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.