I might just be stupid because math is not my strong suit, but it seems like the fact that metric units are able to convert between mass and energy so cleanly is astounding. Especially since the metric system was invented so long before relativity, meaning these units were obviously not designed with this in mind.
What’s am I missing here? Is it possible to write an equivalent equation for imperial units?
In: Mathematics
The concept of mass, energy and speed are not “metric”, though. That equation hold just as well in any unit, even if you use suns, kilocalories and length of bananas divided halflife of the radioactive potassium in a banana. You’ll just have to multiply by some scaling number like you do between kilometers and miles to get the same result.
What matters is that this is a definition that we formulated for those quantities.
And it didn’t even start with General Relativity. E = mv^(2)/2, the formula for kinetic energy, goes back to Leibniz and Bernoulli, contemporaries of Newton in the late 1600s / early 1700s, and so this arrangement of quantities, energy = mass times speed squared (or more specifically, mass times length squred over time squared), predates metric by about a century.
There’s a whole philosophical discussion about how “math describes the universe so well, is the universe made of math” (which I will not go into), but the simple question of units is NOT part of that problem. You can invent your own units whenever you want, and physics doesn’t change. Just remembered to apply that scaling factor when going between different units.
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