From the Planck Scale to the CERN Scale

A Working Resource Page

by Bruce Camber  Initiated in August 2019  Smmary

Editor’s notes: All pages marked as “Working Page” or “In Process” are still quite rough. This page qualifies. Your comments and suggestions will always be welcomed. -BEC


61-to-67: Preparticles, Elementary Particles, Particles

  • PRIMES: 61, 67 (all primes open for the new, transformational testing)
  • Multiples: Notation-61 has Notation-122 (61×2) and Notation-183 (61×3) and Notation-67 has Notation 134 (67×2) and Notation-201 (61×2).
  • Particles: Within the notations 61-to-65 the face and functions of elementary particles would be shaping up for emergence.

51-to-60: Systems

41-to-50:  Relations

  • PRIMES: 41, 43, 47
    1. Notation-41: Notation-82 (41×2), Notation-123 (41×3) and Notation-164 (41×4)
    2. Notation-43: Notation-86 (43×2), Notation-129 (43×3) and Notation-172 (43×4)
    3. Notation-47: Notation-94 (47×2), Notation-141 (47×3) and Notation-188 (47×4)
  • Versus the derivative, subject and object, were intuited within Notations 41-to-50.
  • Possibly within some one of these ten notations, and probably not one of the primes, a geometry of imperfection emerges, the simple object created by five tetrahedrons with its gap of 0.12838822 radians (a 7.356103 degree gap).
  • Fluctuation Compressibility Theorem and Its Application to the Pairing Model

31-to-40: Qualities

  • PRIMES: 31, 37
  • Multiples: Base-2 touches every notation and there are many multiples of 31 and 37 where that multiple by 3 or 5 and base-2 would uniquely share a subsequent notation.
  • Qualia (or pure qualities) are imagined between Notations 31-and-40

21-to-30: Substances

  • PRIMES: 23, 29
  • Multiples:  Many multiples of these two primes, ostensibly multiply the prime by 3, 5, and 7 are uniquely shared with a corresponding base-2.
  • Aristotle’s concept of Ousia or Substances 
  • Kerr and Kerr-Schild metrics (1963)
  • A precursor of the Periodic Table was intuited.
  • The word “‍quine‍” was coined by Dou­glas Hofstadter in honor of Willard Van Orman Quine’s work on indi­rect self ref­er­ence and the result­ing Quine’s Para­dox…

11-to-20: Structures

1-to-10: Forms

  • Notation-0: Mass – PLANCK MASS: 2.176.470(51)×10-8 (kg)
  • Notation-10: 2.22874×10 -5 kg
  • PRIMES: 2, 3, 5, 7
  • Multiples of primes, 3, 5 and 7,  necessarily share a space within base-2.
  • What do we know about forms?
  • Automorphic
  • Plato’s concept of forms was first instantiated for the first ten notations.
  • Decay of the K02 Meson  Consider the mass of the meson and all other particles and begin sorting them by mass and/or charge. This will involve redefining parts of the current Standard Model of Particle Physics. Pions are the lightest mesons and, more generally, the lightest hadrons.

Doublings. In this data stream, a third approach to these concepts is the study of period doubling, bifurcation theory, coming full-circle with our first, most-simple, doubling mechanism, cubic close packing of equal spheres. Here that mechanism is described as stacking. There are other types of doublings, but there appears to be no other doubling mechanism per se.

In Finland, physicist Ari Lehto claims that the period doubling mechanism is a universal property of nonlinear dynamical systems and that it governs the buildup of structures; he says, “…from the intrinsic properties of the elementary particles to the large scale systems with cosmological dimensions.” In our model here, Lehto is asked to consider those notations or doublings prior to elementary particles.

Lehto writes, The mechanism that indicates a high degree of order in nature is not a part of the prevailing theories but it could give a major contribution to our understanding of the physical reality and the origin of the invariant properties and structures of matter.”

The Fourier transform

Please note. We are in the earliest stages of our studies of the Fourier transform, thus the following postulations are simply my guesses more than based on a deep-and-rich understanding of these functions.

Symmetries in motion. The circle-sphere dynamics now transition from basic geometries, to symmetries in motion.

The work of a wide range of people, from Pythagoras (c. 570 – c. 495 BC) to Feynman (1918-1988) to Strogatz (1959-  ) to today’s thinkers and tinkerers within music theory, may find a key function and a new paradigm within the Fourier transform understood from the Planck scale.

File:Circle cos sin.gif

There is an inner transformation (pictured, above right) that I would equate to electromagnetism, Maxwell’s equations and Faraday’s intuitions. Then there are the outer transformations which I would equate with the de facto dialogue between Newton and Einstein and the current wrestlings regarding our understanding of gravity and loop quantum gravity (LQG).

See Sir Martin Rees’ Just Six Numbers.

The internal and external dynamic of spheres. The three dynamic images above are each, in their very special ways, based on our most ubiquitous, never-ending, never-repeating, dimensionless constant, pi.

If in the first emergence there are endless strings of spheres, could it also be a face of Planck Charge, Planck Mass, Planck Length and Planck Time? If the secondary emergence is that inner transformation, in what ways is it the face electromagnetism and an expression of Planck Time, Planck Length, Planck  Mass and Planck Charge? If the third emergence is the outer transformations, in what manner of speaking is this the face of gravity and yet another expression of Planck Time, Planck Length, Planck Mass and Planck Charge?

History should be our guide. How could so many applications not be tied to the fundamentals of our beginning?

A foundational mathematics and physics

The foundations-of-foundations: A Quick Summary. If the first 64 notations are taken as a given, they certainly do not describe physical reality as we experience it or understand it today. Most people have a de facto absolute plenum of space and time within which everything exists and has its being.  Within this model of the universe, the infinitesimal spheres create space, time, mass and charge and these stack, causing a period doubling, thus causing dynamic symmetries to evolve with uniquely defined dynamics at each notation. Those notations or doublings defined by a prime number have an additional uniqueness to interject entirely new dimensionless constants into the overall doubling equations. It seems to follow that from one of these notations Langlands programs would begin to evolve, and then from another, string theory would evolve with its unique language and functions.  The nineteen prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 whereby base-2 begins at 2, and our science of particles and waves begins at 67. What begins at 3? …at 5? …at 7? Which dimensionless constants can be applied; and then upon which of those can more mathematical structures be developed?

Perhaps a number theorist like Akshay Venkatesh of the Institute for Advanced Study can help us. Perhaps we need to go back and reintroduce ourselves to Robert Langlands, Ed Frenkel and other thought leaders among the Langlands group (Robert Kottwitz, Stephen Gelbart, Thomas Hales, Gerard Laumon, V.G. Drinfeld, D. Gaitsgory and others). Perhaps we need to reintroduce this conjecture to our string theory, thought leaders like Edward Witten and Gabriele Veneziano and those testing their conjectures like Krzysztof Cichy.

Language. Because these first 64 notations appear in every way to be below the thresholds of measurement of space and time, there is a need to attempt to simplify set theory with  language, words and expressions, that capture the forms and functions that give rise to the realities we can measure. Wouldn’t it be fascinating to begin to be able to make distinctions between reification, instantiation, hypostatization, and hypothesization? It just may be possible.

Dimensionless constants. All the key dimensionless constants, particularly those considered to be necessary for the Standard Model for Particle Physics, will have a very special role, especially when each is considered a bridge between the finite and infinite.


Although lightly approached within several documents within this website, it is now increasingly obvious that the mathematics, science and philosophy of renormalization needs to be further explored. To deny infinity is to know infinity. So, infinity, both mathematical and conceptual, can be uniquely and independently known through the use of renormalization within any of the sciences, especially physics, and mathematics.

Since the renormalization work of Dyson, Feynman, Schwinger and Tomonaga (1947-50), Nikolay Bogolyubov, Stueckelberg and Petermann (1953) and the work of Wilson, Kadanoff, Fisher (1965 and 1975), scholars have developed ways to capture points within equations whereby infinity becomes equal to 1. Each is a possible clue. Beginning with with Freeman Dyson’s work in and around 1947, renormalization continues to be refined and expanded. In 1973  the Coleman–Weinberg potential was introduced. Like Weinberg  (1993), Dütsch (2013) and others continue that effort.

As with dimensionless constants, every new twist for renormalization demarcates a possible new entry point along the grid especially within the first 64 doublings, yet including the twenty-five primes between 67-and-199: 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, and 197.

Renormalization was a welcomed relief from having to wrestle with infinity. Also, because the concept of infinity was so often associated with religious belief, it was a relief from those discussions as well.  Some of our leading scholar-physicists went so far as to  advocate that space, time and infinity be retired from academic inquiries. Within this model, these three pivotal concepts are further defined and refined.  First, the simple doublings create continuity equations for each of the Planck base units creating a heretofore unrecognized definition of order, relations (symmetries) and dynamics (harmonics) that redefine the infinite and apparently bind the finite and infinite.

Resources and references:

Quantum Mechanics of Paraparticles JAMES B. HARTLE and JOHN R. TAYLOR Phys. Rev. 178, 2043 – Published 25 February 1969