Did you know that all of our units in science are defined by measurements of nature? Each and every one of them is determined or determinable by measuring a specific thing? All of our official units of measurement are now defined by the constants of nature. This is work that was finished and agreed upon very recently. I do encourage you to click that link and read the NIST page about the units, their history, and the constants. It’s extremely well done.
An aside: NIST is a great example of a benevolent government agency. A lot of things we absolutely take for granted are enabled by NIST and we don’t think about it or them at all because they do it so well. NIST makes it such you don’t have to trust something you can prove it and know the reference you received from NIST is the genuine article and will be backed up by the force of law. This is how insanely important units and standards are.
Constants of Nature
From the constants c (speed of light), h (Planck’s Constant), e (elementary charge), ∆νCs (Hyperfine transition of Cesium-133), k (Boltzmann Constant), N~A~ (Avogadro’s Number), K~cd~ (Luminous Efficacy Constant), all of our units of measure can be determined anywhere in the Universe. Use the link above if you want to know what all of them are and what they mean.
For example the meter is defined by the distance a photon covers in a perfect vacuum in 1/299,792,458 of a second. Second is a unit too so that must be derived from nature. That’s what the hyperfine transition is for, that determines the value of a second.
There are other constants of nature not mentioned here that are very important, such as the dimensionless constants. Most famous is probably the fine structure constant α which is approximately 1/137.035999177. 1/137 and it shows up everywhere in quantum mechanics and fundamental equations. This constant quantifies the strength of the electromagnetic interaction between elementary charged particles, the force carrying particle of which is… the photon (light).
Dimensionless constants are special because no matter what unit of measurement you use if you faithfully plug the measurements into the defining formula the units all cancel out. This means that as long as the values were measured well in the correct unit the final number will always be the same as the relationship between those numbers is the same. Whether you are Eridian, Vulcan, Turian, or Human you know the fine structure constant as about 1/137.
Dimensional Analysis
Probably the most powerful thing I learned in Chemistry & Physics is dimensional analysis. You do math on the units themselves as you run the equation, and doing so you check your work. This is why your science teacher was so nutty about including the units. Had we been clued in on this in Middle and High School you too would have been much more conscientious of your units! Using this technique you know if you’re missing something or you failed to do a conversion somewhere. Doing actual physics it gives hints of constants you may need, missing variables, important (or irrelevant) relationships.
You may do a calculation and get out the back side inch seconds per milliliter, which is a goofy unit. Certainly not a Joule (kg × m^2^ /s^2^). Maybe you need to do a conversion somewhere (yes for sure), or you put in a wrong measurement somewhere so it didn’t cancel out. Here’s a genuine what-if starting with dimensional analysis - there are actually lots of xkcd what-ifs with dimensional analysis and Fermi Estimation
E=mc^2^ is Joules equals kilograms times speed of light in meters per second squared. If you put in daltons instead of kilograms you’d get (dalton × m^2^ /s^2^), not Joules. Knowing dimensional analysis you need kilograms/dalton to get the answer in joules. 1.66054 x 10^-27^ kg / dalton. Multiply your answer by that, and you have your answer in Joules because you canceled out dalton and left kilograms in its place! You could transform E=mc^2^ with a conversion constant to get it to pop out any units you want and use whatever units you want and it would still be correct. Yes you could have E be BTUs, m be pounds on earth, and c be in miles per hour. Our units are arbitrary their relationships are not.
Planck Units
We backed into calculable units such they were close to our historical units that we were used to. As in the numbers our instruments were already set up to kick out. What if one set up the equations and constants of nature such that the most fundamental equaled 1? Plank had this idea in 1899 and it actually simplifies things quite a bit. Speed of light is 1 plank length divided by 1 plank time for example. G is 1 rather than 6.67430×10^−11^ Nm^2^/kg^2^. Sabine Hossenfelder on this concept of no units It’s really a fantastic video and you should watch it.
Cursed Units
Sometimes bonkers things come out of units. Either by history, convention, or lazy labelling. There are 3 of these videos. They’re all pretty great.
Conclusion
Consider this the other way… all of these units & constants relate directly to the laws they are involved in. Things we can touch, measure, experience, design, use. They actually are fundamental to the Universe and what makes it up. Magic needs these constants to be different, or be variable - not constant. In doing so you alter the very physical laws that keep the Universe ticking. There are consequences to these constants being something different anywhere, ever. You couldn’t hide the evidence it was done, unless it in fact destroys the Universe itself in doing so such there are no witnesses. But then, you wouldn’t be here reading this… Proof it didn’t because it can’t.