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A Study of Notation #0: The Planck Base Units
The Numbers:
Planck Time | Planck Length | Planck Mass | Planck Charge | Scaling Vertices |
5.3911(13)×10^{-44} (s) |
1.6162(38)×10^{-35 }(m) |
2.1764(51)×10^{-8 }(kg) |
1.8755(41)×10^{-18} (C) | ? |
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, in our private conversations, Wilczek 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. One of those scholars was C. Alden Mead (UMinn). In 1959 Mead began his struggle to publish his speculations regarding the place of the Planck Length within science. 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 began as a study of the finite, but now, also the finite-infinite relation. Within all of 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
The Fabric of the Universe. These measurements, we postulate, are within a nexus of transformation. Here the fabric of the universe is set by many formulas, equations, ratios, and numbers; it is all being woven as a fabric. This nexus should probably include activity and functions within pi (π) within the most simple definitions of the radius of the circle as well as a first group of notations, probably three or more notations (steps or layers), but less than 20.
Questions abound:
• If we assume a pre-Planck Length and pre-Planck Time, are these values within the transformation nexus between the finite and infinite?
• Could these be earliest possible measurements of the movements of the radii and diameters of circles 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 (a STEM project) 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:
Scientists/scholars/experts. Now at work to analyze these numbers as best they can, within the framework of big bang cosmology, it is difficult to go deep and to be rigorous.
Dimensionless constants. What are these dimensionless constants that are never-ending and never-repeating numbers? If Pi is the mother lode, is Euler’s number, e, next? Perhaps it precedes pi. Why? Do all equations that use pi, like the fine-structure constant, qualify as never-ending, never-repeating? 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 Studies: Of the first six selected notations, all are prime numbers. Mathematics recognizes the special role of prime numbers. Our never-ending, never-repeating numbers set within a prime number notation may open another door for discovery by introducing an expansion of mathematical complexity. 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?
There is much more to come. This is a working first draft. It was started on August 26, 2017 in Austin, Texas and is being updated on Thursday, December 13, 2018 in Miami.