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
That formula (and all formulas) still works regardless of the units.
e is typically measured in joules. But an equivalent unit to a joule is a kg*m^2 /s^2.
If you measure mass in kg and c in m/s then you can see how the units of the formula make sense.
Say you instead wanted to measure c in feet per second. Now the output of the formula will be in kg*ft^2/ s^2. It’s a unit that nobody uses but it’s still valid. The results when you actually plug in numbers to the formula will still be correct. Just in a different unit.
You can invent a totally new unit of mass. Call it z. If you use it in the formula you’ll get a correct answer in units of z*m^2 /s^2.
Basically all formulas like these are fundamentally true. We define the units in ways that are most convenient to us.
Latest Answers