Home Relativity Simplified Fractal Universe Euclidean SRT Bosons in 5D Gravity 4-Vectors Propulsion

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The Universe as a Multi-Dimensional Fractal
Recurring patterns through dimensional zooming

From various points of view a fractal-like universe is described. Unlike in usual fractals, recurring patterns correlate with the number of dimensions in the observation, i.e., zooming out and in occurs by adding or removing dimensions rather than changing scale. In this way, the forces of Nature together with their fermions and bosons are ordered hierarchically through their number of dimensions. The first three sections show some examples of physical phenomena that re-appear in spaces with one dimension less or more. The sections describe 1, 2, 3 or 4 dimensional worlds that are closed in the next higher dimension. From section four onwards, this will be put in a broader context, covering all of Nature's forces and particles.
These ideas build on the articles on Euclidean relativity that can be found on www.euclideanrelativity.com.


1. Positive and negative charges are two sides of the same 4D point
2. Photon absorption by electrical charges is the 4D equivalent to mass particles falling into 5D black holes
3. From a 5D perspective the Schwarzschild horizon and the "edge" of our universe are two sides of the same surface
4. What looks like a fermion from " below " (e.g. 3D) looks like a boson from "above" (e.g. 4D)
5. The four forces of nature can be ordered hierarchically, based on their number of dimensions
6. Photons are free quarks
7. Parallels with stringtheories
8. Bibliography


1. Positive and negative charges are two sides of the same 4D point

...explaining why the amount of positive and negative charge in the universe is exactly equal. 

World perception of a point-shaped being

Closed 1D world
Some point-shaped being lives on a circle. His limited 1D vision makes the circle appear to him as a straight line. To actually see the extrinsic curvature he would need to have 2D vision. He is looking at a point in the distance in his circular world. Now he turns around and looks down his circle in the opposite direction. He sees "another" point but this is actually the same point again, looked at from the "backside".

Closed 2D world
You can extend this to 2D worlds, 3D worlds and so on. The basic principle remains the same. In any n-dimensional closed world or manifold (i.e., closed in yet another higher dimension), every point always shows two projections to our "eyes", provided our spatial vision is limited to those same n dimensions. The projections follow geodesics, 1D trajectories like the circular world of the point creature. Once our spatial vision is extended with one more dimension, it becomes clear immediately that we are looking at a single point only.

Flatlander view of points in Flatland

World perception of a flatlander

Closed 3D world
Also for our own 3D world, assumed closed in the 4th dimension, this means that there should be "linked" points in pairs. The obvious candidate is electrical charge which always comes in pairs and is conserved. It does not mean that the link is necessarily between positive and negative charges in the same atom. On the contrary, the linked charges are very likely to be separated by large distances in 3D space.

Why then the asymmetry in mass between protons and electrons? Protons are compound hadrons while electrons are point-like leptons. Although a bit hard to visualize in 4D, a 3D analogue may suffice to get the idea. It's kind of looking at the top of a tetrahedron from above (electron) versus looking at the base of it from below (proton). The corners then more or less represent its 4 dimensions. 

4D geometry of positive and negative charges

4D geometry of positive and negative charges

This has some interesting implications. The "spontaneous" emission of a photon by a charge has its origin in the simultaneous absorption of a photon by its linked companion charge. Since the distance between the two linked charges is arbitrary (albeit depending on the geodesic connection between them), this means an instantaneous transformation of information in 3D. That brings the EPR experiment to mind where something similar happens with two "linked" photons. The seemingly instantaneous information transfer in this experiment indicates that, again, a higher dimension must be involved in the link.

In the next two sections, a similar absorption process as found with charges and photons will be worked out, but now the 5th dimension plays the role as linking and closing dimension, like the 4th did with electrical charges.


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Updated March 24th 2012, Copyright 2004-2012 R.F.J. van Linden

Home Relativity Simplified Fractal Universe Euclidean SRT Bosons in 5D Gravity 4-Vectors Propulsion