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A Study of Notation #0: The Planck Units

The Numbers:

Planck Time Planck Length Planck Mass Planck Charge Scaling Vertices
5.39116(13)×10-44 (s) 1.616229(38)×10-35 (m) 2.176.47(51)×10-8 (kg) 1.875 545.956(41)×10-18 (C 1

Background.  Planck Numbers, All Transformations Between the Finite And Infinite
Although Max Planck began developing these numbers in 1899 and first published them in 1906 (within his book, Theory of heat radiation), nobody paid much attention to what we now know as the Planck units. In 2001 Frank Wilczek (MIT) began publishing three articles, Scaling Mt. Planck (312, 321, 328) for Physics Today. Although other scholars had engaged one or more of the Planck numbers, Wilczek, in our private conversations, took some credit for lifting the Planck units up-and-out of the category of numerology and to have opened the path for others to use and cite the Planck base units.
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There were a few scholars who had even earlier intuitions about the significance of these numbers and dared to write about it. To understand that history, there are many stories that need to be reviewed. For example, in 1959 C. Alden Mead (UMinn) began his struggle to publish his work about the Planck Length. Though finally published in 1964, the article, Possible Connection Between Gravitation and Fundamental Length (Phys. Rev. 135, B849, 10 August 1964), was ignored by the scholarly community. At that time, the Planck Length commanded almost no respect as a fundamental unit of length.
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Finite and Infinite. This project is a study of the finite, yet the infinite has a substantial, abiding and fundamental role. Within these studies the infinite is defined as (1) continuity, that which creates order, (2) symmetry, that which creates relations, and (3) harmony, that which creates dynamics. These three postulations about form and function assume a panoply of necessary-and-abiding transformations. We choose to avoid all religious and theological language and to leave such extensions to each reader.

Three measurements are smaller than Planck Charge: 
•  5.34×10−20 C The charge of down, strange and bottom quarks
•  1.068×10−19 C The charge of up, charm and top quarks
•  1.602×10−19 C The elementary charge, e, i.e. the negative charge on a single electron or the positive charge on a single proton
Questions abound:
•  If pre-Planck Length and Planck Time, are these charges within the transformation nexus between the finite and infinite?
•  Could these be earliest possible measurements of the radii and diameters of circlers and spheres?
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More Research Projects. Even today, support for the Planck base units is far from unanimous. Among our many research projects, a study will focus on those who are not ready to recognize that these Planck units are in any way fundamental units for science.
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Studying and interpreting Max Planck’s 1899 logic to extract each of these base units is also part of our ever-so-slowly emerging secondary school program called Big Board-little universe and the programs of this website, our Quiet Expansion and our Simple, Mathematically-Integrated Chart Of Our Universe. Planck’s logic to select each facet of reality, define each quantitatively, and to define their relations, equivalencies, and ratios will be examined.

Formulas / Ratios:

Planck Time: Planck Time
Planck Length: Planck Length
Planck Charge: Planck Charge
Planck Mass: Planck Mass

Open Questions: On gathering a team of experts to analyze these numbers as deeply and rigorously as possible.

Dimensionless constants. What are these dimensionless constants that are never-ending and never-repeating numbers? If Pi is the mother lode, what follows? Is Euler’s number, e, next? Why? Do all equations that use pi, like the fine-structure constant, qualify? Does any equation that uses the reduced Planck constant (ħ) also qualify as a bridge between the finite and the infinite? Are these keys to understand the simple and most basic formulas that define our reality?
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Prime: Each of the first six selected notations is also a prime number. Mathematics recognizes the special role of prime numbers. Our never-ending, never-repeating numbers set within a prime number may open another door for discovery. Given our working assumption that everything starts simply, how does any group of equations start simply? What are the mechanisms for the simple-to-complex transformations, (1) within a given notation, then (2) between successive notations, and then (3) with other groups of notations? And then, by adding those never-never numbers (all ratios), does that create yet a fourth facet that defines finite-infinite transformation dynamics as well as space-time dynamics within every aspect of mathematics, logic and science?