###### https://www.brown.edu/academics/math/news/2018/03/distinguished-lecturers-series-4418-4618by bruce camber Initiated on April 12, 2018 To be developed over the next few years.

**Background**. In April 2018, I thought that I was making up a new word, *Planckspheres* or* Planck Spheres.* It seemed reasonable. It was a natural progression beyond John Wheeler work to define *quantum foam.* Related to the foam was what he called a geon. Others came up with different names yet similar concepts.

There was the preon in 1974 with Pati/Salam. There are scholars who are still reworking their initial concepts.

Of course, strings and string theory will have a role. The mathematics within Langlands programs will have a role. Even hypothetical particles like instantons will have a role.

All the creative energies of so many, most of it will have a role. The special magic will be in building bridges between them all. Those first 64 notations are waiting in the wings to play their substantial and all embracing role to tie all these related concepts together.

The concept of a plancksphere will be developed well beyond where we are today. The concept had come into my focus as a result of prior homepage articles:

• **Emergence, planckspheres and doublings****:** https://81018.com/emergence/

• **A study of the earliest beginnings**… the first three of 202 notations https://81018.com/growth

• **Our Open Letter To You**: An introduction to a very simple chart of the universe that seems comprehensive beyond belief and imaginative: https://81018.com/imagination/

• **202 doublings define our universe**. Each doubling could also be considered an archetype, cluster, container, domain, group, layer, notation, set, or step. https://81018.com/einstein/

•** The first 64 doublings**: Some might argue that scientists have been thinking about particles and sub-particles since 1815 within the work of William Prout and surely with Ernest Rutherford work in 1920 to define the proton. The definition of the Planck base units occurred between 1899 and 1905. It appears that at no time did anyone ask, “What is in between the Planck scale and the proton scale?” The emphasis has consistently been on definitions of particles and not potential for logic and mathematics to fill in the 64-step gap of doublings. A rather formidable range with real numbers that define physicality had been ignored.

Back in 2015, it had also been the subject of an early analysis of Wheeler’s geon (1955): Quantum foam by John Archibald Wheeler.

[†] This dynamic image was first introduced within this website on January 4, 2016 in an article about numbers, “Constructing the Universe from Scratch.” It has now become the center point within this analysis. In that initial article, the question was asked, “Which numbers come first and why? Which numbers are the most important to know and understand?” The image was also used within the following articles: *Fabric of the Universe *(November 20, 2017, just below point #4), *Consider how symmetries within the first 67 notations actually create space* (Sept. 17, 2017), *Symmetry: Circles-to-Spheres-to-Triangles-to-Tetrahedrons-to-Octahedrons* (September 13, 2017, and most recently, *Possibilities for New Explorations *(October 2018).

## April 2018, The Plancksphere: It seemed to be the most important part of the puzzle so this page became a collection area for any and all articles that made reference to Planck Spheres and sphere stacking.

*A rather odd, helter-skelter collection zone begins below! *

- Howard Georgi within his concepts of “Unparticle Physics.”
- Usurping Quantum Theory – FQXi Community
- Planck Sphere: http://vixra.org/abs/1711.0457v1 The Holographic Principle and How can the Particles and Universe be Modeled as a Hollow Sphere, Michael John Sarnowski, Nov. 2017
- Sabine Hossenfelder states, “The Holographic Principle requires that the number of different states inside a volume is bounded by the surface of the volume. That sounds like a rather innocuous and academic constraint, but once you start thinking about it, it’s totally mind-boggling.” http://backreaction.blogspot.com/2015/09/no-loop-quantum-gravity-has-not- been.html The
**Euler**–**Mascheroni constant**(also called**Euler’s constant**) is a mathematical**constant**recurring in analysis and**number**theory, usually denoted by the lowercase Greek letter**gamma**(**γ**). . - ..d
**efined as the limiting difference between the harmonic series and the natural logarithm**: Here, represents the floor function. https://books.google.com/books?isbn=1304195066, David de Hilster, “The natural progression of photon-snippets travel between adjacent layers — for half-an -instant — these layers alternate; allowing left-hand spirally polarized photons to “ride” the surface of the*Planck-spheres*to the next pair of adjacent Onion-layers. Then next half-time quantum the right-hand spirally polarized photons do…” - L. Mastin, “Singularities, Physics of the Universe, Oct, 2009, https://www.physicsoftheuniverse.com
- /topics_blackholes_singularities.html
- Henry Cohn, Microsoft Research, http://math.mit.edu/~cohn/
**“Sphere packing and the magic dimensions 8 and 24”****“Sphere packing and uncertainty principles”**

*The Geometrical Foundation of Natural Science*, Robert Williams (Dover, 1979)- Victor J. Stenger used the concept, “Planck sphere” (p. 134) within his book,
*The Comprehensible Cosmos: Where Do the Laws of Physics Come From?*(Prometheus Books, 2006) - Gary Cuba, 2004 http://thefoggiestnotion.com/planck_unit_packing.htm
*The Geometrical Foundation of Natural Science*, Robert Williams (Dover, 1979): Sphere packing**Consider Phillip Ball’s work:**- E. Haug that the Planck length can be indirectly measured independent of any knowledge of Newton’s gravitational constant with, for example, the use of a Cavendish apparatus, 2017

- https://en.wikipedia.org/wiki/Zeros_and_poles
- http://en.wikipedia.org/wiki/Pole_(complex_analysis)
- http://en.wikipedia.org/wiki/Simply_connected_space
- http://en.wikipedia.org/wiki/List_of_mathematics_journals
- John Conway on the pole

##### Planck Spherical Unit structure of space and quantum gravity (LQG)

https://forum.nasaspaceflight.com/index.php?topic=41672.msg1612124#msg1612124

d8_thc: “I had to put my sunglasses on to read your statement within these pages: *“If the structure of space itself was made up of overlapping Planck spherical units of the Planck mass, we would have a Bose Einstein Condensate of space, implicating that the surface horizon of these black holes are using this to transfer mass information instantly outward, i.e. the majority of mass is nonlocal due to Einstein-Rosen bridge wormholes (implicating EP=EPR).”*

https://forum.nasaspaceflight.com/index.phptopic=41672.msg1612124#msg1612124

- The Unified Field And Sacred Geometry
- I’ll be processing it for awhile.
**BTW, do you know of any concise history of the emergence of the concept of a Planck sphere?**Thanks.”

- Note: https://www.youtube.com/watch?v=KoELwBYzNDY Nassim Haramein
- Nexus 2010 in Queensland, Australia
- Nov 21, 2016 – … planck density of space using spherical oscillators yields the mass of the observable universe. Next divide surface / volume. And here is calculating the proton rest mass via these same principles but applying the holographic principle .
- Quote: planck masses that fit on surface /
*planck spheres*in volume. - Casmir effect, 1947

- Who are Jan Ambjorn and Renate Loll? 4D nonstring quantum geometry/gravity
- Reference https://www.physicsforums.com/threads/steve-carlip-on-dimensional-reduction-loll-reuter-horava-smallscale-fractality.323417/
- Steve Carlip on dimensional reduction (Loll, Reuter, Horava; smallscale fractalit
- Out of date: https://www.brown.edu/academics/math/news/2018/03/distinguished-lecturers-series-4418-4618