###### by Bruce Camber, 2018

**Back in 1955…**

**Princeton: ** Physicist John Archibald Wheeler, wrote this unusual combination of words for the first time. Today, also known as spacetime foam,** **it has been suggested that this *foam* marks the beginnings of** **quantum mechanics and quantum fluctuations. Also, the study of foam has evolved to spin foam theory and spin networks. It is now a key topic within loop quantum gravity (LQG).

**Who Is John Wheeler and what is this foam? **This page is simply to aggregate as many articles as possible about quantum foam beginning with an introduction to John A. Wheeler and his work:

1. John Wheeler (Wikipedia)

2. Wheeler, J. A. (January 1955). “Geons”. Physical Review. 97 (2): 511.

– – – Bibcode:1955PhRv…97..511W. doi:10.1103/PhysRev.97.511.

3. John Wheeler’s quantum foam (Wikipedia)

4. John Wheeler, Geons, Black Holes, and Quantum Foam

5. YouTube with Wheeler: Quantum ideas, Quantum foam, Max Planck & Karl Popper

6. *Quantum Foam, * (ArXiv), *Y. Jack Ng, University of North Carolina, *

* • Quantum Foam, Gravitational Thermodynamics, and the Dark Sector*

7. Planckspheres. John Wheeler never used the term* per se* but it certainly overlaps.

8. Institute for Advanced Studies: https://www.ias.edu/idea-tags/john-wheeler

9. Roger Penrose, 1971

**A different approach**. As you might imagine, within this website, the concepts of *quantum foam* and quantum fluctuations are treated rather differently. This will be our first attempt to describe both within the context of the 202 base-2 notations. Many updates are anticipated.

First, within our 202 notations, quantum mechanics does not begin in the first notations. Here, quantum fluctuations, which are assumed by most scholars to be responsible for the quantum foam, are associated with a very real geometric configuration. With just five tetrahedrons sharing a common edge (as shown), there is a natural gap within that pentagonal structure which is then extended into the 20-tetrahedral complex or icosahedral complex which is then extended into the 60-tetrahedral Pentakis dodecahedral complex. It is hypothesized that the mathematics of the gap is the mathematics of Wheeler’s quantum foam which is the mathematics of quantum theory. At this time, it is not known within which notation the pentagonal structures first manifest.

**Does the sphere become an incompressible foam?**

At the Planck scale (A0) and its first doubling or notation (A1), circles and spheres are strictly mathematical. These physical manifestations are well below the possibilities of measurement until those doublings are in the range of today’s CERN scale. Yet, by our analysis of the 31st notation, there is a very real mass and charge. Nevertheless, at the A1, the circle and sphere are mathematically defined by dimensionless constants and this so-called foam is an *absolute* limit of space-time (Planck Length-Planck Time). In deference to Max Planck, we had dubbed the “foam” to be *Planckspheres* and then we began finding references in some of the more speculative within the literature to “Planck Spheres.”

See: “Mysteries in Packing Regular Tetrahedra

Jeffrey C. Lagarias and Chuanming Zong

http://ams.org/notices/201211/rtx121101540p.pdf

The Riddle of the Quantum Sphinx: In his Feb. 7, 2018 public lecture at Perimeter Institute, Robert Spekkens explains why he believes that many quantum mysteries are a result of a category mistake concerning the nature of quantum states.

Predictions in eternal inflation, Sergei Winitzki