###### by bruce camber

**Please Note**: This compilation page was initiated on April 12, 2018. Still being edited as of October 15, 2018, it has a ways to go as a working draft.

**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’s *quantum foam*. But when searching for references to the word, there were already many much-earlier adopters.

The concept had come into my focus as a result of these four 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 William Prout’s proposals and surely with Ernest Rutherford work in 1920 to define the proton. The definition of the Planck base units occurred between 1899 and 1905. At no time has anyone asked, 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 – 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).

That was as far as I had come but now 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.

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

Planck Sphere: http://vixra.org/pdf/1711.0457v1.pdf The Holographic Principle and How can the Particles and Universe be Modeled as a Hollow Sphere

http://vixra.org/pdf/1601.0103v1.pdf

Author Michael John Sarnowski

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.

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 ..

http://backreaction.blogspot.com/2015/09/no-loop-quantum-gravity-has-not- been.html?spref=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**). It is defined as the limiting difference between the harmonic series and the natural logarithm: Here, represents the floor function.tw

https://www.physicsoftheuniverse.com/contact/

https://www.brown.edu/academics/math/news/2018/03/distinguished-lecturers-series-4418-4618

Henry Cohn, Microsoft Research, http://math.mit.edu/~cohn/

**“Sphere packing and the magic dimensions 8 and 24”**

**“Sphere packing and uncertainty principles” **

where there are **1979**. *The Geometrical Foundation of Natural Science*, Robert Williams (Dover, 1979): I have begun reading bits and pieces of Williams book:

https://archive.org/stream/geometricalfound00will#page/n21/mode/2up

**2006**. Victor J. Stenger used the concept (p. 134) within his book,** ***The Comprehensible Cosmos: Where Do the Laws of Physics Come From?* (Prometheus Books, 2006)

2004 Gary Cuba: http://thefoggiestnotion.com/planck_unit_packing.htm

*The Geometrical Foundation of Natural Science*, Robert Williams (Dover, 1979): Sphere packing LinkedIn: Congratulations on all that you have seen and experienced. Just wonderful. Just discovered your work through a reference with Gary Cuba’s work: http://thefoggiestnotion.com/planck_unit_packing.htm

I was part of Loeb’s Philomorphs back in 1971; today making a little progress: http://81018.com

**References**:

Numbers: https://81018.com/number

** Consider Phillip Ball’s work:**

- Physics at the Planck time by Philip Ball
- https://en.wikipedia.org/wiki/Critical_Mass_(book)
- https://en.wikipedia.org/wiki/Philip_Ball
- https://www.philipball.co.uk

In 2017 it was suggested by E. Haug^{ [3]} 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.

• 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

I wrote to d8_thc the following note, 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

http://www.ift.uni.wroc.pl/~planckscale/lectures/1-Monday/4-Loll.pdf

Steve Carlip on dimensional reduction (Loll, Reuter, Horava; smallscale fractalit