Can the smart people of SW explain to me "e = mc squared"? Specifically,

I know that it is Einstein's famous formula and means "energy equals mass times the square of the speed of light". What I don't get is how the measurement works. Mass is measured in units of weight, right? Speed, in units of time and distance. How is energy measured by this method? Like, if we're doing metric, let's say you have a mass of one kilogram, and the speed of light is 299,792,458 metres per second. Square that and you get 89,875,517, 873,681,764 kilometres per second... or is it square kilometres per square second?? And then your energy outcome is 89,875,517, 873,681,764 kilograms-kilometres-seconds?? What does that even mean, other than "really really big"? I am sure there are many SWeeps here in the sciences who actually understand it so please explain it to me and the rest of us who dropped math and science after high school. Thank you!

ElwoodBlues · M

First, what is energy? It's a specific quantity that comes in many forms. If you compress a coil spring, you're putting energy in it. If you accelerate a mass, you're giving it kinetic energy. Raise a weight against gravity, you're storing gravitational potential energy. Then there's electrical energy (watts*time) chemical energy thermal energy, etc.

Let's zero in on the mechanical energy: springs, kinetic, gravity. They are all tied together by applying a force thru a distance (the force & distance are in the same direction here; parallel vectors if you like).

So energy is force*distance. What is force? Newton says F=ma, mass*acceleration. What is acceleration? It's change in velocity per unit time. What is velocity? It's change in distance per unit time. SO. putting it all together:
velocity=dist/time,
acceleration=dist/(time²)
force=mass*dist/(time²)
energy=mass*(dist²)/(time²)
Can rewrite it as energy=mass*(velocity²) if we like.

What is a joule? 1 J = 1 kg m²/s²
Those units are kilograms, meters, and seconds, the MKS system.

Finally getting to Einstein, E=mC², the units are right because it's mass times velocity squared. The magnitude is AMAZING because C² is such a huge number. In MKS units, C=300,000,000 m/s ! Call it 0.3 of a billion! Square that and your numbers are astronomical!!

sarabee1995 · 26-30, F

@SW-User It's not a matter of using imperial on earth and metric on the moon. Rather, it's an understanding that pounds measure force ("weight") and grams measure mass.

An object's mass (barring any nuclear fission or fusion or any relativistic speeds) is a constant. It's weight depends on it's acceleration and is most definitely not a constant. You weigh less on top of Mount Everest than you do at sea level because acceleration due to gravity is less. 😁

Harmonium1923 · 51-55, M

I had to go look this up. Energy is measured in joules, which is a measurement equivalent to kg * (meters squared / seconds squared). So mass is measured in KG and the speed of light in m/s.

You’re right about the magnitude. There is an extraordinary amount of energy stored in the atoms that make up an objects mass.