Primordial Sphere (PS) or Infinitesimal-Archetypal Sphere (IAS)

First things first
By Bruce E. Camber, July 30, 2021
[A working, rough draft]

We are all getting increasingly confident that our universe has a starting point. Most everybody knows that the first physical thing was not an atom. It is much too complex. It was probably not a particle or wave or a fluctuation. Not quite complex enough. There are no amount of colors, shapes, directions, feelings, or charms that has causal efficacy. No, it seem that it has to be so much more than all those things and it makes every single one of those things be what each is, yet it is magically more simple.

I believe a sphere could qualify. Initially we’re calling it a primordial sphere.

A scant actual distance, but in our mathematical world, seemingly a galaxy away, there are at least 64-to-66 steps, base-2 exponentiation, or simple doublings, that take us into an unknown abyss where nothing can be measured yet where there is an abundance of numbers, each step taking us simply so much smaller, all well beyond the reach of any measuring device. As many as 66 steps, going smaller and smaller, before we are even close to what we call a primordial sphere or infinitesimal-archetypal sphere.

Two acronyms today: Primordial Sphere or Infinitesimal-Archetypal Sphere. We would say “PS” as if we might want to add an addendum or “IAS” and perhaps, phonetically say inner’sphere. Sounding out just the letters, IAS, might remind some of the Institute for Advanced Study, just down the street from Princeton University. We’ll use both acronyms as we study and refer to the computations of two scholars much of whose work has been largely forgotten. Both are a special mix of scientist-philosopher-mathematician and they were among the first to calculate the base units of our universe. In 1874 George Johnstone Stoney and in 1899 Max Planck made their respective calculations. I say that they are “close enough” to describing this real reality, this first moment to define space-time. Certainly, their figures will be re-calibrated and refined just like the figures for the age of the universe, over and over again. Yet, today, these numbers define a big picture very minutely and get us re-oriented to a profoundly different sense of our universe. Their work became our foundations to begin to define a highly relational universe. We unwittingly backed into the 202 notations of a base-2 grid of the universe. We started with the Max Planck units and discovered an intricately-woven network of networks.* [It would seem if we compared our old television waves to this network, they would appear as a million-lane highway.]

Just 202 notations from beginning of time to today, the Now. The calculation for Planck Time renders a number so small,it is too small to even begin to fathom. One might say, “It’s way smaller than infinitesimal.”

We are generally satisfied to measure things within a second. Today, expensive measuring devices measure within a nanosecond, one billionth of a second (10^-8). Much more expensive devices measure one trillionth of a second. That’s a picosecond (10-12). A laboratory in Germany, a Max Planck Institute, was the first to measure an attosecond, one quintillionth of a second (10-18). In 2016 they proclaimed measurements in the septosecond range, a trillionth of a billionth of a second (10-21). As infinitesimal as that is, the PlanckSecond is many orders of magnitude smaller (10-44).

More to come

Footnotes, References and Resources

The Quantum Structure of Spacetime at the Planck Scale and Quantum Fields, Sergio Doplicher1, Klaus Fredenhagen2, John E. Roberts3 22 June 1994, Research supported by MRST and CNR-GNAFA.

  1. Dipartimento di Matematica, Universita di Roma “La Sapienza”, 1-00185 Roma, Italy
  2. II Institut fur Theoretische Physik der Universitat Hamburg, D-22761 Hamburg, Germany
  3. Dipartimento di Matematica, Universita di Roma “TorVergata”, 1-00133 Roma, Italy.

Relating the Archetypes of Logarithmic Conformal Field Theory, Thomas CreutzigDavid Ridout, 11 Jul 2011 arXiv:1107.2135 

Wess-Zumino-Witten model, Wheeler, J.A.
Geometrodynamics and the Issue of the Final State, Hawking, S.W., Spacetime Foam. Nucl. Phys. B144,349, (1978)
which is in Relativity, Groups and Topology. De Witt, C, De Witt, B., (eds.) Gordon and Breach 1965

On Space-time at Small Distances, Amati, D.,Ciafaloni, M.,Veneziano, G., Nucl. Phys. B347, 551 (1990)

The Search for Higher Symmetry in String Theory, Edward Witten, Institute for Advanced Study, Princeton, Proceedings, Physics and mathematics of strings, 31-39, Phil.Trans.Roy.Soc., London 1988 A 329 (1989) 349-357 doi:10.1098/rsta.1989.0082

Meet the zeptosecond, the shortest unit of time ever measured,  Stephanie Pappas, space.com,  October 25, 2020

Martin Schultze

Attosecond correlation dynamics, M. Ossiander1,2*, F. Siegrist1,2, V. Shirvanyan1,2, R. Pazourek3, A. Sommer1, T. Latka1,2, A. Guggenmos1,4, S. Nagele3, J. Feist5, J. Burgdörfer3, R. Kienberger1,2 and M. Schultze1,4 NATURE PHYSICS | VOL 13 | MARCH 2017 | http://www.nature.com/naturephysics

[1] Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
[2] Physik-Department, Technische Universität München, James-Franck-Strasse 1, 85748 Garching, Germany
[3] Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria
[4] Fakultät für Physik, Ludwig-Maximilians-Universität München, Am Coulombwall 1, 85748 Garching, Germany
[5] Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
*e-mail: marcus.ossiander@mpq.mpg.de; martin.schultze@mpq.mpg.de

John Lane Bell

  • The Continuous, the Discrete, and the Infinitesimal in Philosophy and Mathematics (New and Revised Edition of 2005 book), Springer, 2019.
  • Intuitionistic Set Theory. College Publications, 2013.
  • The Continuous and the Infinitesimal in Mathematics and Philosophy with D. DeVidi and G. Solomon, Polimetrica, 2005.  
  • Logical Options: An Introduction to Classical and Alternative Logics. Broadview Press, 2001.
  • The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. Kluwer, 1999
  • A Primer of Infinitesimal Analysis. Cambridge University Press, 1998. Second Edition, 2008.

Key Dates for this article, Primordial