For some reason the Ampere, a unit of electrical current, is a base unit of the SI, and electrical charge – an actual physical property of particles – is a derived unit. It’s quite comparable to defining velocity as a base unit and deriving length from that. Worth noting is that, from 2019 onwards, the Ampere is defined by the second and the fundamental *charge*.

Well if you’re going to do something poorly, it’s nothing short of dishonest to go any less than *all the way*. In that vein, let’s define a system of units, analogous to the SI, where everything is based on how things change over time rather than the quantities themselves. These units will take the names of SI units wherever they are equivalent.

First and foremost is **frequency**. Quantities changing over time have little use without some concept of time itself. The unit of frequency is the Hertz (Hz), produced by defining the frequency of radiation produced by the ground-state hyperfine transition of caesium-133 (Δ`v`_{Cs}) as 9 192 631 770 Hz. Trivially time, measured in seconds, is derived as Hz^{-1}.

The next base unit measures **velocity**. We’ll call this unit the “ved” (v), with the speed of light in vacuum (`c`) made to be 299 792 458 v. Thus a metre is derived as v Hz^{-1}, or v s if you really want.

Next is **power**. The value of a Watt (W) is realised by defining the Planck constant (`h`) as 6.626 070 15 × 10^{-34} W Hz^{-2}, which then opens the way to numerous other mechanical units as described further below.

Onwards to **electric current**, where this all started. The Ampere (A) is found when the elementary charge (`e`) is made 1.602 176 634 × 10^{-19} A Hz^{-1}. There’s not even a need to try here; it’s already silly.

And the last of the “important”/”necessary”/”sensible” units, **thermodynamic temperature**. There aren’t really units to do with rates of temperature; heat transfer for instance is built around energy. So the Kelvin (K) is what happens when the Boltzmann constant (`k`_{B}) is 1.380 649 × 10^{-23} W Hz^{-1} K^{-1}.

But what of **amount of substance** or **luminous intensity**? Amount of substance is just a quantity – it’s a dimension if you say it is, but doesn’t really need to be. In my mind it’s far better to be more specific, like energy per bond or mass per atom, rather than quantifying “large amount of *something*, but I won’t explicitly say what.” And luminous intensity is radiant intensity as perceived by the human visual system, which can’t even be based in physical constants. So as far as I’m concerned, neither of these are a necessary basis for a practical system of units.

So, to summarise the foundations of the Units of Rate:

Measure | Unit | Definition |
---|---|---|

Frequency | Hz | Δv_{Cs} ∕ 9 192 631 770 |

Velocity | v | c ∕ 299 792 458 |

Power | W | (h ∕ 6.626 070 15 × 10^{-34}) × (Δv_{Cs} ∕ 9 192 631 770)^{2} |

Electric current | A | (e ∕ 1.602 176 634 × 10^{-19}) × (Δv_{Cs} ∕ 9 192 631 770) |

Thermodynamic temperature | K | (1.380 649 × 10^{-23} ∕ k_{B}) × (h ∕ 6.626 070 15 × 10^{-34}) × (Δv_{Cs} ∕ 9 192 631 770) |

And some derived units:

Measure | Unit | Definition |
---|---|---|

Time | second | Hz^{-1} |

Length | metre | v Hz^{-1} |

Energy | joule | W Hz^{-1} |

Pressure | pascal | W v^{-3} Hz^{-2} |

Force | newton | W v^{-1} |

Mass | kilogram | W v^{-2} Hz^{-1} |

Electric charge | coulomb | A Hz^{-1} |

Electric potential | volt | W A^{-1} |

Magnetic flux density | tesla | W A^{-1} v^{-2} Hz |

Completely cromulent.

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