E = MC^2

A friend’s question spawned the following post:

To understand Einstein’s energy-mass equivalence, It is helpful to check the balance of the units on either side of any equation:

So …  E = M x C^2

A joule is a measure of energy which is defined as a (kilogram x meter^2) / second^2

Now let’s look at the units: 

Energy’s  units: (mass x distance^2) / time^2

And on the other side:

M x C^2 units: mass x (distance/time)^2

Which equates to (mass x distance^2) / time^2

So Einstein’s equation balances insofar as the units are concerned. … a necessary condition. But is it sufficient?

All we know is that the “distance” measure must be  really big because a very little mass translates into a huge amount of energy. (The sun has been doing this for billions of years and has billions to go … loosing just a relatively small amount of mass.)  Why is this distance how far light travels in a second … 186,000 miles … seems to have been determined heuristically … but I’m not sure?

But it does make for a bit of physics black magic if not the precise  number.

STAND UP FOR EINSTEIN!