A highly-integrated, most-simple, mathematical model of the universe


If The Universe Starts At The Planck Scale…

by Bruce E. Camber Key Reference: Reformulating Space, Time, and Infinity 2019!

At some point in the near future, there will be a major paradigm shift. Simple logic tells us that things start “simple” before becoming complex. Planck Time and Planck Length are simple, quite possibly the smallest and most simple units of time and length. So, why not entertain a very different model of this universe that begins with the Planck base units? It is highly-integrated, 100% mathematical and predictive, comprehensive, and overlooked.

PQE. Key scholars within a selective, scientific group, Physics of Quantum Electronics (PQE), have been writing and presenting papers since 1971. They have become a real force in shaping scientific thinking. The report from their Winter 2018 colloquium1 was provocative. As a result, I wrote to several participants2 to invite them to comment on our simple model of the universe defined by just 202 progressive doublings of Max Planck’s base units. Those units, calculations done in 1899, were little used and relatively unknown. That changed when an MIT physicist and PQE author, Frank Wilczek, wrote three articles, Scaling Mt. Planck, for Physics Today (2001).

Numbers. In my emails to PQE participants, I quickly introduce our rather idiosyncratic model of the universe defined by doubling the four Planck base units, and then each result, over and over again. A most simple chart (and scale) of numbers emerges:  202 doublings (base-2 notation) go from Planck Time to the Age of the Universe today.

Please consider these numbers:

Planck Base Units. First, assume that the Planck scale indeed “starts at the very beginning.”

The First Second of the Universe. Planck Time is so small it takes 143 progressive doublings to reach .60116 seconds. Before the 144th doubling, the universe finally hits that one second mark. The commensurate Planck Length doubling approximates the distance light travels in a second.

Light Year. Between notations 168 and 169, a light year emerges; and rather predictably now, the Planck Length approximates the distance light travels in a year.

Planck’s little equation for Planck Time: Planck Length (lP) divided by light equals Planck Time (tP). Throughout all 202 notations, the ratio is a variable of the speed of light yet always within .1% of the value established in-a-vacuum.

Light. Taken together, Einstein’s well-known formula and Planck’s base unit equations, it would seem that all four Planck base units throughout the entire progression are fully integrated and so fundamentally bound together, they could be a Janus face to each other.

Large-scale universe. Within the 197th notation, large-scale structure formation finally begins within the 300-million year mark. The 202nd notation is approximately 10.9816 billion years so almost all of this simple model is about the very early universe where real data is lacking.

Euler. Taken together, it all appears to be an application of Euler’s exponentiation.

Small-scale universe. This model redefines a very small-scale universe with numbers that are too small to measure but important for string theory and those seeking to define dark energy and dark matter. The model accurately orders the human-scale from protons to satellites. And, it defines a natural inflation that approximates the epochs of the ΛCDM model.

It is hard to get anyone’s attention so I am glad you are here.

Thank you.

With a bit of analysis, this model redefines space, time, and infinity. Newton’s absolutes are placed in time-out. All of the doublings (or notations or groups or sets) are always active, never-ending, and never-repeating (perhaps the beginnings of a new concept of time symmetry). And, yes, I believe this is a very good description of our expanding universe. – BEC

Summary: A focus on a few key ideas

This summary of on-going work is an evolving list with links. It will begin to appear somewhere within every homepage, de facto a Table of Contents for the website. 1. All the Numbers: A Highly-Integrated Mathematical Model. These 202 base-2 doublings outline the universe; and, by definition include everything, everywhere, for all time.

2. Doubling Mechanism: These doublings are a basic mechanism of the universe.

3. Unified Theory of Mathematics. The simplicity of this model encourages the development of an extensible platform starting with the most simple mathematics and geometry then building to include the two Standard Models, Langlands programs, string theory, and more.

  • Euler. The universe is fundamentally exponential. Euler’s identity is universal.
  • In process: Each notation will be analyzed, notation by notation. It will be within this format this unified theory could possibly unfold. Wouldn’t the role of prime numbers be to determine when new mathematical systems can be introduced?

4. Infinity. Given light’s pervasiveness, three aspects of light are taken as qualities that appear to be shared with the infinite. These are:

  • Continuity. Order / numbers, first within the dimensionless constants, never-ending, never repeating, and then with the progression of spheres.
  • Symmetry. Relations / Geometries, first with the symmetry of the spheres, then the symmetry within the tetrahedrons and octahedrons that are generated.
  • Harmony. Dynamics / Space-time where two symmetries actively interact as a moment of space-time; it is a qualitative moment we experience as harmony.

5. The qualitative opens the way to value and ethics.

Endnotes and Footnotes

1 Questions. Asking evocative questions, one’s that make you think, is a talent that Socrates and good professors employ. The report from their Winter 2018 colloquium is a bit Socratic.2 The Few. A specially-focused email was first sent to Roland E. Allen, Suzy Lidström, and Girish Agarwal of Texas A&M University; Nikolay Zheludev of the University of Southampton (UK), and Wolfgang Schleich of the Ulm University (Germany). Then, once this page was nearing completion, an email was sent to a few of the other participants.

Challenge us. Coach us. We need all the help we can get.

Which concept is strongest? Which is weakest?

PLEASE NOTE: Many of the links below may take you to a page outside this website.

An excellent resource to translate any of our pages by its URL:


The Physics of Quantum Electronics (PQE) is over 50 years of Conferences many of which have very good Summaries.

If you liked this page and website, please do not hesitate to follow us on Twitter or Linkedin.

More References, Resources, and Research

The Principia

Though part of the intellectual debates about boundaries, going back 3000 years and more, our particular brand of it comes from Sir Isaac Newton, a point of view formalized in his 1687 book, generally known as The Principia.

If you look up into the heavens on a clear, crisp evening, it looks like it goes on forever. That’s Newton. Another person might say, “It goes just as far as the current expansion of the universe.” To which one of the kids quickly ask, “Well, what’s behind that?” To which I would reply, “infinity.” And, of course, that begs the question, “What’s infinity?”

Infinity is not an easy concept to grasp. As a recent college graduate in 1969, I remember asking myself, “How can we take religion out of infinity and make it more accessible to everyone?” The effort by scholars has become a formal discipline called renormalization. And like so much of scholarship, it is not easy for regular people to understand. Even scholars have problems with it. Freeman Dyson worked on it back in 1949 and more recently, Steven Weinberg “re-formalized” it in 1986. Infinity is such a character; it needs to be corralled so the work of mathematicians and physicists can go on. Of course, it can’t be corralled, but it can appear to be tamed enough to carry on one’s work without getting bitten too badly.

Physicists developed this means to avoid engaging the concept of infinity, then they made that work an art form, and then a fine science unto itself. Initially called renormalization, the process began in earnest with KG Wilson: “His work in physics involved formulation of a comprehensive theory of scaling: how fundamental properties and forces of a system vary depending on the scale over which they are measured. He devised a universal divide-and-conquer strategy for calculating how phase transitions occur, by considering each scale separately and then abstracting the connection between contiguous ones, in a novel appreciation of renormalization group theory.

Max Planck
Max Planck

Max Planck

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather… science advances one funeral at a time.” – Max

Planck’s quote: https://quoteinvestigator.com/2017/09/25/progress/


The Net Advance of Physics: RENORMALIZATION


A Note from the Editor:  This image has been used by many on the web to describe quarks and/or the smallest “things” within the physical universe. Google’s image search helped. In our model of 202 notations, this image may be in the range of Notation-55 to Notation-65. In September 2020, it was also used on this top-level post. – BEC

The Physics of Quantum Electronics (PQE) is over 50 years of Conferences many of which have very good Summaries.

Physics of Quantum Electronics (PQE) Today



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