Black Hole Quantum Gravity Theorem
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.
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