## Monday, September 27, 2010

### According to Einstein's famous equation, how many food calories are there in a single gram of mass?

Exactly 105 years ago today -- Sept. 27, 1905 -- Albert Einstein published his paper "Does the Inertia of a Body Depend Upon Its Energy Content?" in Annalen der Physik, introducing the world to his famous equation, E = mc2. Except E = mc2 didn't actually appear in Einstein's original paper; Uncle Albert described his formula in prose, using different variables to express both energy and the speed of light. Translating from the original German, Einstein wrote:
If a body gives off the energy L in the form of radiation, its mass diminishes by L/V2.
The V in this case is the 1920s-era standard variable for the speed of light (which Einstein argued was constant). Thus, if you wrote out the mass-energy equivalence equation as Einstein originally described it, you'd get m = L/V2.

The upshot of Einstein's mass-energy equivalence and the relativity it helps describe is that all matter can be converted into a predictable amount of energy -- a large predictable amount of energy. Fortunately, only in very rare circumstances can matter be efficiently and explicitly converted entirely into its equivalent energy. We don't unleash all of our food energy when we digest it, for example, because we're unlocking its chemical energy, not its nuclear energy. That's a very good thing, as E = mc2 would make your average slice of cheesecake exponentially more fattening (and destructive).

According to Einstein's famous equation, how many food calories are there in a single gram of mass?

Carrying out the unit conversions for E = mc2, a single gram of matter is worth roughly 21.5 billion food calories (which scientists refer to as kilocalories; actual chemical calories are much more minute than the values appearing on nutritional labels).

Thus, that aforementioned eight-ounce slice of cheesecake would contain roughly 4.9 trillion food calories of mass-equivalent energy. More, if you add the raspberry drizzle and chocolate ganache.

Back to the energy value of a mere gram of mass, the nuclear weapon dropped over Nagasaki in 1945 converted almost precisely one gram of plutonium into energy -- it fissioned the plutonium core into lighter elements that in total weighed roughly 1 gram less than the original core --  releasing an explosion equal to 21,000 tons of dynamite. Thus, that plain eight-ounce slice of cheesecake is worth 4.8 million tons of TNT, provided you could find a way to annihilate it completely (that's annihilate in the physics context, not annihilate in the "I've got the munchies" context).

And you thought its Weight Watchers points value was scary. That's not just gnarly nutritional nightmare, it's a thermonuclearly thought-provoking slice of the Truly Trivial.