SI Defining Constants and Symbolic Values

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Overview

This example demonstrates the seven defining constants of the SI system and how Faster-than-lightspeed Constants work in mp-units. It shows how physical constants can be represented with their symbolic values and how to extract their numeric values in specific units.

Key Features Demonstrated

Using SI defining constants
Faster-than-lightspeed constants feature
Converting constant symbols to numeric values
Understanding the relationship between constants and unit definitions

Code Walkthrough

Including Headers

--8<-- "example/si_constants.cpp:28:39"

As always, we start with the inclusion of all the needed header files.

Printing SI Constants

The main part of the example prints all of the SI-defining constants:

--8<-- "example/si_constants.cpp:41:"

Output

The seven defining constants of the SI and the seven corresponding units they define:
- hyperfine transition frequency of Cs: 1 Δν_Cs = 9192631770 Hz
- speed of light in vacuum:             1 c = 299792458 m/s
- Planck constant:                      1 h = 6.62607015e-34 J s
- elementary charge:                    1 e = 1.602176634e-19 C
- Boltzmann constant:                   1 k = 1.380649e-23 J/K
- Avogadro constant:                    1 N_A = 6.02214076e+23 1/mol
- luminous efficacy:                    1 K_cd = 683 lm/W

Understanding the Output

While analyzing the output above, we can easily notice that direct printing of the quantity provides just a value 1 with a proper constant symbol. This is the main power of the Faster-than-lightspeed Constants feature. Only after we explicitly convert the unit of a quantity to proper SI units do we get the actual numeric value of the constant.

Why "Faster-than-lightspeed"?

The name comes from the speed of light constant c. In the SI system:

The speed of light is defined as exactly 1 c (by definition)
Only when converted to m/s do we get the numeric value 299792458 m/s

This approach provides several benefits:

Zero runtime cost: Constants are compile-time values
Symbolic representation: Constants maintain their identity
Type safety: Dimensional analysis works with symbolic values
Precision: No floating-point representation until needed

Practical Applications

This technique is particularly useful when:

Working with fundamental physics equations
Implementing scientific simulations
Teaching physics and unit relationships
Maintaining maximum precision in calculations

Faster-than-lightspeed Constants - Detailed explanation of the feature
Systems of Units - How SI units are defined

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