###### by Bruce Camber, February 2018

**Background**: In December 2011 we began asking everybody and anybody, “Can we multiply the Planck Length by 2 over and over again? Is each result a meaningful number?” Prior to that time, I knew Planck’s name, a little about his 1918 Nobel prize, but not much more. I had just begun to explore the question, “How far within can one go dividing each successive tetrahedron and octahedron cluster in half?” The answer seemed to be, “To the Planck Length.” That begged the question, “What is the Planck Length?”

Eventually we will analyze every element in the equation above. For now, these resources are being used to learn more about the Planck Length:

- Our first expert, John Baez, The Planck Length. John told us that we were being idiosyncratic to multiply the Planck Length by 2 over and over again. We relied, “Yes, but is it wrong to do? Is logically flawed? If the Planck Length can be doubled, then what might cause it to double? Isn’t everything in nature and life sustained by doubling?”
- Laurence Eaves, University of Nottingham, helped us with a YouTube video in 2012.
- Frank Wilczek: Scaling Mt. Planck I, II & III encouraged us to continue exploring the definitions for the Planck Natural Units, base units, and fundamental units.
- Wikipedia: Scale of the universe, i.e. orders of magnitude,
- Sally Riordan, M.A., Management Consultant, London
- Roger Ellman: ArXiv article,Gravitational Equivalent Frequency and the Planck Length
- NIST, “Planck length“, NIST’s published CODATA
- “Quantum foam”. New Scientist. Retrieved 29 June 2008.

**What is the Planck Length? Frank Wilczek says**:

“The Planck length, formally, is a combination of fundamental constants that has dimensions of a length. I discussed this in some depth in the enclosed pieces. Perhaps the most physical interpretation emerged many years after Planck’s original numerology.

“It is as follows:

“In quantum mechanics, all dynamical variables fluctuate. Thus for example there is no sense in which a particle can have a definite position and momentum at the same time (uncertainty principle).

“In general relativity, the geometry of space-time is a dynamical variable. Space-time can be bent by energy and momentum; in fact that is how we account for gravity.

Putting these two together: the geometry of space-time fluctuates.

“Now you can ask when the fluctuations in distance between two points becomes comparable to the distance itself. It turns out this occurs at distances approaching the Planck length.

“I should emphasize that the Planck length is not a substance or law, just a rough concept. So for example twice or half the Planck length would be just as good as the Planck length itself, as a concept — it’s basically a matter of convention which you use.”

**Overview**:

**Also being considered**:

- Bekenstein, Jacob D (1973). “Black Holes and Entropy”.
*Physical Review D*.**7**(8): 2333. Bibcode:1973PhRvD…7.2333B. doi:10.1103/PhysRevD.7.2333 - Borzeszkowski, Horst-Heino; Treder, H. J. (6 December 2012).
*The Meaning of Quantum Gravity*. Springer Science & Business Media. ISBN 9789400938939 - Carr, Bernard J.; Giddings, Steven B. (7 December 2017). “Quantum Black Holes”.
*Scientific American*.**292**(5): 48–55. Bibcode:2005SciAm.292e..48C. doi:10.1038/scientificamerican0505-48. PMID 15882021 - Cliff Burgess; Fernando Quevedo (November 2007). “The Great Cosmic Roller-Coaster Ride”.
*Scientific American*(print). Scientific American, Inc. p. 55. - Dirac.pdf”.
*vk.com*. - Klimets, Alexander P (2000). “Geons – Candidates for the Role of the Initial Microblack Holes and Their Importance for the Planck Physics”.
*Fizika B*.**9**: 23. Bibcode:2000FizB….9…23K. “Klimets_A_P_Postigaya_mirozdanie.pdf”.*vk.com*. - T. Regge, Nuovo Cim. 7, 215 (1958). Gravitational fields and quantum mechanics
- John Whitfield, “Sharp images blur universal picture”, Nature, (31 March 2003).