2011The Natural Theory of Space Quantum

Space is not the existing illusion of our senses; instead, space is quantized and defines itself physically per the (Fibonacci[1]) infinite sequence:

Fibonacci Space:

For example, the “speed of light” c (Einstein[2]) is limited because the particle (photon) does not truly travel through (Newtonian[3]) time and continuous space.

In fact, the particle travels through contiguous space quanta, one by one.

In the Newtonian sense of velocity through continuous space, there should be no limit to velocity. In quantum space, the analogy to Newtonian velocity is the spatial travel across quantum boundaries. Each boundary crossing is the “same” event for light and its velocity is bounded by c in the “sense” of a time t.

There is no real time t; instead, the “particles” travel only in space from one quantum to an adjacent quantum.

As the “growth” sequence itself, successive quanta are different in “size” by the factor:

φ=1.618

A two dimensional visualization of quantum spatial boundaries is suggested by the Fibonacci spiral[5].

A Five Dimensional View of the Spiral:

Physically, we cannot achieve 2 from 0 and 1. We can only achieve 1 from 0 and 1. Following, we can achieve 2 from the adjacency of 1 and 1. And so on.

We do not live in five dimensions; instead, we live in three.

The natural sequence begins with the seed values 0 and 1. Perhaps we could visualize 3 from 5 and 5 from 8. But we cannot visualize 3 from 4 or 8 from 9. Physical relevance is solely the traverse across adjacent natural boundaries.

Wave Mechanics:

Wave mechanic principles (Schrodinger[6]) show:

and so the approximation

ΔxΔk ≥ O(1).

One result (ramification) is a temporally related uncertainty in measurements.

Wave mechanics mathematically defines observations (perceptions) differing from Newtonian continuity; however, wave mechanics is a physical discipline that utilizes the concept of time t,

e.g. Δk depends on a perceived time t (and mass m)

The mathematical (Fourier[7]) representations (transformations) are not physically real in the sense of a time t.

Boundary Size:

One possible (sensual) estimation in one dimension of spatial boundary size (between adjacent quantum) could be suggested by:

(Width of boundary)^{2}= Constant x (Time required sensually for continuity)

(In similar mathematical form to E=mc^{2}.)

Using orders of magnitude 10^{-27}“sec-cm” suggested by wave mechanics and estimating the “speed” of sensory communication in the range 10^{-3}sec – 10^{-6}sec, we would then estimate the magnitude:

b ~ 10^{-16}to 10^{-18}meters (for example)

Contiguity of space quantum should be mathematically defined beginning with the natural sequence. That is beyond the scope of this letter.

Intermediate Review:

While we can mathematically achieve 2 from 0 and 1, we cannot physically achieve two from nothing and something.

Intermediate Summary:

Time is not physically real. It is a neurological simulation of continuity from a real spatially contiguous universe.

An Eight Dimensional View:

In Fibonacci space, our 3-dimensional experience intersects with eight separate five dimensional regions at each boundary.

The boundaries are supposed to be relatively small in a spatial (and energetical) sense.

In the entropical sense, an energy compatible with a boundary region could exist “within” a boundary neither moving forward or backward.

In that case, it seems the specific energy may experience one, several, or all of the intersections.

At such an event, the energy (particle) could traverse among three-dimensional regions of our (experiential) Fibonacci space.

Space is not subject to our views of arithmetic; instead, space is defined by the natural sequence. Contrary to our sensations, time is not physically real. Time is a good measurement approximation in our macroscopic physical world and “historically” is built into all units of energy, measures, and our perceptions.

Space and energy directionally build the concept of entropy.

The dimensionality following from Fibonacci space also implies boundaries. The boundary dimensions are suggested by quantum (wave) mechanics.

Negative entropy should be achieved by exacting the correct energy. Not the most or least energy; instead, the correct energy corresponding to the spatial boundary.

References:

[1] Leonardo Fibonacci, Liber Abbaci, 1202.

[2] Albert Einstein, Relativity: The Special and General Theory, 1916.

[3] Sir Isaac Newton, Principia, 1687.

[4] Euclid of Alexandria, Elements, circa 230 BC.

[5] Diagram transcribed from Wikipedia, 2011.

[6] Erwin Schrodinger, Quantisierung als Eigenwert Problem, 1926.

[7] Joseph Fourier, Theorie Analytique de la Chaleur, 1822.