sense, greater than that of light speed. This because these particles are accelerating in the dimension of time and not of space; looping out towards the future. The faster an object travels the more particles it emits. These particles are actually space-time manifolds, slices of the original object that travel into the future at tremendous speeds. Each of the manifolds are holographic (fractal) replicas of the original object. This means that as the object accelerates and more and more of these manifolds are ejected, its aspect (apparent size) begins to shrink in agreement with the Lorentz contraction.

Its over-all mass, however, is not depleted because the fractally encoded manifolds are representations of how the object appears at any one instance of time, and therefor each of them contain fractal information of the current state of the mass of the object in respect to its reference frame. Combined manifolds do not increase the mass of an object either, meaning that the mass is a fractal component of the entire structure. When an object, like a person, is at rest, they are the result of all of their space-time manifolds interfering with one another, to become a coherent image of themselves at any one moment.

The history, past, present and future of an object can be represented by an almost infinite number of space-time manifolds. The collective manifolds are fractal, because at any one time they all collapse to form one whole.

In the case of a large object, like the planet Earth, each separate instance of time in the life of this object is a separate space-time manifold. Due to the length and complex history of planet Earth the combination of this set of space-time manifolds at anyone instance is enough to warp the fabric of space itself.

I have already made clear that, in the case of an accelerating object, the loss of space-time manifolds does not decrease the mass of the entire object. So, I would appear to be contradicting myself by suggesting that the accruement of manifolds would lead to increased mass. But, again this is really not the case. It is true that larger objects of a similar density have more mass, but they also have a greater number of manifolds. This suggests that, on average, mass is equivalent to longevity. The more massive a body, the more manifolds it contains and the further these manifolds extend in 4-d space-time.


Again this is something that we also see on a more manageable scale with animals. For instance it has been suggested that elephants and mice have the same amount of heart beats (close to a billion) in their lifetime. But, in the case of the mouse, they are just happening at a far more rapid scale than when compared to the elephant. LCT would suggests that the reason for this is to do with the relationship between total body mass and longevity, although exceptions are sure to apply in the case of living animals, where so many variables exist.

Traditionally physicists have had a hard time marrying the concepts of Special and General Relativity with the weirdness of Quantum Mechanics. Layer Cake Theory (LCT) attempts to address this disparity and it does so in a very unexpected manner, by supposing that a massive object traveling at the speed of light is essentially equivalent to a particle that travels through a double slit grating. While the latter generates an energetic wave of probabilities stretching across space, the former is comprised of a highly energetic 4-dimensional probabilistic wave-form that stretches across time. A comparison between both Quantum Mechanics and Relativity, according to LTC is as follows;

Quantum Mechanics                                                   Relativity

---

Wave-particle duality                                                   Matter/mass accelerating towards
(as expressed by Young Slits experiment)                the speed of light.

---

the same particle/space being in two                       The same temporal instance being
or more different places at once                                being in two or more different instances

---

The accretion of matter/atoms creating                   The accretion of space-time manifolds
the renormalistion of quantum uncertainty              creating stable time

---

THE EYE OF PROVIDENCE

Unifying Gravity with Electromagnetism


Albert Einstein is credited with having unified the force of gravity with the electro-magnetic force, but this is not entirely accurate. While he did manage to prove that gravity bends light (space-time) around heavy objects, he was unable to account for what gives these objects their mass, in the first place. The current theory suggests that there is an energy field (the Higgs Field) which perturbs the motion of particles through space and time, slowing them down and making them massive. The discovery of the Higgs Boson will allow physicists to fully unify gravity and electro-magnetism together with the weak and strong interactive forces. In short, it will supply the necessary ingredient towards a Grand Unified Theory of everything.


In this post, I would like to present my working theory of how gravity and electro-magnetism arise out of the Higgs Field with the use of interactive visual displays. In the case of a large body, like the Earth, motion through the Higgs Field creates its mass, which in turn creates its gravity well. I submit that the interaction between the resulting gravity well and the Higgs Field goes on to produce the electro-magnetic field around the Earth. This occurs in two ways, one for the electrical force, and another for the magnetic. I will focus on the magnetic force first.

The Earth's gravity field can be represented as a series of lines (world lines) converging on a single point. Actually it is a bit more complicated then that, but the above illustration will help to serve the point.


As we know from the last post, the Higgs Field can be depicted as a series of horizontal lines that exist across space and time. By the same token, the rasterized pixels on your computer screen can be seen to represent the omnipresent Higgs field. As you scroll up and down through this page, notice how the radial lines of the image interact with the horizontal/rasterised lines of your computer screen to create a moire pattern that embodies the characteristic field lines of the magnetic field. The faster you move it the more pronounced are these seeming field lines. I propose that what you are seeing is an accurate simulation of how a gravitational field would behave whilst moving with respect to the Higgs Field. Try it again with this image.

Now click on a non-responsive part of your browsers and move it side to side across you computer screen. This will help you to see the effect more clearly. Moving the browser window in wide circles shows a rotating moire pattern. The tighter the circles become the less intense the field and the more disorganised the pattern appears.


Physics is all about finding underlying causes to the fundamental forces, and this is exactly what I am doing here. If this visual effect can seriously be considered to form an underlying cause to the creation of the Earth's magnetic field, then we can proffer a number of statements about the production and behavior of the field itself:


Firstly, the field can be said to be produced by the interaction of the hyperbolic curvature of gravity with the holographic grating of the Higgs Field, which – as I explained in the last post – is intrinsically linked with time. This suggests some kind of closed feedback loop, where the energy of any truly large object (e.g. the Earth) is converted into mass via its interaction with the Higgs Field; which in turn produces a gravity field that reciprocates with the Higgs Field to produce the magnetic field of the Earth.


Secondly, continuous observations of the Earth's magnetic field reveal it to be moving. This motion has been accelerating in recent years, and scientist assume that this means that a pole shift is underway. However, they do not claim to understand what drives these periodic shifts in the orientation of the magnetic field. The above interactive displays would suggest that these magnetic flips are due to the relative motion of the Earth's gravity field with respect to the Higgs Field. Also the strength of the magnetic field is dependent on how fast it is moving with respect to this field.
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Thirdly, if gravity is capable of producing an electro-magnetic field around the Earth, in conjunction with the Higgs Field (which is analogous to space-time) then gravity must be electric in nature. Why? For the simple reason that the only thing that gives rise to a magnetic field is an electric one. This should be of no surprise to us as Einstein already proved a link between gravity and the electromagnetic forces, nearly 100 years ago.
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Einstein realised that gravity had the ability to slow down  time, and that this effect was subject to the strength of the field. Gravity is always strongest on the surface of a any object (like the Earth) with its strength trailing off the further you travel from the Earth and self-negating at the core of the planet. Thus time flows faster in the upper atmosphere and in the core than it does at sea level. I propose that these time differentials between the different areas of the Earth's gravitic field, as it rotates, produce an electro-kinetic charge differential.


There are a number of reasons why this might occur. The first one is intuitive, suggesting that the energy differentials of different areas of rotating space and time interacting with one another produce charges which are then as much the creation of the temporal sphere as they are of the physical processes of the three spacial dimensions. A practical consideration might be that the relativistic effect of time contraction may give electrically charged bodies in the upper atmosphere (for example) more time to act upon the lower levels where time moves more slowly.


As a visual aid to the above concepts, take a look at this informative video on how the dots operate on a DJ's turntable operate.
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The modular periodicy of the dots create a laterally expanding pattern when under rotation. When the pitch fader is at zero location the row of big dots appears to be stationary. However, above and below it the dots are moving off in opposite directions. This is similar to the way that time passes slower on the Earth's surface and quicker above and below it. The strobe light can be thought of as analogous to the flicker-rate of the holographic grating of the Higgs Field (see last post).

We can think of gravity as an electro-kinetic force created out of the energy differentials of curved space time. This goes a long way to explain such electrical atmospheric phenomena, such as sprites, as well as the fly-by anomaly observed by research satellites in recent decades.
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Knowledge of gravity's relationship to electricity has been known about for sometime. In particular the work of T.T. Brown, who coined the phrase electro-gravitics to explain the unnatural ability of electricity to defy the power of gravity (see Lifter Technology). For those who do not believe that lifters can defy gravity, I present this video of a lifter in a vacuum chamber at NASA. For those who are skeptical about the idea that gravity is related in anyway to electricity I urge you to consider that the object of the Grand Unified Field Theory is to show that these, and all other forces, are all aspects of the one force.

This concludes my presentation of the Unification of Gravity with Electromagnetics.

HOLOGRAPHIC TIME GRATING

The Large Hadron Collider is getting closer and closer to its stated aim; finding the Higgs Boson. The Higgs is a particle which acts as an exciter to the proposed Higgs field, and thusly gives mass to matter. The main determinant in an objects mass is the amount of energy the object is divested of. However, this energy is only really converted into mass in the presence of the Higg's field.

The blue/green zig-zag line depicts the path

of a particle as it moves through the omni-

present Higgs Field. The straight green line

shows a different particle moving at the speed

of light, and therefore avoiding the Higgs Field

altogether.

The green/blue zig-zag line is the path of a particle that is stationary – i.e. moving with respect to time (the vertical axis) only. It will keep bumping into the field lines (black lines) of the Higgs Field because it is traveling in an over-all perpendicular trajectory to said field lines. A particle that is traveling at the speed of light (on the other hand) warps space-time according to the Lorentz contraction thereby moving in a diagonal trajectory. This means it avoids the field lines altogether and therefore has no mass and shed loads of energy.Time does not pass for it, it travels in space only. 


The particle which encounters the Higg's field has its energy divided by the speed of light squared, as per Einstein's famous equation E=mc^2. This means that its large energy value is divided by an almost equally large constant, giving rise to a relatively small amount of mass.

The Higg's field is described as omnipresent, which means that it exists everywhere in space and time. If this is true how could any particle avoid it and in doing so become massless? Diagrams which are devised to show particles interacting with the Higg's field, depict the field as a series of horizontal lines. I submit that these lines are, in fact, equally distributed in time as well as space, meaning that you would encounter precisely the same field lines if you were traveling at relatively low speeds, as you would if you were not traveling at all. This suggests that the Higg's field is akin to some kind of Holographic Time Grating. A particle which is traveling in the time axis only is continuously bumping into this field (which is time itself) causing a zig-zag motion, which slows it down and gives rise to mass.

Stylised diagram showing ordinary space

and Lorentz Contracted space in the same graph.

Now this is all very interesting. But what is even more interesting is how the omnipresent Higg's Field interacts with matter on a 4 dimensional level to create reality, as we know it. For a demonstration of how this happens please watch the video below.

You may have noticed that the interference patterns (which are holographic in nature) are, for the most part, composed of zig-zagging lines; just like our particle trajectories.


What this means is that beyond (or outside of) the Higg's field there exists an expansive holographic interference pattern that is 4D in nature. This interference pattern is the mesh of everything that will exist, everything that has existed and everything that could possibly ever exist. In short, it is God i.e. a self-organising pattern that is timeless and intelligently designed.


But if an omnipotent God exists with a map and a timeline to all of creation, how can free-will be also said to exist? 


Only parts of an object's entire 4-d wave function can be interpreted through the minute, straight-line apertures of the Higg's field grating, at anyone time. These snapshots, or 3D manifolds of the objects exist – played out one after another – but they are not to be thought of as sequential, existing as they do through-out the entire spectrum of the waveform.


This 4D wave that describes all of the possible interactive and internal states is, of course, holographic in nature, and therefore, a fractal. This means that any part of the information of the entire wave function can be accessed at any one time, much like a computer can access files on a hard-drive.  It is by the same application of the above process by which free-will is preserved and restored.

DIRAC SEA PROGRAM

Is the infinite negative charge of the Universe proof of a creator?

One of the surprising revelations made by Dirac in his attempt to unify quantum theory with the relativity was the discovery of the infinite negative charge of the Universe – known as the Dirac Sea. According to modern-day scientific thought, infinity is not a real number, it is merely a concept. For this reason, Dirac theory should be dismissed by the science as an impossibility. However, due to the applicability of Dirac's equations, and the seemingly 'sound' basis of their argument, it has been accepted as fact.


A solution to this incongruity can be allocated by positing the existence of a creator intelligence. This supernatural entity would have been able to set the negative energy value of the Universe to infinity, in the same way that a computer programmer can set input infinite parameters fields in computer simulations. This is the only solution that allows the Dirac Sea and the consensus view of infinity, as it is perceived today, to peacefully coexist.


One of the main philosophical arguments against the belief in the existence of an omnipotent creator deity who controls the fates of men, comes from Gautama Siddharta (or Buddha of the East). He more-or-less states that an antinomian perspective of God results in a lack of concern for morality, on man's part. This argument is inconsequential to science as many of the emergent views of quantum theory and the many universes theory preclude us from the existence of freewill anyway. Science generally removes God from the equation because it is an 'unnecessary' hypothesis with little or no empirical evidence to back it up.


But, as I have shown, if we continue to insist upon an infinite negative charge in the energy state of the Universe, and the impossibility of infinity existing as an empirical value, then a creator hypothesis suddenly becomes a very necessary hypothesis. As for the issue of whether or not we have free will under quantum mechanical laws I will go some way to address this in further posts. Suffice it to say, for now, that the Buddha was right and free will exists. However, as I have previously pointed out, the facts clearly indicate that an intelligent designer may must also be at the reigns of the Universe.


In order to limit the number of regressive divinities (i.e. who created the creator) we could imagine a neutral charge universe or a Universe it which the only charge is a positive one; negativity therefore being an abstract construct (like infinity) employed to delineate our material existence from that of the creator's world.

THE MATRIX OF LEADERSHIP

Reinstating the Timespace Continuum

Some months ago I was pondering how space and time interacted on a fundamental/local level whilst walking home from the shop. I imagined that the ground was divided into a grid of squares, which had numbers on them. To begin with all of the squares were numbered '1', the next second they were numbered '2' and so on... I thought to myself, if I am moving at one square per second then the relationship between my movement and time is symmetric. If I stand still the numbers on the grid change regardless, and the only difference in me moving is which square I stand on at any given second.

In this image we see a man walking. The first line of our space time matrix shows the local time at 1 second. If the man were standing still we could say that he is moving in a vertical direction, downwards with time. If the man moves one square per second then his progression takes a diagonal route down through the matrix (the coloured line). Therefore in order to counteract the downward motion of time, this person would have to be traveling very fast indeed. This is the basic concept behind Einstein's Theory of Relativity, where all speeds are charcterised by a direction in 4-dimensional space-time. I had never fully understood that statement until I began thinking of time in this manner.

As we can see, the diagram divides up the differing speeds into angles of 45 degrees. Ordinary motion takes place at 45 degree angles to time, and light speed travel takes place at a further 45 degrees, making a total of 90 degrees. This is what I think Einstein had originally intended for his diagram of space-time, where 90º equals the sum of all possible speeds, there being no room left for any further acceleration. However, in Minkowskian diagrams the speed of light is often characterised by an angle of 45º, for convenience sake. Although this method allows for further areas of acceleration, these are usually discounted by conjectured time-paradoxes.

This diagram endeavors to show how the different speeds correspond to directions in 4D space-time. The top of the central spike being the sum of all possible speeds is depicted as being at 90º to the slower time-based regions. This diagram also bears relation to the Mexican Hat theory, where the physical laws only appear symmetrical when viewed from the top of the graph i.e. the region of most energy.

With the recent discovery of the neutrino particle traveling faster-than-light, we must logically assume that more potentially feasible regions of acceleration exist in the graphs than previously thought. My own musings on this subject lead to the development of instructive matrices utilising the 45º angle for the 'c' axis, not out of mere mathematical convenience but because that is what makes most logical sense.

The numbers in the first column show the flow rate of time, as observed by an individual (known as A) at rest, where as the diagonal line - consisting entirely of 1s - shows the amount of time experienced by an individual (known as B) traveling at the speed of light. As we can see, if B travels along the diagonal line for 3 seconds and then drops out of light speed, time resumes its normal vertical (downward) tracking. B is now on a different column to A, which expresses the fact that he has moved in space. However, both are on the same row, and indeed can never be on separate rows, because only the present moment exists. Comparing A's clock with B's clock will show a difference of 3 seconds, but the number above and to the right will show the universal time, as marked by all objects in space.

When I speak of 'universal time', I do not refer to the Newtonian concept of absolute time, which is demonstrably false, but rather to the shared commonality of what is known as 'the present' with respect to all reference frames; both of scale and acceleration. While the concept of what constitutes the present may expand i.e. dilate, at speeds approaching that of light, the free-scale nature of space-time  prevents this scaled-expansion from being in anyway important to its over-all conception of what constitutes the present.

Einstein's Theory of Relativity states that because the laws of physics are the same (therefore constant) in all reference frames, the point of view of one reference frame is as good as another. So if time has appeared to stop in one reference frame, then this means that time has indeed stopped across the entire spectrum of space and time, based solely on this one reference frame's point of view. This I feel is a grievous error, because as the above matrix shows time is implicit in all motion. If time stops we can still ask how long it stopped for.

In contrast, relativists have always assumed that due to the constancy of physical laws in all reference frames that the space-time continuum must be disconnected and broken up into individual non-relatable fragments. This is to forget that space and time are fundamentally related, that they are a continuum, and that movement in one represents duration in another.

Interestingly, this very matrix appears in a table by 15th Century mathematician and polymath Sir John Dee. Dee claimed to use the table to communicate with angels. Metatron is the leader of the angels, and is also the name of a potent device in the Transformers series; the Metatron Cube. Another device of importance in this series is the Matrix of Leadership. Therefore, being a child of the 80's and a spirited fan of science fiction, I dub the above matrix, the Matrix of Leadership.

The Lorentz Transformers

STELLAR OBSCURA

Black Hole Quantum Gravity Theorem

In order for a theory of quantum gravity to work in needs to be able to deal with gravitational singularities on the quantum scale. In my post, Hyperbolic Perspective and Quantum Gravity I outlined a theory which describes how gravity works on very small scales, but it is clear that something else is needed entirely for it to describe a gravitational singularity on the quantum scale.

The Inter-Dimensional Merry-go-Round

In the wake of his discoveries - regarding length contraction at speeds approaching that of light - the world renowned physicist Albert Einstein attempted to unify this concept with the gravitational spin of the Earth. He knew that the surface of the Earth rotated much faster than its core, and this meant that it must also undergo a more pronounced length contraction. The object he used to imagine this type of geometric contraction was the merry-go-round. He proposed that if a merry-go-round were to spin at very high-speeds, the outer-edge of the disk would undergo a length contraction forcing its edges to curve upward. From this he deduced that space itself was curving and this led to his Theory of General Relativity.

Just as a black hole warps space to an extreme degree we can imagine a merry-go-round that is spinning so fast that the resulting curvature warps it into a sphere. Shifting an object from one dimension into another higher dimension is an excercise in trans-dimensional geometry, which is exactly what we have done here, taking a flat 2-dimensional disk (merry-go-round) and turning it into a 3-dimensional sphere.

In the case of a super-massive star that is about to turn into a black hole, we need to imagine that we are taking a 3D sphere and transforming it into a 4D sphere.

As the star shrinks its surface is becoming more and more length contracted, which corresponds with an increase in the degree of space-time curvature and thusly in gravity. Although we can deduce from this that gravity is at its strongest with respect to the surface of an object, we also know that the force of gravity continues, as in the case of the Earth, down through the mantel to some degree until a null-point is reached at the core. It should be apparent, therefore, that the quantum singularity of a black hole is not 'the centre' of anything, but is in fact only that region of the gravitational field which corresponds to the surface of the star. This means that the entire surface of the super-massive star along with its gravitational field has turned in on itself, and its entire surface area (or circumference) has been reduced to zero. 

You might be wondering where the mass of the star has gone that produces these gravitational effects.When a star collapses it can be said that its entire mass is undergoing a length contraction, in all 3 dimensions. This is a Special Relativistic effect, which implies that the mass of the star is accelerating towards a central point, faster and faster. It reaches the speed of light (the event horizon) and then necessarily exceeds it. Once the star reaches twice the speed of light (at the plank scale) it turns itself inside out, resulting in the gravitational singularity. This effect is known as length expansion and is dealt with in the post titled Direct Relativity.

From then on the singularity can be described as an aperture into the 4th dimension. This is just like the aperture of a camera, or more accurately a camera obscura. In a camera obscura, light is allowed into a receptacle through only one point of entry (the size of a pin-hole). This has the effect of focusing the light at oblique angles creating an inverted (up-side down) image on the back of the black-out receptacle. A gravitational singularity has the exact same effect on the stars mass, only - by virtue of it being a 3-dimensional aperture - it turns the star inside out as well as upside down. In this way the singularity can be seen as a twist in the fabric of space-time, occurring at the Plank Scale.

Although a singularity cannot be said to have any sides, for the sake of argument (and common sense) lets imagine that an asteroid is being dragged towards the right-hand side of a black hole. From a holistic point of view i.e. one that spans all dimensions, the asteroid is actually being dragged towards the left-hand side of the star's mass, because the singularity has inverted the stars orientation. This type of inversion is what makes it reminiscent of the camera obscura.

In Hyperbolic Perspective and Quantum Gravity, I used a hyperbolic tiling to express how quantum particles, which are under a high degree of magnification, do not exhibit a noticeable degree of hyperbolic distortion (i.e. gravity). This same image could be used to describe a cross-section of the Earth's gravitational field; in which the bulk of space-time curvature is perceived at the edges and dead-space or null-point seen at the core. In order to create a singularity, all we need to do is invert the hyperbolic curvature. 

However, this still does not help us visualise where the star's mass has gone and what is taking place in the fourth dimension. In order to do that I will reduce the number of dimensions down and flatten out space into just 2 dimensions. The grey areas, which denote empty space are merely the result of flattening out the 3-4 D environment out into a 2D image. Such artifacts are regularly observed in map projections, when trying to reduce the curvature of the earth into a 2-d image. As in the case with the map projections no such areas of empty space really exist and motion from one area of space to another can be achieved without undue effort. This then is the fundamental domain of a black hole.

Here we see that the lines of force generated by the gravitational field of the star are being inverted through the singularity at the Plank Scale. What this tells us is that the boundary plain to the four dimensional universe is the 2D limit of the Plank Scale. To understand this same diagram from the point of view of the star in the 4th dimension we need to invert the image. I find this image to have striking correlation to a torus, or a flower. Marko Rodin would say that this is significant. I tend to agree, but I won't be dealing with exactly why this is so until a later date.

So you might be wondering, what is so new about this? Well, physicists generally assume that the mass of the star, while being compacted to an infinite density, remains in this dimension. Others (Marko Rodin for one) have supposed that the singularity may be a gate-way to another dimensions, whereupon the black hole shifts output to produce a white hole. I maintain that when the stars mass falls into the fourth dimension it remains in a static condition; for the obvious reason that there would not be enough mass to support the singularity otherwise.

The reason why the time does not impinge upon it is to do with relativistic laws, but more importantly, because in the 4th dimension time becomes space - and space becomes time. The only way that the star can gain or loose mass (not likely) is through its interaction with the 3D time-based universe. But if the black hole is frozen in time, does that not mean that it should be left behind, as time moves on in our Universe? It should, but because space acts like time in the 4th dimension the mass of the star is continuously dragged along into our time-frame of reference.

The fact that the fourth dimension is intrinsic to the geometry of singularities has been known about in the computer gaming industry for decades. This industry uses a 4-dimensional algebra set, known as the quaternions, to create smooth graphics and to allow for uninterrupted rotations around a 3-D environment. Without the use of the quaternions something known as Gimbal Lock occurs, which is basically defined as a singularity. This means that from a fourth dimensional perspective the singularity does not exist. Refer to the previous two diagrams.

If it has been known that quaternions, and therefor the fourth dimension, are intrinsic to the production and erasure of singularities, then why do physicists insist on thinking of the black hole as being something which exists in our dimension alone? Mathematicians have noted that quaternions/octonions are primarily spatial representations and therefore do not include time as a part of their framework. But I think that they are missing the point. There is no real fourth dimensional space, in my opinion, 4-d space looks exactly like 3-d space only we have swapped one of the spatial dimensions for a time dimension – see post; Within the Octonions for a fuller explanation of this.

As a final way to visualise what is taking place with the stars mass, take another look at the video of the rotating tesseract. Imagine that small cube at the centre of the structure is the uncollapsed star. Then, as the cube rotates, notice how it becomes distorted (length contracted) and finally turns itself inside out.

WITHIN THE OCTONIONS

In the second to last post, I outlined a theory of quantum gravity which utilises hyperbolic geometry. But there are a few interesting elements to this that need to be looked at in more detail. On his site, John Baez gives a very accurate breakdown of what hyperbolic geometry is and how it can be constructed from simple, everyday Euclidian geometry;

Take a bunch of equilateral triangles. Glue them together so that 3 meet at each corner. You get a regular tetrahedron.

Then take a bunch of squares. Glue them together so that 3 meet at each corner. You get a cube.

Next, take a bunch of regular pentagons. Glue them together so that three meet at each corner. You get a regular dodecahedron.

This is fun! We're getting a series of Platonic solids.

Next, take a bunch of regular hexagons and glue them together so that three meet at each corner. Now the angles of the hexagons add up to 360 degrees, so we don't get a Platonic solid. Instead, we get a tiling of the plane. It looks like a honeycomb that stretches out forever in all directions.

Next, let's take a bunch of regular heptagons and glue them together so that three meet each corner. Now the angles add up to more than 360 degrees, so we get a tiling of the "hyperbolic plane". The hyperbolic plane is like the opposite of a sphere, since it's saddle-shaped at every point instead of bulging out at every point. In fact the sphere and the hyperbolic plane are the two most symmetrical forms of non-Euclidean geometry. The sphere is "positively curved", while the hyperbolic plane is "negatively curved".

We can input this series into a table (of sorts) to get a better sense of how the geometry develops;

Tetrahedron;……3D, 4 triangles,…...3 meeting at each vertex

Cube;……………3D, 6 squares,……3 meeting at each vertex

Dodecahedron;...3D, 12 pentagons, 3 " " "

Hexagonal tiling; 2D, ∞ hexagons,…3 at each vertex

Hyperbolic plane;4D, ∞ heptagons,..3 at each vertex

What is interesting here is that we go from 3 dimensions, back to 2, and then straight to 4. This corresponds with what I wrote in Direct Relativity, where an object that is accelerating beyond the speed of light goes from 3 dimensions, to 2 and finally to 4. In this sense we can think of the above series as representing what happens to space as an object accelerates, and shows that it essentially "turns itself inside out". Acceleration is equivalent to an increase in energy, this energy reaches its limit at the hexagonal 2D plane. But, were it possible to go beyond this limit more dimensions would have to be added. This means that extra-dimensions equal an increase in energy/information.

7,3 hyperbolic tiling shows 7 linesconverging on an axis.

When we think of 4-dimensional space, we often think of the three dimensions of length, breadth and height, along with a fourth spatial dimension at right angles to each of these. But what the above series shows us is that when we introduce the fourth dimension this breaks the continuity of the first 3 dimensions, into something more like six. This break in continuity occurs so that each axis remains equidistant from one another around a central point. We must therefore think of each of these 3 dimensions as being comprised of two separate values, much as we do in daily life. Height is broken into; up and down, breadth into; left and right, and length; into forwards and backwards. In reality there is no break in continuity. But from the point of view of an outside observer, like ourselves, the inclusion of a fourth spatial dimension results in an apparent disconnection of these dimensions.

The 4/7 dimensions of hyperbolic geometry

 and the quantum scale

Time is often thought of as the fourth dimension, but it should also be noted that, in some sense, time is just another spatial dimension. So the heptagonal (7,3) tiling is an accurate description of 4-dimensional space-time and the hyperbolic curvature that creates gravity. We should also note that whereas the 3 spatial dimensions each have 2 components; up/down, forwards/backwards etc. the time axis only has 1. This lack of symmetry may account for the reason why time only moves in one direction; from past to future, and never the other way.

If we were to remove one of the seven dimensions, it does not matter which, the other six will rearrange themselves into the infinitely tiled hexagonal plane of only two dimensions. Lets say, for argument sake we can remove the "up" dimension. This results in time taking the place of the up dimension, and therefore time no longer serves the function of duration in this instance. Without time we also lose the use of the 3rd dimension, because as I stated in Direct Relativity, our conscious is a 2-dimensional plane, and can only access the third dimension by moving into it (and time is a function of motion). Despite this, the hexagonal plane will continue to possess the appearance of being 3-dimensional, due to the fact that its structure still contains all the necessary data for l, b and h implicit in its geometry.

The hexagonal tiling still has all the informationof 3-dimensions implicit within it. In fact, becausethe cubes can be viewed in two different waysit may even imply a 4th dimension.

It is obvious that since time is the fourth spatial dimension it needs the other three to build on. But what is less obvious is that without time, space, as a 3-dimensional construct, also ceases to exist in a useful manner. Therefore, time and space are inextricably linked in this geometric fashion. The more intense the curvature of space the less time is seen to pass, because time is becoming space.

The hyperbolic plane shows a description of space-time viewed from the quantum scale. At this magnitude space appears flat, but in the distance the accumulative effect of matter is shown to curve space-time. Since Einstein related space-time curvature to acceleration, it appears that from the point of view of the quantum world, space is being accelerated at the macro scales. Acceleration is further linked to time dilation and therefore time ceases to exist in the meso-macro scale for all particles and hadrons in the quantum world. Could this account for some of the strange behaviour, as seen by us, on the quantum scale? I think it must.

As already noted, the hyperbolic plane is a description of how matter interacts with space-time and not anything else. One of the key principles of matter is that it is always changing. Time is the rate of change. Therefore, matter is time, or more accurately an expression of space-time. We could redraw our seven axial model of space-time, in which the primary spatial dimensions are preserved and the 4th/7th dimension becomes bent into a loop (see Fano plane). This looped time is essentially matter. In this regard, we could ask does matter create the curvature of space-time or does space-time curvature create matter? It is a chicken-and-egg phenomenon.

The Fano Plane Order 2could be used to describe thesix directions of space along withthe looped dimension of time,which is also matter.

Just like with normal perspective, when we zoom in on a particle that particle grows in size making all the other atoms and particles appear smaller. By zooming out again, all their relative sizes are made uniform, making all of space appear flat again. Continuing to zoom out at would warp space in the opposite direction, giving space the appearance of one of the Platonic Solids or simply a sphere. Again this is related to Scale Relativity where being zoomed in on an object at the quantum scale is equivalent to stopping, and zooming out the equivalent of accelerating. From this perspective flat space-time i.e. what we normally perceive space as, is equivalent to space traveling at the speed of light (see Direct Relativity). 

The heptagonal hyperbolic plane is linked to the number 168, and by extension to the Klein Quadric, PSL (2,7), the Fano Plane and Octonions. We have seen already that the Fano plane relates to space and time, as does the number 168 (24 x 7). The fact that the numbers 24 x 7 (as in 24 hours, 7 days a week) should crop up in our formulas for space time implies that our local description of time, as denoted by the rotation of the Earth around the Sun and the geometric division of the circle into 360º, is somehow intrinsic to the nature of higher-dimensions and the universe on a cosmological scale. How could this be, when we have so long been told that Earth and our solar system are no longer the centre of the universe? The answer, I think, lies within the Octonions.

We have already looked at space as a 7-dimensional construct, at least at very small scales, but the 8-dimensional algebra of the Octonions would ask us to look again. Octonions have 7 dimensions plus 1; this extra dimension is a projective point, which I maintain may be linked to consciousness. Reality, as a whole, must be projected from the conscious mind of the individual perceiving it, just as the Buddhists and mystics have been saying for thousands of years. This in itself would explain why the structure of time and space in our locale are inextricably linked with the underlying mathematical laws that the human mind has been developing over the ages.


We already spoke of time as resulting from the asymmetry of the 7 dimensions of hyperspace. But, if consciousness represents the eighth dimension then shouldn't it provide the symmetry needed to prevent the forward motion of time? Well in some ways it does; consciousness provides us with a memory with which we can skip through the events of our lives without a great deal of difficulty.


However, the arrow of time is still very much a persistent factor in our daily lives, and cannot be dealt with so easily. A more comprehensive view then would suggest that the eighth dimension is a fractal dimension containing all of the previous 7 dimensions on repeat down towards infinity. This makes sense because consciousness is the only place where we can be aware of dimensionality and of the passage of time. It is also clear that consciousness, and life in general, is a self-referencing organism that would sit well alongside our definition of a fractal system.

For more information on how the number 168 relates to time and the speed of light see my first post; Scale Relativity.