Why this equation?
March 30, 2011 4:33 PM   Subscribe

Why is the equation E=mc2 arguably the most famous equation in physics?

In fact, it's often the only equation that I'll see or hear when random sciency stuff is being said. I'll hear Newton's first and third laws (although never the second, which is most easily stated as an equation), and maybe something nonsensical about quantum mechanics, but no equations.

I understand, that as an equation it's short, has an exponent and looks spiffy, but how did it rise to prominence. The physicists I know all go to E2=m2c4+p2c2, (well, except when talking about the mass of particles in terms of energy) which is a lot more awkward, at least visually. So how did that equation, out of all of them, come out of the relativity manuscript and end up in popular consciousness? (If you look at the wikipedia article, they have it displayed on an office building and an aircraft carrier, not places you normally look for equations writ large on.)
posted by Hactar to Science & Nature (17 answers total) 3 users marked this as a favorite
Because it's distinctive, and easy to remember.
posted by Chocolate Pickle at 4:36 PM on March 30, 2011 [2 favorites]

I would suggest a combination of a few factors led to the equation becoming so (in)famous:
  1. The rise of scientist-as-celebrity
  2. The dawn of the nuclear age; the equation is basically an explanation of the direct relationship between matter and energy
  3. It's a short equation, thus very easy to memorize, and additionally has a built-in rhyme

posted by Civil_Disobedient at 4:38 PM on March 30, 2011 [3 favorites]

It's like the surprising reveal at the end of a centuries long detective story. "In the end, it turned out Energy and Matter were one and the same." The equation is the world's shortest story, Hemingway notwithstanding.
posted by mariokrat at 4:43 PM on March 30, 2011 [20 favorites]

Wasn't it also on a chalkboard behind Albert in a photo of the times?
posted by Freedomboy at 4:44 PM on March 30, 2011 [1 favorite]

People associate it with a "genius" (Einstein, whose name is literally synonymous with genius) making a "discovery." That's what laypeople remember. No matter how right you are about how most scientists these days use a more refined equation, the general public doesn't keep up with the current scientific standards. By definition, laypersons don't know much about the technicalities of scientific disciplines. We remember a few basic concepts, especially ones we can link to the ideas of "genius" and "discovery."
posted by John Cohen at 4:45 PM on March 30, 2011 [2 favorites]

Best answer: I'm 90% sure that it's because every single article about atomic bombs in the 40s, which a lot of people read, used that equation to explain how they worked.

I'm not sure how to look it up, though.
posted by empath at 4:47 PM on March 30, 2011 [5 favorites]

How to look up "e=mc^2", i meant, to see when the usage started picking up.
posted by empath at 4:47 PM on March 30, 2011

Best answer: Because it's the theoretical basis for the bombs that destroyed up two cities, ended a world war, and began the American Century.
posted by orthogonality at 4:51 PM on March 30, 2011 [2 favorites]

Best answer: It's not only distinctive in its simplicity, it was a rather shocking result that exemplified a scientific revolution. The mass-energy equivalence is not exactly an intuitive result, but it defines the nature of stuff itself. Everyone knows what energy and matter are, but they seem like distinct concepts; my desk doesn't naturally belong in the same category as a bunch of electricity. E=mc2 firmly insists that to the universe, they are convertible. And what's the speed of light got to do with anything? The amount of energy contained in my stapler is its mass times the speed of light squared? And why doesn't the material matter? Shouldn't a pound of water contain less energy than a pound of TNT? It's completely insane, and yet, it's a fundamental law of the universe.

E=mc2 sums up a modern revolutionary discovery of science in two variables and a constant. We haven't had a scientific revolution that pithy since "Eppur si muove" (which Galileo probably didn't actually say, but the point stands).

Besides, this Time Magazine cover didn't hurt either when it comes to getting eyeballs on things.
posted by zachlipton at 4:58 PM on March 30, 2011 [9 favorites]

Einstein is a celebrity. Sure, people have heard of Newton and people can cite his first law (often paraphrased as an object at rest stays at rest unless acted by another force) and many his third (to every action there's an opposite and equal reaction). How many know his law of universal gravitation? Gravity is a simple thing and the formula is simple algebra. But no one knows it. How many people know of Maxwell's equations? So everyone knows the famous guy's equation because it's synonymous with genius.

It's recent. Yes, I know Einstein's not the first to go over the idea and yes I know there have been really neat break throughs since, but up until recently, people lived through it and it's just been keeping on. Gravity is old news.

I'm willing to bet the vast majority of people who know it don't know what it means. But it's OK, they excuse themselves because it's physics and physics is hard. People not knowing how to deal with simple things like interest (and subsequently how much their car loan or mortgage is actually going to cost them) is not something people would be OK with saying "oh, yeah, I don't know that". So E=mc^2 is a nice sound-bite that the masses can trumpet whenever they need something that means "smart".
posted by Brian Puccio at 4:59 PM on March 30, 2011 [2 favorites]

Response by poster: I never considered the atomic bomb angle on this. And I never saw that time magazine cover. This makes a lot more sense now.

Thanks everyone!
posted by Hactar at 5:13 PM on March 30, 2011

Probably because it's one of the only equations that someone with high school algebra can get. Not the physics implications, but just what the hell is going on with the math. Three "variables" and an exponent. There are plenty of kids in 7th grade who basically know how to deal with those things. It's a startling simple equation containing a hugely significant proposition, the basics of which can be understood by laymen.

Doesn't hurt that it was one of the most revolutionary insights in physics, which is hands down the discipline which has been the most successful at describing and predicting the natural world. Just about every discipline, scientific or not, has had a phase where it's tried to emulate the success of physics. Indeed, the success of physics is significantly why SCIENCE! is viewed with almost religious awe in modern culture. despite the fact that nothing else has been able to duplicate that kind of certainty.
posted by valkyryn at 5:14 PM on March 30, 2011 [2 favorites]

I am working my way through Why Does E=mc2 (sorry, don't know the code to make the 2 a superscript) by Professor Brian Cox and Jeff Forshaw. It's definitely "rocks for jocks," i.e., science for the nonscientist, but does a great job of explaining the significance of the equation and what it actually means. If you want to do some reading about the phenomenon, I think this is a great place to start.
posted by That's Numberwang! at 7:21 PM on March 30, 2011

Personally, I've always found the uncertainty principle and Dirac Equation to be the coolest two equations in Physics.

Also, <sup>2</sup> makes 2

posted by schmod at 7:38 PM on March 30, 2011

NOVA did a special two-hour episode, "Einstein's Big Idea," on this a few years ago. Here's the associated website, which has a lot of good material on it. The full episode isn't there, but it is well worth watching if you can get your hands on it.
posted by DevilsAdvocate at 8:12 PM on March 30, 2011

Another point that I think is worth making is that it's hard to wrap your head around how revolutionary Einsteinian Physics really was. E=mc2 is a convenient shorthand symbol for that entire sequence of discoveries, including special and general relativity. These discoveries were so striking because they, for the first time in hundreds of years, turned Newtonian Physics on its head. In a very short period of time, science (not just Einstein certainly) concluded that there's no such thing as aether, time isn't constant, space isn't constant, mass isn't constant, energy and mass are directly related (see E=mc2), and a bit later, the idea of general relativity, which basically says that gravity is really just curved space and time. That's like waking up one day and realizing that your whole life is really the Truman Show. Or, to put it in the context of earlier scientific progress, Copernicus started a scientific revolution because he said the Earth orbits the Sun. Einstein (and others!) started a scientific revolution because he said the entire Universe doesn't even obey the laws of time and space and motion we've been so accustomed to.

And, it's not like this was just all about science either. Just as the world changed and religions were threatened by heliocentrism, the Einsteinian revolution brought with it a great cultural movement of its own. Dali claims that The Persistence of Memory wasn't inspired by relativity, but it there really a better symbol of just how revolutionary this all was than the fact that one of the period's most famous works of art consists of melting clocks? Personally, I don't think it's an accident that we got the emergence of Cubism, Expressionism, M. C. Escher (heck, one of his most famous works is Relativity), Willard Quine, Merce Cunningham, John Cage, the Jazz Age, Gertrude Stein, and Kurt Gödel (this line of reasoning should not be foreign to the GEB fans in the audience) around the same time as Einsteinian physics emerged. These are all artistic movements, artists, and theorists that brought the notions of deconstruction, paradoxical relationships, uncertainty, and relativism to the forefront of their fields. That's a huge artistic movement, and thanks to newly available mass communication technologies, it could spread as a far wider and far faster than anything like it had ever spread before, bringing a great cultural movement too. The symbol for all this change? E=mc2 sums it all up in a nutshell.
posted by zachlipton at 9:33 PM on March 30, 2011 [2 favorites]

Best answer: I'm not sure how to look it up, though [...] "e=mc^2", i meant, to see when the usage started picking up.

Google Ngrams doesn't seem to care for punctuation—and I am not particularly adept with Google Ngrams— but this graph of the occurrence of "MC2" over time is probably telling.
posted by mumkin at 11:43 PM on March 30, 2011 [2 favorites]

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