Gap theory and simple geometries…

Editor’s note: A working document that has come out from behind the firewall (December 2024) so it can be criticized and further developed. It was started in August 2023 and needs a bit of group think to move it along. Thank you. -BEC

Types of gaps
By Bruce E. Camber (pre-first draft)

Between Notations 0-to-202

All dynamic gaps are analogous yet some gaps begin with a five-tetrahedral gap, then involve a five-octahedral gap (our working model), and may include other combinations of gaps. found within the icosahedron and dodecahedron. Most current thinking about gaps are limited to Notation-202. The work of many associated with the James Webb Space Telescope (JWST) are reviewing data from Notations 196-and-197. It defines a range from within 171.68 million years to 343.15 million years to 686.29 million years from the start of the universe. Notation-196 begins within 171.575 million years from the start. There are size, mass and energy (coulomb) definitions for each notation.

We start at both ends and work toward the middle. Notation-0 which is defined by the Planck base units. Notation 202 (8.9 billion years) currently covers a span of about 300 million years and may go back to the current observations by the JWST teams. Notations 1-to-50 may be domains most generally without gaps. The first gaps would be perhaps defined at the lowest energy state closest to a perfect vacuum. Logically it would be between Notation-0 at the Planck scale and Notation-1. However, there is never a perfect vacuum, yet the lowest possible is within an infinitesimal range that is simply beyond measurement by physical instrumentation.

  • Yang-Mills & The Mass Gap. The mathematical foundations of the mass gap understood through Yang-Mills is simple geometry and simple math using Max Planck’s base units and base-2 notation to establish the boundaries and boundary conditions. Those units render 202 notations from the first moment of time to this day. Each notation represents a scale from 0-to-202 and although the mathematics and geometries are scale invariant, the results within each scale are unique.

By Notation:

_____________________

Unusual time in our history.

There is major angst among those scientists who follow the James Webb Space Telescope. They know deep within their hearts and minds they should no longer say “after the big bang.” Scholars know it’s too hot to cool. Scholars know there is no tweaking that bang enough to fit it into 300 million years with newly-observed galaxies. They know we’ve got to move on, but there is no where to go. Unless of course, we’re willing to start at the very beginning. 

I believe, eventually, we all will.

Reintroduce Lemaître’s primeval atom as a Planck Sphere defined by the latest updates of Max Planck’s 1899 natural units, and those dimensionless constants that define them, and the continuity-symmetry-harmony of pi(π). That would be a very simple start indeed.

Recognize that the big bang’s epochs are all now processes. This is key. Nothing changes except how we understand “after the big bang.” If all are processes, all active equations, we will need to grasp an even deeper nature of time, but a second will still be a second. Scholars have been wrestling with this one for years; there are many groups, especially Loop Quantum Gravity, that have already introduced this rather new and somewhat-difficult concept of time.

Recognize the infinitesimal. Give it depth and texture. Multiply it by 2 over and over and over again. If PlanckTime is the first moment of time, there are 202 notations to the current time. That chart includes everything, everywhere for all time (TOE). Each notation is always active. There are no less than 64 notations below the CERN scale. That domain is for mathematics, geometry, logic and no less than nine other disciplines that are defining the grid that begins to bridge the Standard Model for Particle Physics with the Standard Model for Cosmology.

In 2011 we backed into those 202 base-2 exponential notations; and, though encouraged by Freeman Dyson and Frank Wilczek, scholars knew that it did not sit well with the big bang theory. John Baez and others told us that it was idiosyncratic. But, we’ve persevered. Recent homepages tell more of that story: A Perfect Start, Simple Logical Concepts, and Facts & Guesses about “Planck Scale Physics”. 

You know something is happening when Scientific American allows a title, “JWST’s First Glimpses of Early Galaxies Could Break Cosmology.” Break cosmology? They are saying, “Break the Big Bang theory.” Throughout the world there is an impatience with the haughtiness of science. Where is judiciousness? Where is the nervousness for possibly being wrong? Just the title alone tells us how open we have become and how impatient we are with arrogance. Thank you Scientific American.

The JWST is breaking paradigms. Paradigms do not break or shift easily. Here Thomas Kuhn’s 1967 work, The Structure of Scientific Revolutions, is coming alive. The JWST is changing the rules of the game.

Returning to Lemaître and his concept of a primeval atom, one might wonder why nobody thought to assume the Planck base units manifest as infinitesimal spheres. Yet, science has had over 100 years of discovering new particles. Nobel prizes have been abundant. It was easy to be particle centric until there were no more particles to find. Lemaître was in the early stages of those discoveries. He rubbed shoulders with Einstein and all the greats of his day. And, even Max Planck ignored his natural units. It was easy to ignore them just as most people ignored Dirac’s inordinately large numbers. 

Also, geometry lost its punch. There are still most basic concepts that we have not taught our students. They do not know the difference between geometries of perfection (no gaps) and geometries of imperfection (gaps). At the most infinitesimal scales, attractors and repellers have not been assumed and the relation between gravity and electromagnetism remains a mystery. When the work of Milnor and Smale are engaged within the infinitesimal, a new paradigm for gravity will emerge. Like mass-energy, space-time, a gravity-electromagnetism formula will emerge and we will begin to understand how the universe grows from that single infinitesimal sphere to tredecillion spheres per second, to the galaxies we have now observed within 300 million years of the start.

Keys to this page, gap-theory

• The last update was 17 December 2024.
• This page was initiated on 27 August 2023.
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• The headline for this article: Types of gaps
• First teaser* is: Gap theory and simple geometries...

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