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

The metric units, any unit, is just a word we use for a phenomenon on nature.
Einstein’s formula says that energy equals the mass of an object times the seepd of light, times the speed of light. It does not even have anything to do with math if you look at it this way.

Aliens who do not have any of our systems will observe the same thing and will agree with Einstein.

Scientists use a system called SI-Units. You know this as the metric system but technically the terms are not the same.

The unit for Energy is called Joule (J).
But you can also tell by the formula that Joule so not really it’s own thing.
If einsteisn formula is true and we use SI units, then we can translate it to 1J = 1kg * (m²/s²)
The reason for this is that kg is the SI unit for mass, while meter per second is the SI unit for velocity.
The SI units are designed in a way that this is easy and intuitive. But you could easily replace kg with g, but then you would have to add 1000 to the equation unless you want to change the definition of how much energy 1 Joule is supposed to represent.
I don’t know how to convert the SI units to imperial system but you can easily do it.

It would translate to

1 Joule = 2lbs (assuming 2 lb = 1kg) * (1550*inches²/s²)

1m² = 1550 square inches is what I got from Google.

Energy can also be described as N*m (newton times meter) or W*s (Watts times second). This makes sense since there are many ways to convert and describe energy.

How can Einstein’s formula be tested? For example by measuring a radioactive particle and measuring it again after it split up and measuring the particles it splits into. If you add all those up there is still some mass missing. The missing mass is the energy that got emitted. Same happens with chemical reactions. The mass will not be the same as the mass of each atom that got combined, it can be slightly heavier if there is some binding energy.

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