Quantity Calculus, Fundamental Constants, and SI Units

Area of Science:

• Metrology
• Physics
• Chemistry

Background:

• The International System of Units (SI) is set for a significant revision.
• The 26th General Conference on Weights and Measures is scheduled for November 2018.
• The revised SI will be implemented on World Metrology Day, May 20, 2019.

Purpose of the Study:

• To update a 2011 analysis of the SI in light of the impending revisions.
• To demonstrate the continued relevance and utility of quantity calculus.
• To provide expressions for SI base units and defining constants under both current and revised systems.

Main Methods:

• Review of the quantity calculus.
• Analysis of the seven defining constants in the current and revised SI.
• Derivation of expressions for SI base units and relationships between unit magnitudes.

Main Results:

• Expressions for the seven current and revised SI base units are provided.
• Relationships between the magnitudes of revised and current SI units are established.
• Numerical values of current SI defining constants in revised SI units are derived using quantity calculus.

Conclusions:

• The quantity calculus is a valuable tool for navigating SI unit revisions.
• The paper provides a comprehensive update on the SI, incorporating the latest changes.
• Understanding the relationships between old and new SI units is crucial for scientific consistency.