###### • Center for Perfection Studies • Related Homepage • New Orleans • USA • February 2017 •

**Alternatives to Big Bang Cosmology** This page began in 2016; work continues until fluctuations are better understood.

## An Exploration for Quantum Fluctuations Within Base-2 Exponentiation

**Introduction**.

**Background**. In December 2011, this project began by following embedded geometries, smaller and smaller, by dividing the edges of the tetrahedron by 2 and connecting the new vertices. In 45 steps following Zeno further and further within, we were in the domain of particle physics. In another 67 steps within we were in the domain of the Planck scale. In our naï*v*eté we then multiplied our little tetrahedron by 2, and in 90 steps were were out to the age and size of the universe.

Today, it is a mathematical and geometrical model based on the Planck units.

Why didn’t Max Planck and Albert Einstein do the simple math? Why did it take the extreme naïveté of high school people? It is anybody’s guess. It seems logical. It looks logical. But…obviously it dumbfounds the scholars within the academic community. Since 2011, we have asked hundreds of our best for advice. Very little has been given to us.

We know this much. Geometry and mathematics are real realities and Aristotle made a mistake when he thought one could tile the universe with just tetrahedrons. He missed a very simple and seminal gap.

Given the lack of understanding in this realm of physics, we postulate and hypothesize that this gap pictured above started the first fluctuation in the universe.

**Measurement**: Our chart of base-2 exponentiation ^{[1]} starts with the Planck base units and goes to the Observable Universe and Age of the Universe. It has just 202 notations. It is logical and simple, and a potential alternative to big bang cosmology.^{[2]}

The *first-possible physical* measurements in our universe happen in labs like CERN (Geneva, Switzerland). Estimates of the ionic radius involved in their heavy ion collisions range from 30-to-300 picometers or approximately 3.9077×10^{-11 }meters at the 81st notation to 3.12618×10^{-10 }meters at the 84th notation.

Collider measurements are within the scale of the 67th notation (2.38509×10^{-15} meters), the 66th notation (1.19254×10^{-15} meters) yet some say down as small as 1.16459×10^{-18} meters at the 56th notation. These and the other numbers in the 200+ columns are real numbers, all multiples of the Planck base units.

Today these numbers are all just simple mathematics and imputed geometries and this system of numbers is not yet recognized by the academic-scientific community to be meaningful or significant.

**Potential Significance**: By themselves these numbers create a rich panoply of possibility. We believe it would be unimaginative not to try to do something with them, so we enter the domain of the mysterious quantum fluctuations. Unlike current theorists, their “out of nothing” is for us as many as 67 notations where distinctions between notation 2-to-66 are expected to be as great as those within the next 67 notations (67-134), and then again within the next 67 (134-201) that follow.

**Pi And Never-ending, Non-repeating Numbers**. The animated image (just above, on the left) challenges us in unusual ways. Looking for other possible parts of the puzzle, we accept the logic and necessity of a singularity, but conclude that it is a dynamic transformational nexus between the finite and infinite whereby there is a complete unification of all the basic forces of nature, the Planck base units (aka Planck scale), the dimensionless constants, and a very special class of circles and spheres.

**That is our working hypothesis**. We further postulate that this working premise creates an environment to build a panoply of bridges from the Planck scale to all current physical theories whereby each notation is a domain for unique predictive values. The challenge will be to recognize the mechanisms that would confirm or deny these hypotheses and postulations.

**Fact Gathering: The Tools of this Art**. The first thing we did was look for the possible parts of the puzzle. Of course, there are the Planck base units. There are the 202 notations. There is the speed of light — Planck Length divided by Planck Time — within each and every notation. These are our starting points.

The universe appears to be logically divided into three scales. The small scale from notations 2-67, the human-scale from 67 to 134, and the large scale from 134 to just over 201.

The next big observation is that the progression of epochs defined by big bang cosmology is well-defined by the natural inflation within base-2 exponentiation. Simple logic seems to suggest that each currently-defined big bang epoch can readily become a process within the base-2 model. And, significantly, there is no need for an actual *big bang*; natural inflation is quite enough.

Within our *Top Ten Reasons to Put Big Bang Cosmology In Time Out*, we now turn to a few of the many enigmatic questions^{[3]} within cosmology. Perhaps within the base-2 model we can find answers or something new.

SPECULATIONS:

**More Postulations**. These first 67 notations could be the deep systems structure of the universe that give rise to richly-textured quantum fluctuations, cosmic microwave background radiation (CMBR), homogeneity and isotropy, dark energy and dark matter, magnetism, and gravity (defined by General Relativity). Big bang cosmology has no answers. Given that the base-2 model is simple, it may hold rather simple answers. This article is our first to enter this configuration space starting at notations 0,1 with a point (vertex), then a line, a circle, a sphere, a tetrahedron, and then tetrahedrons and octahedrons. That animated image (top left) demonstrates a process that apparently has not been studied much beyond the problem of stacking cannonballs. (Thomas Hales followed up Thomas Harriot’s work)^{[4]}

**The Art**: Using dimensional analysis within the first 21 notations, there are over a quintillion base-8 vertices with which to experiment and build initial systems! Sophus Lie could make millions of his E8 structures. Within just the first ten notations, there are 134,217,728 scaling vertices. Possible analogues include the protein machines or nanomachines within the body. Other analogues could include genetic code machines.

**The first ten notations**. We’ll call them axiomatic machines (systems) that extend the continuities inherently defined by Planck base units (length, time, mass, and charge). Our rather experimental and unique use of Planck Temperature renders a number very close to Absolute Zero (0°). These axiomatic machines are also defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or*ħ*or quantum mechanics), the Coulomb constant (or*ε*_{0 }or electric charge or electromagnetism), and the Boltzmann constant (or*k*_{B}or*temperature)*. All “things” within these notations are uniquely defined by pi. These are not physical things; these are*ontological things*, or perhaps axiomatic things. We will be working on the nomenclature as we go along this path.

So, let’s build some simple mechanisms, then work with the art (and magic) to bring all that richly-textured phenomena of the universe to life! Let’s see what we can do with the most artistic and unpredictable of that group, *quantum fluctuations*.

**Transformation Nexus**. Once the singularity is multiplied by 2 (the form) or by 8 (the function), it is no longer the Planck singularity or Planck Epoch; it becomes the first possible transformation nexus between the finite and infinite.

Could it be that from this beginning, everything, everywhere, shares these eight vertices. “*Ridiculous? Poppycock?*“

**We ask that you hold those judgments in abeyance**. To get into this model will require stretching, suspending judgment and imagining in rather new ways. With eight vertices the universe might organize those vertices as five tetrahedrons with a small space between the fifth and first tetrahedron. There is one extra vertex. It is elegant. It is imperfect. It creates degrees of freedom (7.356103 degree gap or 0.12838822 radians).

Couldn’t this be the birthplace, the earliest beginning of the quantum fluctuation?

Could this possibly be a key process that is extended throughout all 200+ notations? Of course, those who know molecular geometry readily recognize the figure.

**In the next doubling there are 64 vertices**. Seven-plus-1 is established. The next 13 vertices extending from “The Seven” create a mathematically whole figure, an absolute figure of six tetrahedrons whereby there is potential action because the base is a perfect structure, a hexagonal plate.

Each cannonball is a vertex. Or, is it an infinitesimal circle or sphere? …both? Given that we are working with the five basic Planck units with real numbers that define each unit, the vertices are 134,217,728 scaling vertices. a real manifestation within space-and-time.

**The animated image (gif for “Graphics Interchange Format”) of the cannonball stack tells a powerful story**.

The all-important quantum fluctuation seems like an art form on one hand and a fundamental energy source on the other. Open this conceptual roadblock and we find a truly golden rainbow. Although each roadblock is a face of this small-scale universe, perhaps quantum fluctuations would best be known as the art of the universe!

### Working Notes:

* The most important fact about the new model is that each of the Epochs defined within Big Bang Cosmology are all logically replicated here. *All of our data is simple math and it is a fully predictive model of the universe without the bang! Numbers

**The world’s leading cosmological theory is challenged**. Though our little model is little-known today, that is about to change. Big bang cosmology is going to be placed on ice and assigned to timeout.

*The Art*, Mechanics & Systems

*The Art*, Mechanics & Systems

**Let’s start at the very beginning: Notations 1-10 **

**Please open the chart in a new window.**

Each of the Planck base units, considered to be part of the so-called singularity, has a real number associated with it. Though the formulas for deriving the numbers of each Planck base are readily understood by many, watching how the numbers progress along their scale is new.

In the first ten notations, we assume the numbers represent vertices that will double and slowly become structure.

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