Why do the units in e=mc^2 all work out for such a clean equation?

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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

27 Answers

Anonymous 0 Comments

Units in the metric system are based on a handful of fundamental properties: time (second), mass (kilogram), distance (metre), temperature (°C or K, they change at the same rate so if it’s temperature difference then it doesn’t matter which; absolute temperature, kelvin, needs to be used in an energy calculation though), amounts of stuff (moles) and a couple of others.

Other properties have units that are derived from these, for example Force = mass x acceleration so 1 newton = 1 kgms^-2. Energy = force x distance so 1 joule = 1 kgm^2s^-2. Pressure = force / area so 1 pascal = 1 kgm^-1s^-2 and so on.

E = mc^2 is a fundamental property of the universe, determining how much energy we can release from matter (or how much energy we need to put in to create matter). We do this all the time in chemical reactions, though the amounts involved are so miniscule that we approximate to the law of conservation of mass (e.g. burning 1 mole, 16g, of methane in 64g oxygen releases about 890kJ of energy, at the cost of less than 10ng of mass: a rounding error in a total system mass of 80g).

Using different units wouldn’t change the fact that E = mc^2, merely the numbers involved due to conversion factors.

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