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.

DIRECT RELATIVITY

In order to progress further with my theory of quantum gravity, I must first reveal to you the principles of Direct Relativity. Direct Relativity deals with how the laws of physics behave in respect to a body traveling faster than the speed of light. It then uses these same principles to investigate the fractal nature of space-time, and to observe some unusual consequences at and beyond the Plank Limit. Following the discovery of a close association between my work and Laurent Nottale's Scale Relativity, I decided that there must be more to the theory that needed close attention. I began with looking at the concept of space-time being fractal at the quantum limit of the plank scale (as previously stated by Nottale) and tried to unify this concept with Einstein's Theory of Relativity.

What happens to an object traveling faster than light (FTL)?

One thing that struck me from my research into Relativity, is the comparative lack of work done into what happens to an object's subjective experience of time at speeds exceeding that of the speed of light. The rationale behind this comparative dearth of information stems from one of the tenets of Relativity itself; i.e. objects of appreciable mass cannot even reach that of the speed of light, let alone exceed it. With the recent discovery of neutrinos traveling just beyond the speed of light, physicists are being forced to rethink this assertion, but it is generally accepted that if an object were to travel faster than light it would necessarily be traveling backwards in time. However, this assumption cannot be derived from any of Einstein's mathematical proofs. For instance, when we try to input speeds in excess of 'c' into Einstein's equations for time dilation, we invariably get the square root of a minus number, which is imaginary. Being an imaginary number it is accepted that physicists have no idea what this number actually represents in reality.

Graphic Source;
http://www.physlink.com/education/askexperts/ae283.cfm

One place where imaginary numbers do find application is in the area of fractals; like those of Mandelbroit. For this reason, a graph depicting the change in the rate of the flow of time with regard to an objects acceleration is (to some degree) a fractal graph. Fractals are geometric objects - albeit of a very special kind, having no absolute scale. In order to unify them with relativistic principles of time dilation, over all possible accelerations in 4-dimensional space-time, we would have to think of these varying accelerations as representing one complete geometric form in space-time i.e. a fractal form.

The length contraction which objects undergo when approaching light-speed is a fore-shortening produced by its rotation into the unobservable 4th dimension. When an object is coasting along at the speed of light, this contraction; known as a Lorentz transformation, reaches zero, meaning that the object has rotated fully 90 degrees with respect to our 3-dimensional spacial reality and is now directly traveling in the 4th dimension of time. Logically, when an object travels FTL its rotation with respect to our universe would increase further still, literally turning the object, and the universe around it inside out! If the object were an egg, for example, the entire universe would now be contained with in the bounds of the egg, and the egg itself would fill the entire universe! This exact same effect can be observed when viewing visualizations of rotating hypercubes, where the inner cube will deform and literally appear to turn itself inside-out. It should be noted, however, that these visualizations expressly deal with projections of hypercubes into 3D space, and therefore neglect to show the results of such a rotation on a 3D manifold/slice of a 4D tesseract, which to our eyes would look just like a cube.

To address this imbalance, I will attempt to describe what such a rotation would look like to our eyes. If an object rotating in 4-dimensional space-time is equivalent to one accelerating towards the speed of light, then we can expect our cube to undergo a runaway acceleration as it is being rotated. By the time it reaches the speed of light, it will have turned a full 90º to each of the x, y, and z coordinates of 3D space, and should almost completely vanish from sight. Rotating the cube a further 90º (a total of 180º) should accelerate it to twice the speed of light, completely turning the object inside out, with the added result of it vanishing from our universe altogether.

If this were the case, I would have no other choice but to concede that the object had traveled into the past. Remember that the Lorentz transformation is the result of a foreshortening of an object into the fourth dimension of time. If we consider this dimension to be at right angles to all 3 Cartesian axes, then we could not expect the Lorentz transformation to be observable in our universe. The idea that such a transformation would be observable suggests to me the possibility that an object traveling FTL will begin to undergo an inverse expansion, and thereby become visible in our universe; following the initial length contraction of light speed. This raises some interesting questions such as; What physical properties might you expect to emerge from an object undergoing such an extreme rotation through 4-dimensional space, which is energetically equivalent to it traveling at twice the speed of light?

Relativists have always assumed that any object or particle traveling faster than the speed of light must lose mass. However, measurements taken of neutrinos traveling more than light-speed have revealed no such mass reduction. An explanation for why this may occur is derived from the proposed (above) law of  inverse expansion. When an object is accelerating, energy must be put into drive this acceleration. According to Einstein's Theory of Relativity this increase in energy corresponds to a geometric increase in the object's mass. Furthermore, this mass increase must be proportional to the over-all length contraction. When an object begins to exceed the speed of light (as in the case of the neutrino), we can imagine that its mass continues to increase, while its length begins to undergo an inverse expansion. Since length contraction and increased mass are proportional at speeds approaching that of light, we might find that the universe has difficulty reconciling the resultant disparity of an object undergoing mass increase and expansion, at super-luminal speeds. It is my speculative belief, therefore, that the inverse expansion cancels out the predicted mass increase; meaning the overall mass of the object remains constant. This single concept may be the mechanism that lies behind the constant mass observed by physicists in the Cern/Opera Neutrino discovery.

Direct Relativity (DR)

So far we have only discussed the relationship between length contraction and acceleration. However, it should be possible for an object to undergo a Lorentzian length contraction without undergoing any acceleration. I suspect, for this to occur, the rotational force would have to be applied upon the entire object by a higher-dimensional energy source, and not from any force generated in this plane of reality.

The inability of the universe to differentiate between certain key aspects of the Theory of Relativity at super-luminal speeds should also be observed at very small scales; for example the Plank Limit. The Plank Scale is the lower limit of length in the universe, these are quanta of space which are so small as to be only divested of two dimensions. It is my belief that these innumerable two dimensional quanta are in fact the boundary planes of an equally large number of hyper-dimensional objects; and therefore of a separate, parallel universe. For the sake of argument I will make these objects tesseracts, as these are the most commonly known and easiest to visualize. But, remember these are not the so-called 3D projections of 4D objects that we are so accustomed to seeing in books and videos on the subject. The quanta I will be referring to are rather 3D manifolds embedded in our reality.

Each of our 3D manifold cubes consist of 144,000 quanta stacked together (this number was chosen to show that they are finite in size, and therefore very small). As these cubes rotate in 4-dimensional space, their different faces will either appear to be contracting or expanding - depending on their degree of rotation with respect to space-time. But, because an ordinary cube of space is symmetrically speaking (and every other way) equivalent to one undergoing an inverse Lorentzian transformation, the universe will treat both objects as having the same mean energy ratio. Obviously, this is also true of cubes which are either expanding or contracting, for if a cube is undergoing a contraction it could either be (energetically speaking) accelerating towards the speed of light, or decelerating from twice the speed of light down to light-speed. Conversely, a cube of space which is expanding could either be, energetically speaking, decelerating from the speed of light or accelerating beyond it. The matter becomes even more intractable, however, because all of the cubes are made of a potentially infinite number of 2D quanta (see; differential equations), and therefore, any distinction between where one cube might end and another begins is entirely arbitrary. Nevertheless, distinctions are part of human life and, all things being equal, one distinction is as good as another. 

The blue line in this graph shows an object steadily accelerating towards the speed of light. The green line shows one decelerating from the speed of light to zero. The two velocities mean values are represented by the red line, to show that they are ultimately a steady state system.

The point of all this is that; space, at the down to the Plank Scale must have a constant, steady level of energy, as determined by the inverse law of expansion, and that all of this energy, must in some way be derived by the interaction of our Universe with that of a parallel Universe that exists just beyond the boundary mark of the Plank Scale. The cubes are contracting into, and expanding out of this dimension (the 4th dimension of Einstein) like a kaleidoscope. A kaleidoscope only gives you a beautiful and symmetric view of the world, but nevertheless it is fractured and incomplete. In order to see the entire universe on this scale we would need to view it with 4/5 dimensional eyes. 


Direct Relativity suggests that space is not really fractal on very small scales, but kaleidoscopic. This approach may, therefore, give an alternative viewpoint as to the nature of time in the universe (because time and the rate of change would be emanating out of the dimension beyond the Plank Scale). 

Universal Consciousness 

When I say that the Universe has trouble differentiating between a normal cube of space and one that has undergoing Lorentz expansion, people may think that I am advocating some kind of conscious at work at this level of space. But this is probably correct in some way, because I am saying that just as our minds have trouble differentiating between what is the front and backside of a Necker cube, the Universe has the same problem with regard to certain aspects of Relativity which also lack a certain frame of reference. Look at this video of a Necker Cube rotating and notice how it switches direction every now and again. Now imagine a hyper-dimensional Necker Cube of space that is rotating at the Plank Scale without any sense of which direction it might be traveling in and you will see why the universe might have trouble, in this respect.

Furthermore, the rotating cubes could make an arbitrary quanta appear to move out of one cube and into another. If this perceived motion was then coupled with a run-away acceleration pieced together from the randomly determined Lorentz transformations, then you could have numerous quanta appearing to jump around in different directions exceeding all known speeds, bashing into one another, becoming one another, and then dropping back to rest in the blink of an eye; Chaos in other words. All of this motion would be an illusion, but because the Universe cannot tell what is illusion and what is real at this level, it all becomes real to some extent. 

Symmetrical and Biological Considerations of DR

Nevertheless, there is order; and the Universe is particularly aware of this order, otherwise we could not exist. It is my belief that the symmetry observed between a cube of space at rest (at the Plank Scale) and one that has just undergone an inverse Lorentz transformation, is directly responsible for all of the symmetries that we see in the natural world; and that includes the physical form of the human body. From the point of view of Direct Relativity, the right hand side of your body is energetically at rest, while the left hand side is traveling at twice the speed of light, and the axis of symmetry that runs between your body is traveling at the speed of light. None of them are in fact touching, but because of the Universe's strange inability to see any difference between these three disparate states of acceleration at the lower realms of matter, stasis is observed at the higher ones. This is not to say that any part of your body is really traveling at any of the aforementioned velocities, it is merely a projection of the rotations of reality at the smaller levels on up, and this projection provides the chiral symmetry we have come to expect of biological organisms, as well as, perhaps, their evolution through time.

Regardless of what you might think of the principles at work here, if you take anything away with you from this post; please let it be this. Your consciousness (or sense of self) occupies that area of the body, which corresponds to the (length contracted) axis of symmetry, which itself corresponds to the speed of light. This means that your consciousness, at this very moment, is already traveling at the speed of light; something which modern Relativity does not even begin to address (although it does not violate any of the known laws, as consciousness is not known to have any appreciable mass). Something of this is already known and spoken about in Buddhism, Hinduism, Taoism (and numerous other Eastern philosophies) that the human soul (or consciousness) resides on the central channel of the bodies subtle energy-or Chakra- system. The author of the Tibetan Book of Living and Dying has this to say on the subject;

There are 72, 000* subtle energy channels in the body, but three principal ones; the central channel, running parallel to the spine, and the right and left channel, which run either side of it.

This is very interesting, because the right and left channels are invariably coloured red and blue (respectively) in all cultures which deal with the subject of the subtle energy body; including the West. This red and blue could therefore correspond to the red and blue shifts known to accompany a mass accelerating passed a chosen space reference point; in this case the central channel. Interestingly, practitioners of many religions pray with their hands together, as if focusing their attention on the 2D consciousness plane of the central channel.

Furthermore, the fact that consciousness resides in a 2-dimensional (length contracted) manifold, embedded within the human body, means that consciousness exists strictly on the level of the Plank Scale. This means that what we are observing, when we look at the world, is directly connected to what is going on down at this scale and, more importantly, how it can be so that the human mind is capable of effecting matter at the minutest of scales simply by observing it. So it would appear that the question of a universal consciousness overseeing this level of reality has been somewhat answered; you are that consciousness and this world is partially the result of your inability to comprehend yourself; I think.


*This is exactly twice the number (144,000) I proposed for the embedded quanta manifolds above. This is not entirely coincidence, as it reflects my belief, that the chakra system, on some level is a model for the workings of the entire universe; on both large and small scales.

HYPERBOLIC PERSPECTIVE AND QUANTUM GRAVITY

One of the problems that physicists have in uniting gravity and the quantum realm is that gravity does not appear to interact with particles (like electrons) on small scales. Mathematicians and physicists, when dealing with this force on such a scale, often have to utilize infinities in their equations to express the domain of countless other particles that exist in the vicinity of their particle model. 

My solution to the problem of how to unify the concept of gravity with the particle realm is simplistic and geometric, and for this reason, utilises almost no mathematics. The solution to this problem can be stated in one word; perspective.

When a particle (like an electron) is directly in your field of view, it will appear much greater in size than all of the other particles stretching off into infinity in any given mathematician's model. Furthermore, it will occupy the central position of your frame of reference (your field of view).

From a geometric consideration, perspective is no different from gravity on these scales. Gravity is the result of the combined mass of millions upon millions of particles. It is also, according to Einstein, the equivalent to the curvature of space-time. This curvature consists of more than 3 dimensions and is thus a hyperbolic curvature.

The Poincare disk is a Euclidean description of hyperbolic space. The area in the centre of the disk is closest to you, while the areas at the periphery are receding off into the distance. Notice how the shapes (in this case a mixture of octagons and pentagons) become more distorted as they recede, while the same shapes in the centre of the disk display little or no distortion whatsoever. This is Hyperbolic Perspective.

By combined these observations with what we know of Einstein's Theory of General Relativity we arrive at the understanding that the closer you are to an object on the quantum scale the less hyperbolic distortion (gravity) can be seen to have a noticeable effect. The sea of particles on the periphery must have a combined gravitational field which distorts space-time, and this is exactly what we see at the periphery of the Poincare disk where the effects of the hyperbolic curvature are most notable.  It, therefore, follows that trying to observe the effect of the distortions of gravity on a particle (for example), while directly observing this same particle, is a kin to trying to catch a glimpse of the back of your head in a mirror; something I am sure many of us have tried as children. Just as in Heisenberg's Uncertainty principle, whereby the observer changes the reality, I believe our observations of the minute areas of space-time effectively flatten out the incumbent distortion making the force of gravity appear redundant, when in fact it is every bit as prevalent as any other region of the hyperbolic curvature.

In order to directly observe how gravity distorts particles across the board, we would have to manufacture a type of imaging technique which would take into account oblique light rays whilst directly observing the object. A possible contender for such a technique would be something along the lines the work of photographer Vincenzo Giovanni Ruello, and his Theory of Angular Filming.

The entire theory as outlined in this post can also be, briefly, stated in terms of Scale Relativity (Sc.R.). According to my own version of Sc.R. zooming in on a particle is equivalent to slowing down and/or stopping. Conversely this means that everything at the periphery appears accelerated, and therefore under the influence of gravity, as deemed by Einstein's GR. 

You will notice that this theory deals with scales roughly down to the size of an electron, for scales below that and down towards the Plank Scale, a new theory is likely to be needed. This theory I hope to outline in subsequent pages of Direct Relativity. That post is now available at;

http://directrelativity.blogspot.com/2012/02/in-order-for-theory-of-quantum-gravity.html

SCALE RELATIVITY

Recently I developed my own version of Einstein's Theory of Relativity, which was based on the idea that speed is geometrically analogous to scale; meaning that slowing down is equivalent to zooming in on an object/place and speeding up is equivalent to zooming out. The theory, which utilized the concepts of fractal cosmology, namely that space and time are fractals, appended with what I thought to be a new concept; which is that light is itself a fractal. A quotation from my notes may serve to illustrate my point more clearly;

  …acceleration and rapid travel in general is the equivalent of zooming up through all of the distance scales from the minute; cm, mm etc, to the largest volumes of kilometres, as if we were navigating our way through a dense forest of metre markings (or whatever the lines on a ruler are called) at high speeds.
We have also said that this kind of accelerative geometric zooming has no real effect on the metering scale of light, which is therefore 'freescale' and fractal.

From out of this section, and perhaps one or two others, was born my concept (or what I thought was my concept) of 'fractal acceleration', which would combine formulae of acceleration and fractal mathematics together. With the ground work done of effectively visualizing my concept, I went onto the internet to try and see if anybody had gone in the same direction, and more importantly developed the mathematical systems for fractal acceleration, which I in my mathematical illiteracy, had not a hope of achieving. Lo-and-behold, in a little known work called 'Fractal space-time and microphysics' by Laurent Nottale I found the exact equations I had envisaged. Realising that Nottale must followed a similar line of reasoning to my own in order to develop his theory, I back-tracked through his work to uncover the concept of Scale Relativity, which (rather unsurprisingly) bore all of the hall-marks of my own work.

Laurent Nottale's Scale Relativity Theory states that Einstein's Theory of Relativity holds true, not only at all rates of acceleration, but also at all scales i.e. from the Plank scale up to the cosmological scale. If all scales are relative, there can be no absolute scale measurement in the Universe. A freescale universe implies that space, and therefore time, must also be fractal. A large component of my own theory is that space-time, and by extension light, are fractal in nature.

I would like to begin by comparing my observations, trite though they may appear, with those of Nottale's. First, I will reproduce  observations on the issue of scale and acceleration, as they appear in my notes;

Traveling at faster and faster speeds in space-time is equivalent to traveling at a slow and steady pace whilst zooming out i.e. bending light and space to form an arch around that which you wish to travel.

In this graph we see a craft (red line) accelerating to 2/3 

of the speed of light across a distance of 450,000 miles.

While the occupants of the craft are fundamentally aware

of the overall distance travelled, relativistic effects come into

play whereby A and B (and everything in between) under go a 

length contraction making them appear much closer together.

Notice how the distance traveled in each graph remains exactly the same, even though the distance between A and B appears greatly lessened. This length contraction that they are undergoing is equivalent to the length contraction experienced by hypothetical occupants in a hypothetical craft traveling at close to the speed of light.

The purpose of these graphs is to show how the relativistic effect of length contraction and the concept of zooming out from one scale measurement to another are intrinsically linked. On a side note, in Lewis Carrol's classic The Adventures of Alice in Wonderland, Alice is given to eat something which makes her grow in size. From her perspective it appears that the room she is in is shrinking. From a relativistic point of view her perspective must be considered correct, meaning that Alice's overall size remains the same and it is Wonderland that is shrinking. Think about that next time your socks shrink in the washing machine...

Zoomed in, or normal zoom = 0 mph                               Zoomed out;

                                                                                the distance between 

                                                                              objects appears smaller.

 Top ruler; zoomed in - large interval. Bottom ruler; zoomed out - intervals appear smaller.

Nottale's early observations and motivations, from the article on Scale Relativity on Wikipedia;

Two everyday observations are, that if we look at an object at a very small distance, say through a microscope, then even the slightest movement of this object will appear very fast; if on the other hand we look up to the sky and follow the movement of a jumbo-jet we sometimes wonder why it doesn't fall down, because from this distance it appears to be almost standing still.
Is this a pure subjective perception? The passengers in the jet will say that the clouds rushing by prove that the plane is moving fast, whereas the earth below is nearly standing still. And if the 'object' under the microscope were an ant that just woke up from coma, it would observe itself moving - relatively to the surface it is bounded to - with merely a few centimeters per minute.
This is reminiscent of the situation where one walks inside a train. Oneself observes walking rather slow, while an observer outside will add the velocity of the train to the walking speed, and say that the person inside the train is walking fast relatively to the ground. A similar observation led Galileo to formulate a relativity principle of motion. Likewise the former observations led Nottale to formulate scale relativity.

Comatose ants aside, I think you will agree that conceptually, at least, the two ideas are almost identical.

Continuing with my own notes, then;

6.The importance of understanding acceleration in terms of zooming in or out on a given plane or vista becomes clear when we apply it to Special Relativity. SR states that the speed of light remains constant at all speeds and at all rates of acceleration. Since the speed of light is determined by its wave function interval, we can go further and say that the interval for the speed of light remains constant at all zooming acceleration scales (via the relativistic effect of time dilation). If when zooming in/out the speed of the interval remains the same then we can say it is a fractal. Light, therefore, must be a fractal; not only in terms of scale, but also in terms of formulae of acceleration. The concept of light being a fractal is not new. I have already discussed the concept in Note 2; where I said space-time are fractals. The fabric of space-time is indistinguishable from that of light, generally speaking; so light must also be a fractal. Light is a fractal waveform with Phi 1.618 as its ratio divisor.

7. So what happens to a craft that is accelerating (ostensibly) from the view point of timespace/spacetime?

In this diagram we see our fictional craft accelerating from an interval close to the value of 'c' where time is flowing normally, to the periphery where time has stopped flowing altogether. The mathematicians will note the semblance of this theory and the previous diagram to Cantor's Function.

Interestingly, Einstein's equations provide two reason as to why matter (in its grossest form) cannot travel at the speed of light (and both appear mutually exclusive). One is that a mass will get heavier requiring infinite amounts of energy to propel it, and the other, perhaps less well known, is that the same mass will take an infinitely long time to reach said velocity. To me this smacks of Xeno's paradox in which it is impossible to reach some stated limit if the distance traveled is continuously divided by half. This paradox is resolved by pitting two different infinities against one another and also in differential equations, all of which relate back intrinsically to Cantor's work. Just as the mathematician can reach a workable approximation of Phi 1.618, so it is that, from a theoretical point of view, that a mass could eventual reach the velocity of 'c', provided increased mass was not a consideration.

From the polar coordinate point of view of the same graph, we see how a ship accelerates out from an interval relatively close to that of 'c' out to the periphery where intervals are much larger. Alternatively we view the centre of the diagram to be an aleph point receding off into infinity. Either way the craft will eventually reach an average curvature (Phi 1.618) which is typified by the outer perimeter where the time intervals have receded off into infinity.  I would also like to draw your attention to the fractal pattern generated at the centre of the image (below) and the tripartite nature of the six inner strata, as they conform to ancient triskele symbolism.

As I have said before, acceleration and rapid travel in general is the equivalent of zooming up through all of the distance scales from the minute; cm, mm etc, to the largest volumes of kilometres, as if we were navigating our way through a dense forest of metre markings (or whatever the lines on a ruler are called) at high speeds. We have also said that this kind of accelerative geometric zooming has no real effect on the metering scale of light, which is therefore 'freescale' and fractal.

The rendering of the above diagram also recalls, to my mind at least, the Hunab Ku, a supposed representation of a Mayan deity, known as the "supreme god." The New Age interpretation of this symbol posits the Hunab Ku "as evidence for Maya monotheism and suggested that it was represented by the symbols of a square within a circle or a circle within a square, the square representing measurement and the circle representing motion." http://en.wikipedia.org/wiki/Hunab_Ku

In subsequent posts I will expound my Theory of Direct Relativity and more importantly Layer Cake Theory, but for now I would like to conclude this section by saying a few things about the fractal nature of light and what else that might entail. Although I do not have the technical expertise to prove this, I nevertheless believe that the orthogonal relationship between the electromagnetic forces in a light wave expresses the Golden Mean 1.618. My belief is informed by the discovery of the Golden Ratio in the DNA spiral, and studies which show that light in the form of bio-protons alter functions (i.e. resonate) within the aforementioned molecule. If we divide the speed of light 186,282 kmps by the Golden Ration 1.61803399, we get these figures;

1. 115,128.607

2.   71,153.392 

3.   43,975.214

4    27,178.177

5.   16,797.037

That last one 16797.037 bears relation to the 168 (167.97) of Octonions, General Linear Group (3,2), the Klein Quadratic; and by extension the Fano Plane and all of time as we know it on this plane of existence (namely 7 x 24 = 168).

This method of interpreting numbers conforms to the occult practice whereby numbers of a similar ilk e.g. 147, 714, 417 etc are considered in some sense equivalent. While this method may not be common practice for modern day mathematicians, there is no denying the debt of gratitude this field owes to the occult sciences.

An interesting account of occult chemists and their clairvoyant investigations into atomic structure, which also yielded the figure 168, can be found here; http://smphillips.8m.com/article-37.html, and here http://www.chem.yale.edu/~chem125/125/history99/8Occult/OccultAtoms.html

Zooming down to the Plank Scale is geometrically equivalent of stopping completely. Zooming up to the cosmological scale is the equivalent of traveling at, ostensibly, infinite speeds. Because light has fractal applications, when we zoom in on the universe from a cosmological scale down to a quantum or meso-scale, we are zooming in on the same exact beam of light, deep and deeper. All of the information appears contained within one highly energetic beam of light that is freescale. Viewed head on this ray of light is like a spiral (with properties of Phi 1.618). As it propagates through space i.e. rotates in 4th dimensional space it appears to expand; click on image to view animation.

Contrary to observation, the universe may not be expanding at all. The perceived expansion may simply be an artifact, or illusion generated by the revolving fractal light field. Einstein questioned if the Universe rotated, but abandoned the concept when Hubble's evidence for expansion became known. If the universe is, to all intents and purposes infinite, what form do you think a rotating and expanding universe might take?


The answer, of course, is a spiral form. Just like the spiral animation, the perceived expansion may simply be an illusion generated by a hyper-dimensional spiral Universe revolving in the 4th dimension; time.