Physical Constants

Fundamental Physical Constants

**Goals**:

1. Group, then rank order the constants by fundamentality, importance (use by other constants), and place (use by scholars, i.e. citations),

2. Relate to a notation or set of notations where there is a natural link to the Key Ratio and historic discussion.

**Background**: On September 18, 2019, the Planck base units needed further definition. We assumed that what was found consistently on the web was not necessarily good enough. We turned to the expert studies of the National Institute of Science and Technology (NIST). Are there in fact 64 notations or doublings the Planck Length and Planck Time ? …from the first moment of time? Does Planck Time encapsulate the first moment? Our analysis had begun with the help of data accrued by John Baez. It was time to come back around to that data and to analyze each judgement and conclusion that was based on the Baez work.

**353 NIST Fundamental Physical Constants**:

**Editor’s note**: This list of fundamental physical constants is directly from the National Institute of Science and Technology (NIST). It is replicated here: (1) to provide a one-step access to the **Numerical value**, the **Standard Uncertainty**, the **Relative standard uncertainty** and the **Concise form**, (2) compare quickly to Wikipedia’s list of dimensionless constants, the Aguirre, Rees, Tegmark, Wilczek list of 31 necessary for the Standard Model for Particle Physics, and the list of 26 by John Baez. At some time the work of Simon Plouffe, who identified over a billion such constants (computer-generated), may also be engaged.

**Goals**:

1. Emerge with two columns, one of the 353 NIST constants and the other as ranked by fundamentality, importance (use by other constants), and place (use by scholars, i.e. citations),

2. Relate to a notation or set of notations where there is a natural link to the Key Ratio and historic discussion.

What is the path from a dimensionless physical constant to a fundamental physical constant? What is dimensional analysis? See the Buckingham **π theorem** and nondimensionalization and natural units and system of measurement.

What are the dimensionless physical constants?

What is the hierarchy problem?

Planck units use the gravitational constant *G* (a constant of proportionality) measured in a laboratory to just four digits. The modern notation of Newton’s law involving *G* was introduced in the 1890s by C. V. Boys. The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment