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