One plancksphere / plancksecond, a natural-but-unorthodox expansion

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The Expansion of this Universe

The Universe expands in two most simple ways. It gets older and it gets larger. Also, it appears to be adding mass and energy. Over the years, rates of expansion have been estimated but in no way confirmed. Within our little model, which takes the Planck units as a given and applies base-2 notation to encapsulate the universe within 202 notations,1 there is an explicit rate of expansion. First, actual numbers are generated for each notation. So, of course, with the four Planck base units, one could readily calculate a hypothetical rate of expansion of the universe.

The question is asked, “What would it look like?” Particularly, might those Planck units with all those dimensionless constants that define their being, manifest or concresce as a primordial sphere? Others have suggested as much and referred to that sphere as a plancksphere.1a If taken as a given, within our base-2 model, the first functional activity would have to be sphere stacking. Then, using concepts that date back behind Johannes Kepler,1b that stacking would seem to generate a second functional activity, cubic-close packing of equal spheres.1c One might conclude that this simple start is the same for each of those 202 base-2 notations that define the universe and the current expansion of the universe.

Review: We are unaware of any other proposed model of the universe that begins with the Planck base units and assumes (1).the first manifestation of physicality is a plancksphere;  (2).each plancksphere is defined by all the Planck base units and those dimensionless constants that define each of them; (3).doublings are caused by the constant flow of planckspheres; thus, (4).every notation is necessarily always active.

Admittedly quite naive, our discovery process has been going on since 2011.2 It seems logical. However, there is so much controversy and mystery surrounding the concepts involved with the expansion of the universe, our hope is that this simplicity might be a welcomed change and worth some time to analyze more critically in light of recent troubles cited in so many current articles about the expanding universe.3

Formula: One plancksphere per plancksecond.4
Here the most infinitesimal of all possible spheres is being “extruded” at the fastest possible rate. Of course, it is all much too small for any possible physical measurement. Yet, plancksphere-by-plancksphere, this model quite literally defines the earliest foundations of the universe as it goes up to Notation 64. Our generally-accepted foundations begin around Notation-64 and go up to Notation-80 within the Periodic Table. The universe as we have come to know it extends from Notation-65 to Notation-202.

That rate of expansion is assumed to start at Notation-1 and to continue right into Notation-202 and to this very second, today. Such a simple start also appears to be a most simple redefinition of the following:
.The old aether.5 Today it goes by many different names, analogues like Wilczek’s grid or spin foam, and things like fractal-like ‘invariant set’ geometry IU in cosmological state space. That’s such a sweet combination of images. We will begin to collect all such imagery and compile it within our “aether” document.
.Dark matter and energy.6 The first 64 notations of the 202 are a complex layering, a domain of foundations within-and-upon foundations. Again, well-beyond the reach of measuring devices, it was easy to intuit that it was the long-sought-for dark matter and dark energy that would quite literally fill and define all 202 notations. A profoundly dynamic, ever-changing, hypostatic domain, there is plenty of room for Langlands programs and string theory and all those speculative ideas from Quine’s atoms to spin networks. Now, Natalie Wolchover, a Quanta magazine writer, was complaining in a tweet; it went something like this, “Everybody has a dark matter and dark energy theory except me!” I volunteered the concepts outlined here, but she didn’t take that bait!
.And, of course, this all amounts to a new concept to define the expansion of the universe.

Redefining space, time & infinity
This model requires redefining space, time, and infinity; and, that is exactly what some of our best scholars have been asking from us — a redefinition of our fundamentals. Of course, they would never expect that it could come out of a high school.

We went back to the four Planck base units and tried to follow the logic that we learned as children, i.e. “Start at the very beginning” and “Go back to the basics.”

  1. Planck Time. To create a baseline for a rate of expansion, it is extended from the first instant at Notation-1 to one second between Notation-143 and Notation-144.
  2. Planck Length. Using the second as the benchmark, we look to determine the size of expansion per second. We assume the first expression of a length within space-time is the diameter of the sphere.
  3. Planck Mass and Planck Charge. Using Max Planck’s inherent logic, we calculate the total mass and charge of the universe by each notation and particularly at one second.

At one second:
Planck Time: 5.391 16(13)×10-44 seconds
If we assume one plancksphere per plancksecond, that would render somewhere around
539,116,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres per second. That is “539.116” followed by 37 zeros. It has a name, five hundred-thirty-nine tredecillion or 539.116×1042 units.

Planck Length: 1.616229(38)×10-35 meters
The diameter of one plancksphere is equal to one Planck Length.
In one second, the planckspheres will push out to about 299,792.458 kilometers, first as the smallest possible sphere, perhaps momentarily, a line, then perhaps like a sheet, and then as 3-D, wall-to-wall planckspheres. Besides base-2 doubling, we will be scrutinizing the possible functional role of period-doubling bifurcation.

Planck Mass: 2.176.470(51)×10-8 kilograms
At one second the mass is equal to 4.036862067×1034 kilograms, an aggregated mass of all the planckspheres. The estimated mass of our sun is 1.989×1030 kilograms, so the density at this stage of our universe would suggest functions involved with neutron star masses.

Planck Charge: 1.875 545.956(41)×10-18 coulombs
At one second, the charge has expanded to 3.47877437×1023 coulombs. Obviously a formidable amount of coulombs per second, we will need some help to see if there is a logic to it all.

This first second is set with a limited number of seconds within this universe.

The commonsense “What if?” questions
• What if the universe starts with the Planck base units, what’s the first “thing” created?
What if the first thing created is a sphere defined by those Planck base units? Remember:
539,116,000,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres per second.
What if there is an endless stream of spheres and the first functional activity is sphere stacking?
What if sphere stacking opens cubic close packing of equal spheres and tetrahedrons and octahedrons are generated? Doesn’t the rest of Plato follow?
What if the concept of infinity has been so tainted by philosophies, we miss its most simple definition — continuity creating order, symmetry creating relations, and harmony creating dynamics. We’d add, “Please keep all other definitions to yourself. Those are not necessary here.”

Do scholars hold master keys to unlock these doors?

Planck. In 1944 Max Planck published a very unusual claim about the very nature of matter. He said, “All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.” Max teases us, yet his statement is far from any practical analysis. It comes from The Nature of Matter, Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797, Berlin, 1944

Wheeler. One of the great physicists of our time, John A. Wheeler, said in 1990, “It-from-bit symbolizes the idea that every item of the physical world has at bottom — a very deep bottom, in most instances — an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-or-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe.”  Journey Into Gravity and Spacetime, JA Wheeler, Scientific American Library, W.H. Freeman, NYC, 1990 Also see: Simons Foundation.

Wheeler pushes the spirit of Max Planck’s “This mind is the matrix of all matter.” In his lifetime, however, he was unable to give us a framework for the universe on the order of his now famous quote: “Behind  it  all  is surely an idea so simple, so beautiful, that when we grasp it  — in a decade, a century, or a millennium —we will all say to each other, how could it have been otherwise?

Palmer. In May 2018 Oxford scientist, Tim N. Palmer, takes Wheeler just a bit further: “A finite non-classical framework for qubit physics is described that challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the primacy of a fractal-like ‘invariant set’ geometry IU in cosmological state space, on which the universe evolves deterministically and causally, and from which space-time and the laws of physics in space-time are emergent.” Tim is in the Department of Physics of University of Oxford and this quote comes from his article, Experimental Non-Violation of the Bell Inequality, MDPI, p. 415. Again, there is no structural paradigm to start and grow this universe.

de Rham. The long-standing frustrations of leading scientists around the world are once again summed up by physicist, Claudia de Rham, in Quanta Magazine, “We’re coming up with such a ridiculous answer that it really forces us to re-investigate every single assumption that we made along the way to get there.” This quote appeared in an article, The Physicist Who Slayed Gravity’s Ghosts, by Thomas Lewton, in August 2020.

All are generalities, and all are in need of specificity; the base-2 model gives us an abundance of specificity and predictability. It has a simple-yet-comprehensive mathematical structure! Few other models can say that.

In conclusion…
I am a bit stubborn. In 1971 and 1972, certainly impressionable years for me, I began contemplating the question, “How do we define a perfect moment within space and time?” Quantum physics and her fluctuations had discounted perfection as a concept. Everything, everywhere was wobbly. Yet, even within the chaos, there was a deep order, but fundamentally things were not deterministic… but… but… That is when I began developing the concept of a moment of perfection that was defined by an extremely heightened sense of order/continuity, relations/symmetry and/or dynamics/harmony. It was a lens through which I have looked at our universe for the better part of 50 years. It was a handicap… but now, it seems to have been the preconditioning that prompted that walk within the tetrahedrons and octahedrons back to the Planck base units; and ever-so-slowly, it is responsible for this page today. –BEC


Endnotes and Footnotes

[1] The 202 base-2 notations. Our first chart started in 2011 in a high school and it quickly became obvious that this would be a long-term project. Our first, rather-simple chart based on Planck Length evolved into a more comprehensive chart based on all four Planck base units. Hypothesized was the very first unit of space-time-mass-energy was a sphere defined by the Planck units and called a plancksphere. The charts were used within our sixth-grade, advanced-placement, math-science class. The best students got very excited about it. Here they had the entire universe in a mathematically-ordered progression from the first instant of time to the current day and expansion. Simple parts of this chart could be introduced in the first grade! There are many math manipulatives associated with the project. Also, there are many dynamic graphical interfaces that demonstrate the basic dynamics of the Fourier Transform, cubic-close packing, and sphere stacking (aka Johannes Kepler).

Yes, it is a curious group of numbers that engenders speculative thinking and, quite obviously, idiosyncratic conclusions.

[2] Discovery process since 2011. Our simple story has been told many times on many pages throughout this website, however, this link goes to the very first page about our discovery process. It all began on Monday, December 19, 2011. When asked about it, we began reflecting on the question, “Why Now?

[3] Articles about the Expansion of the Universe: Such an important issue, with this posting, we will begin gathering, sorting and prioritizing a new page that builds on the concepts of expansion, inflation and natural inflation. As a start, here are recent Google articles about the expansion of the universe. Some (Adam Riess and David Gross) are sounding the alarm!

[4] One plancksphere per plancksecond: According to Google’s search engine, the first time that micro-formula was used in a searchable document was our homepage on October 16, 2020. The next time was within the October 21, 2020 homepage. Now, within this homepage, we have begun to analyze what it means. It seems a bit odd that we’ve been staring at this definition for almost ten years… it has taken that long for this model to begin to sink in and break down the old models.

[5] Aether: In 1971-1972 we reconsidered the Michelson-Morely work and asked questions about fields within fields, but we did not have the most simple starting points, the Planck units. Wilczek’s grid is not basic enough. Penrose’s conformal cyclic cosmology  is too general. A “PlanckGrid” of planckspheres, stackings-and-packings might open a more systemic expansion of the universe so our first article about the aether will now be the focus of updating as an aggregation point for concepts that can expand this concept of a PlanckGrid.

In this theory, the laws of physics derive from a primal fractal-like geometry IU in state space” in “Bell Inequality Violation with Free Choice and Local Causality on the Invariant Set” by T.N.Palmer, Oxford, March 2019

[6] Dark Matter-Dark Energy: In October 2018, our first article about dark energy and dark matter was posted and within it were already concluding:
“The most-constant, most-intense stream of infinitesimal spheres, planckspheres, since the first moment of time until this current moment, is the expansion of the universe right now. Within this model, everything is literally connected to everything.” Until just recently, we had not thought about or even tried to calculate a rate of expansion.


References & Resources

I’ve begun to follow the work of three doctoral candidates: Andrea Di Biagio (La Sapienza), Marios Christodoulou (Oxford), Pierre Martin-Dussaud (Aix-Marseille Univ, Université de Toulon) who are trying to formulate an experimental environment to determine if time is ultimately discrete and digital.

Scholar-experts in string theory, Michael Duff and Gabriele Veneziano, have been re-engaged.

What Constitutes Emergent Quantum Reality? Perhaps we can learn something new from a Complex System Exploration from Entropic Gravity and the Universal Constants, Arno Keppen Space Pole, Circular Avenue, 1180 Brussels, Belgium



Michael Esfeld, From the measurement problem to the primitive ontology programme, May 2019, perhaps as part of a Festschrift-turned–tribute for GianCarlo Ghirardi. For more see the Esfeld ArXiv collection.

Claudia de Rham says, “We’re coming up with such a ridiculous answer that it really forces us to re-investigate every single assumption that we made along the way to get there.”

Reinhold A. Bertlmann reflects on his work with John S. Bell at CERN and beyond. His three articles remind us all why we were trying so hard to figure out the EPR paradox and Bell’s inequalities. I only met Bell for a couple of brief meetings at CERN. Back in 1980 in Paris, I studied with Costa de Beauregard one day, then the next day with Jean-Pierre Vigier at the Institut Henri Poincare. One day Vigier took me down to d’Orsay to meet Alain Aspect and discuss his work in light of Bell’s work. Bernard d’Espagnat joined those discussions. More to come…

Tim N. Palmer “...2011 cracked opened a door to look at your “‘…invariant set‘ in cosmological state space…”



Replying to Netflix, The Queen’s Gambit: It seems everybody is missing the power of the game of chess and how it trains the mind to think within 64 squares yet that process takes you way-way out of that box! As a global community, we are each on a path to capture those abilities. For more: and



Afterthoughts: There are so many brilliant people in this world, I often wonder why we have any problems at all.

Within this work, with every new little insight, there are new key words to research. For the past three “top-level pages” also known as homepages, the issue has been “one plancksphere per plancksecond.” If you were to do some keyword research on the web, you would find that there are only our three pages to be referenced. Be sure to include the quotes. There are thousands of references that use one of those words.

As a result of writing this article, I’ll now attempt to understand the 2003 article, Spacetime at the Planck Scale written by Paola Zizzi. Although a quick read reveals many places where we have parted ways, her references and her work over the past 16 years will be of great interest. She just may be the kind of person who would critically assess what it is we have been doing since 2011. That would be most valuable. –BEC


Key Dates for expansion

  • The template for this document emerged on October 30, 2020.
  • This page was first posted on November 16, 2020.
  • Collaborations for this document began on October 30, 2020 with scholars who had been introduced to this site at an earlier time.
  • The URL for this document is
  • The Prior Homepage:
  • The tagline: One plancksphere / plancksecond, a natural-but-unorthodox expansion
  • The last update of this page was on December 8, 2020.