The Apprentice’s Guide to Physics: An Introductory Quest Through the Mechanics of the Universe

Units are the steadfast way to seal your spells after casting. Units give your numbers meaning. The international system of units is called the SI system (from the French Système International d’Unités). It defines seven base units Table 3.1.3, which form the foundation of all measurements in the magical realms of science include the seven SI base units: kilogram (\(\text{kg}\)), meter (\(\text{m}\)), second (\(\text{s}\)), mole (\(\text{mol}\)), ampere (\(\text{A}\)), kelvin (\(\text{K}\)), and candela (\(\text{cd}\)).

While units tell you how much of something you have, dimensions tell you what kind of thing it is. Dimensions Table 3.1.3 are the elemental ingredients behind every physical quantity: mass \([M]\text{,}\) length \([L]\text{,}\) time \([T]\text{,}\) electric current \([I]\text{,}\) temperature \([\Theta]\text{,}\) amount of substance \([n]\text{,}\) and luminous intensity \([J]\text{.}\)

Dimensions help you see through the illusion of numbers. For example, the dimension of length can be measured using many different units: meters, feet, centimeters, light-years, and so on. No matter which unit you choose, the underlying dimension, "length" is the true quantity being measured.

Units and dimensions are powerful tools for checking whether your work makes sense. When you cast a spell (or perform a calculation), you can examine whether the units and/or dimensions on both sides of the equation match. If they do, your spell is likely valid. If they don’t, you may have miscalculated or miscast.

In your quest through physics, units and dimensions will act like your spellcraft syntax checker, quietly verifying your logic and guiding you toward equations that make physical sense. Be careful, though: if the dimensions or units do match, that only means the equation is dimensionally consistent. It doesn’t guarantee the equation is correct or useful, just that it’s dimensionally consistent.

A wonderful location to dig deeper into units and dimensions is at the National Institude of Standards and Technology (NIST).

Looking for a quick refresher on SI units? Try SI Units

¹

www.nist.gov/pml/owm/metric-si/si-units

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Want to dig a little deeper and learn how each SI unit is defined experimentally and some historical context? Check out NIST: Definitions of the SI Base Units

²

www.nist.gov/si-redefinition/definitions-si-base-units

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With units in your toolkit and dimensions as your compass, you’re ready to navigate the equations of the universe. Always label your quantities, track your dimensions, and remember: a well-crafted spell or equation begins with knowing what kind of magic you’re working with.