On defining a dynamical behaviour of spacetime geometry on all scales


  1. What comes before Quantum Gravity? (this page)
  2. Quantum Gravity and Damiano’s Anselmi, December 23, 2022
  3. Quantum gravity, October 18, 2018
by Bruce E. Camber, Initiated on October 22, 2018

The Planck Scale: Many scholars are in search of “…a consistent theory of quantum gravity which describes the dynamical behaviour of spacetime geometry on all scales,†” And, to push the boundaries of that scale, the Planck scale may have more to contribute than meets the eye.

Introduction. Between the Planck scale and “CERN-scale of measurements,”1 there are 67 doublings (or notations or causal sets) of the Planck base units. Perhaps it might be better to start at the first doubling and to observe the logical possibilities. Essentially we’d be building a unified theory of mathematics, yet this one would be based more on John Wheeler’s sense of simplicity that he describes in his introduction of this articleHow Come the Quantum?2 (1986). It is a totally different starting point, but the same intellectual challenge that faced Robert Langlands when he first started writing his programs.

The plancksphere. Both Max Planck and Wheeler anticipated the smallest possible three-dimensional sphere. It makes building that unified theory of mathematics a bit easier. It gives substance to Causal Dynamical Triangulations (CDT), Regge calculus, fractal structure, 2-D spacetime, and the flavors of the simplex. It introduces stacking and doubling where each of the CDT expressions can be included at an appropriate doubling.

Imagination. With imagination working overtime, the emergence at the Planck base units, the most-simple plancksphere, may well account for dark matter and dark energy (possibly a relatively simple calculation). Using conservative calculations, by the 20th doubling there could be 1,152,921,504,606,846,976 scaling vertices but perhaps just 1,048,576 stacked planckspheresIt seems to be a geometer’s dream. By 42nd doubling there could be about 1,099,511,627,776 (one trillion plus) stacked spheres and by the 64th over 4.611686×1018 stacked planckspheres and the scaling vertices, beyond imagination, at 6.2771017×1057 vertices.  Now, all of this could  become a geometer’s nightmare unless, of course, we learn something more about groups, sets and notational transformations!

Scholars. Most of the scholars to whom we ask questions, the typical request is, “Help us debunk our simple model.”  What’s wrong with our starting point? The basic concepts are simple but the entire orientation seems to open old questions in new ways. Are there new possibilities where there is confusion?

Redefinitions. Within this space, space-time is derivative, discrete and quantized.  So one might ask, “…then what’s infinite?”  We recognize that part of our conundrum is to redefine the infinite and we choose to define it with mathematical terminology — continuitysymmetry-harmony — and anticipate that this finite-infinite transformation may possibly further define the renormalization process.  More to come: What’s a point?


If this is a thesis, what would be an antithesis and synthesis? Would you like to help write it?

Endnotes, Footnotes,  References and Resources:

Editor’s note: As you’ll see, this page is based on an email to Prof. Dr. Renate Loll of the Netherlands.


1 •  CERN-scale of measurement: CERN labs readily claims to be able to measure interactions within a space of 2.38509×10-15meters. Questions can be asked if they are able to measure interactions within a space of 5.962725×10-16 meters.  Where the Planck Length is 1.616229(38)×10-35  meters, and if this length and the other three base units are taken as a given to define the first manifestation of a space-time moment, what does it look like?

2 • John Wheeler: If you only read the first paragraph, you will get a sense of the good spirit of John Wheeler. This article speaks volumes: How Come the Quantum?  From the Annals of The New York Academy of Sciences, December 1986.

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

Key documents that were recently homepages:

October 16: Looking in the dark for Dark Matter & Dark Energy
October 12: What would you do with this model of the universe?
October 1: The first 64 notations out of the 202
September 28: An Open letter about nature of light
September 20: “Gravity, Oh Gravity… Why Such Gravity?”
September 19: On Validating The Efficacy of our Model.
September 17: Open Letter (email) – Many similar notes are sent to scholars everyday.
September 14: Your critical review is encouraged.
September 12: Questions – Frequently Asked Questions.
September 5: Commonsense – It is not common and it is not a sense.
August 31: Reviews – You are invited to review an alternative to Big Bang Cosmology.
August 26: Problems – We all must become problem solvers.
August 5: On embracing the functions of our Universe
August 2: This Simple Scale of the Universe
July 23: Big Bang Theories Unnecessary In Light Of A Natural Inflation
July 12: An addendum to the Standard Models and for all algorithms
July 8: Compilations of concepts that could give rise to the 202 doublings
July 4: Revolutions: Foundational Concepts & First Principles

June 21: Planckspheres, dimensionless constants, doublings
May 18: Alternative to the Big Bang theory

April 30: Emergence & Growth from the first moment in time
April 21: More about emergence, growth, and imagination
April 18: Einstein’s Postulates

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

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