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

You are just a little confused about the difference between units and physical quantities.

I think it will be easier to understand if we think about a simpler formula, like the one for speed (velocity) for example.

Speed equals distance traveled over time:

v=d/t

That is the general formula using physical quantities. No units are assigned to either the velocity, distance or time.

When applied to something in reality each of these physical quantities will have a specific value.

Lets say you like to listen to “Cotton Eyed Joe” over and over and while walking home from school you notice that you pass exactly 10 street lights in the same time it takes to listen to the song one time.

That means that you are walking with a velocity of 10 sl/ceJ (10 street lights per cotton eyed Joe). So 10 street lights are the distance (d) and cotton eyed Joe is the time (t) in our first formula

But that same velocity is also 3.24 knots which is 3.24 nautical miles per hour. Where nautical miles is d and hour is the t in our first formula.

Or 0.1 km/min where every minute you travel 100 meters.

Or 37.3 mph where every hour you travel 37.3 miles.

The units can be what ever you like, what matters is their real life quantity.

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