The Universe as n-Dimensional Fractal

If the strong nuclear force is indeed the field to be associated with a 3D Euclidean space-time X₃ and bosons and fermions are mutually dual then the bosons of the electromagnetic field must be the dual of the fermions of the strong nuclear field, i.e., a photon is just another variation of a quark.

	x₁	x₂	x₃	t
1	e	e	v	-	photons
2	e	v	e	-
3	v	e	e	-
4	e	e	-	v	up/charm/top quarks?
5	e	-	e	v
6	-	e	e	v
7	v	e	-	e	down/strange/bottom quarks?
8	v	-	e	e
9	-	v	e	e
10	e	v	-	e
11	e	-	v	e
12	-	e	v	e

Dimension table for 3-dimensional particles

The table on the left shows a possible ordering of such 3D particles in a 4D world. Each 3D particle has speed c in the proper time dimension of its own rest frame. This dimension is indicated by the letter “v” ("velocity" dimension). The other two dimensions are indicated by “e” (“existence” dimensions). The quarks rotate in 4D, which may be the background of their Cabibbo mixing.
Charge is determined by the number of existence dimensions in our 3D space. Each existence dimensions represents ¹/₃ unit of charge (positive or negative). In fact, charge only becomes "real" and measurable charge once the three "e" dimensions come together. That's why photons show no "real" charge.
Mass (energy) is determined by the velocity dimensions. The total mass of a compound particle may ultimately be determined by the sum of all velocities of all sub-particles, sub-sub-particles and so on. A 3D quark may on its turn be a bound state of yet more fundamental 2D particles (W, Z, neutrino's?).
Quark combinations must always lead to a compound particle consisting of all four dimensions.
Possible examples:
2 x "4" + "9" = 2u + d = proton
"4" + 2 x "9" = u + 2d = neutron
"4" + anti-"8" = u + anti-d = anti-p⁺

How to imagine such 3-dimensional particles and the dimensions that they consist of? The picture on the right and the animations below try to visualize this.

Visualization of n-dimensional particles

Conceptual overview of elementary particles and
the dimensions that they consist of

A basic property of the model is that all dimensions are orthogonal in every point and closed. The model has some similarities with p-branes in stringtheories. It starts with a simple model for a particle with zero "e" dimensions and 1 "v" dimension. That results in the yellow circle in the top right corner of the picture. The actual particle is a zero-dimensional point, moving around in the circle with velocity c, like in the first animation. That circle represents the proper time dimension for the particle.

The next step is the red horn torus below the yellow circle. This represents a particle with 1 "e" dimension and 1 "v" dimension (note that a sphere does not fulfill the model's requirement on orthogonal dimensions). The actual particle is a 1D circle, orientated like the yellow circle in the previous model. It moves along the surface of the horn torus, in the direction orthogonal to the circle, with velocity c (second animation). The circle thus shrinks and stretches depending on it's position on the surface. Once its passes the center of the horn torus, it's diameter will be instantly zero, while the diameter will reach it's maximum when the circle passes the outer edge of the horn torus. The surface of the horn torus represents the proper time dimension for the particle.

Finally, we can visualize a particle with 2 "e" dimensions and 1 "v" dimension (e.g. a quark). This is shown in the combination of the red horn torus with the blue balls. A single instance of the pair-of-blue-balls is drawn here; the complete model actually consists of an infinite number of blue-ball-pairs with growing diameter that together represent the third (proper time) dimension. The torus now represents the actual 2D particle, while it moves along the surface of the blue balls with velocity c. The net effect is that the torus inflates until it reaches an infinite size when it reaches the top of the blue ball, and then begins to deflate again until it reaches the point where the two blue balls touch. It's size is zero then. After that, the whole cycle repeats itself. The "infinite" size that the torus reaches at a certain instant, is a result of the fact that we cannot observe the higher dimensional space that the whole construction is embedded in. For an observer with 4D spatial vision, the size would always remain finite, like we always observe the size of the moving circle as finite in the previous model.

Note that the way that this model would really show itself to us totally depends on the actual dimensions that play the roles of "e" and "v" . The description of the third model in fact applies to a photon (because all 3 dimensions exist in our 3D space). The instants of zero size correlate with the moment of absorption or emission of the photon by a charged particle while the intermediate states represent it's journey between emission and absorption. The instant of infinite (undefined) size allows the change of its path towards another charged particle (the animation actually shows a scene where the photon is emitted and absorbed by the same charged particle). The surface of the horn torus reflects the quantummechanical probability spread of the photon's position in space. At the moment of absorption (read: measurement) this probability instantly converts to 100% at the position of the absorbing particle.


Particle with 0 e and 1 v dimension	Particle with 1 e and 1 v dimensions	Particle with 2 e and 1 v dimensions