One Hundred Years of E=MC2

Eric Ward writes "To mark the one hundredth anniversary of Einstein's famous equation, E=mc2, NOVA has gone live this month with a Web site that features exclusive content and podcasts from ten of the worlds top physicists. This once-in-a-lifetime gathering of top scientists such as S. James Gates, Jr., Brian Greene, Neil deGrasse Tyson and Nobel Laureate Sheldon Glashow simplify what the equation means to our world today and the effect it has had on their careers. NOVA online also details how Einstein grappled with the implications of his revolutionary theory of relativity and came to a startling conclusion: that mass and energy are one, related by the formula E=mc2. Viewers will also find lesson plans through the award-winning NOVA Teacher's Guide and a special library resource kit."

Comments

Re:serious question

[RealityProphet]

But it's all about the units. If c is expressed in light-seconds/second rather than meters per second, or worse yet light-years/second then the "logic" of that argument is exposed as just hype. So the real issue comes down not to the equation e=mc^2 itself, but the selection of the units that e, m and c are expressed in. Use a different unit and, as I try to show above, the whole thing breaks down.

I think you are making the mistake that, for example, a 4-slice pizza is smaller than an 8-slice pizza, because, as everyone knows, 4 is less than 8. However, the pizzas are exactly the same size, it is just that the slices are larger in a 4-slice pizza.

Is there some science behind the selection of the units involved that allows this equation to be so simple, or are we to believe that some serendipitous magic just allows this to be an exact equation and the units somehow just happen to match up?

Yes, there is a very challenging derivation of this simple relationship. It is just math, and it is not magic. I won't do the derivation, but I will show that the units do, indeed, make sense:

Energy is a force acting through a distance: F x d
Force is a mass undergoing an acceleration: F = m x a
Acceleration is a change in velocity over a change in time: A = deltaV/deltaT, whose units are length/time x 1/time. Let's use metric. That would be m/s x 1/s.
Substituting the units back into the general energy equation, we get:
E = F x d = m x A x d = kg x (m/s x 1/s) x m. If we pair the 1/s with the meter from "Force acting over a distance" The units are:
E = kg x (m/s) x (m/s), which are the same units as Einstein's famous relation. So, yes, the units do make sense, it is not serendipitous that this works out, and the reason it is so famous is because it is so simple.