How would 10 top physicists—two Nobel Prize winners amongthem—describe Einstein's equation to curious non-physicists?

**Nima Arkani-HamedTheoretical PhysicistHarvard University**

When first encountering relativity, what really struck me about it more thananything else was actually how incredibly simple the underlying ideas were. Thebig point wasn't hidden in some minutiae of some deep mathematics, or thesestunning, very striking assumptions—that the speed of light is constantand that physics looks the same in all frames of reference—and from thesetwo seemingly innocuous assumptions come this incredibly different worldviewthan the standard Newtonian picture of the world.

But now that we understand it, the more profound lesson is that things thatseem incredibly different can really be manifestations of the same underlyingphenomena. Before Einstein, before *E = mc ^{2}*, there was no evenpossible thought that just a hunk of material, any old hunk of material, waspregnant with enormous quantities of energy that you could release if only youcould harness it. That was not something anyone even thought about, that justany piece of material has so much energy in it that if you could harness all ofit, it could power an entire city. And yet these amazing facts about the world canjust be sitting all around us waiting for the correct eye, for the correctangle to understand them properly. So that's the legacy that theoreticalphysicists are trying to carry on today.

**Janet ConradExperimental PhysicistColumbia University**

*E = mc ^{2}* is a very fundamental statement about the idea ofwhat mass is, and that mass can be equivalent to energy. And we can actuallyconvert mass into energy. But the thing that I wanted to say is that

*E =mc*is not the whole of the equation that Einstein wrote down.And it's worth talking about what the whole equation looks like, because it'svery related to what kind of research I actually do. The research that I do ison a particle called the neutrino. And for a long time we thought thatneutrinos were massless particles. And when I started, my sister said how is itpossible that a particle can be massless? Because when she thinks about aparticle she thinks about a little speck of dust or something like that.Whereas when I think about a particle I think about a little packet of energycoming out of this equation from Einstein,

^{2}*E = mc*. And, infact, the whole equation is

^{2}*E*is equal to

*mc*, theamount of energy the particle would have if it was sitting still, plus theextra energy that it would have if it has any motion. And if you think about itin that equation, if you now say

^{2}*E*is equal to

*mc*plus this energy of motion, you could set the mass equal to zero and you stillhave energy. And so as far as a particle physicist is concerned, there's stilla particle there. It's just a particle that can't ever stop. It always hasenergy of motion. It's always going the speed of light. So for me there's a lot more to the equation than

^{2}*E = mc*. It matters a lot to myfield.

^{2}**Sheldon GlashowTheoretical PhysicistBoston University**

This is the 100th anniversary of Einstein's development of the special theoryof relativity and so, of course, I went back and looked at his original papers,at least translated into English. And it really is amazing. The paper that hewrote in September of 1905 developed a basic idea of *E = mc ^{2}*,except it was more M=e/

*c*, same equation. But he argued inthis paper that when an object emits light, say a flashlight, it becomeslighter, that the decrease in mass would be equal to the amount of energyradiated, divided by the square of the speed of light. And that was kind of aseparate development in addition to the theory of relativity, and it iscentral, because what I'd like people to understand is that once upon a timethere was a law of conservation of mass. Lavoisier, in the 1700s, showed thatwhen you have chemical reactions, the mass of the reactants is the same as themass of the final products. That was a keystone to science, and a secondkeystone was the law of conservation of energy developed in the 19th century.

^{2}And what *E = mc ^{2}* does is tell us that both of those laws arewrong—mass changes. When I combine hydrogen and oxygen to make water, themass of the water is not equal to the mass of the hydrogen and oxygen. It's alittle bit less. And when you take water apart into hydrogen and oxygen, themass of the hydrogen and oxygen is a little tiny bit greater than the mass ofthe water, and that difference is the amount of energy that you supplied totake the water molecules apart. So this is a pretty trivial effect. Lavoisiercouldn't possibly know this, because it occurs in the 10th decimal place ordinarily. Ifyou burn a ton of fuel, maybe a few micrograms of matter disappear and areconverted into energy, so you don't notice it. You do notice it at nuclearreactors. There, a significant fraction of the mass is converted into energy.And you certainly notice it at particle accelerators, where we convert energyinto mass.

**Brian GreeneTheoretical PhysicistColumbia University**

*E = mc ^{2}* is certainly a simple equation to write down, butit's a very subtle equation in some ways. You really have to keep your head onstraight to recognize what the symbols mean in any given situation. Withpractice it's not hard to keep it straight, but it certainly is not an equationthat reveals all its subtlety in the few symbols that it takes to write itdown.

Einstein's main goal throughout much of his life was to unify concepts inphysics that at first sight seemed completely separate, but through his geniushe realized that they're actually different facets of the same thing. This iswhat he did in special relativity. He showed that space and time, two ideasthat we had since the days of Newton and have long thought to be completelyseparate ideas, he melded them together into something called space-time andshowed that they were actually two sides of the same coin.

After he united space and time together with special relativity, he realized acouple of months later that an outcome of that was to merge together two otherideas that had been around for a long time but had also been thought to bedifferent. He put together the concept of mass and the concept of energy andshowed that they are actually the same thing when you think about themcorrectly. So his equation, *E = mc ^{2}*, the

*E*is for energy and the

*m*is for mass, and he showed that given a certain amountof mass you could calculate the amount of energy it contains. Or,alternatively, given an amount of energy, you can determine how much mass youcan create from it. So mass and energy, he showed, are the ultimate convertiblecurrencies. They are different carriers of some fundamental stuff that you cancall energy, with mass simply being one manifestation of energy. But there areother manifestations: heat and light, radiation, and so forth. These are nowrecognized to all be different facets of one idea, one entity called energy.

**Alan Guth Theoretical PhysicistMIT**

It's very hard for me to remember when I first heard the equation *E =mc ^{2}*. I always have regarded it as something that, at least as aphrase, is familiar to just about everybody. Probably it's easiest toexplain by explaining how things looked from the point of view of Newton before we knew about

*E = mc*. In that context energy and mass weretwo completely different things. What Einstein showed is that the thing thatNewton called mass really was just a reflection of the total energy of theobject. The very existence of the object had a certain energy associated withit called the rest energy or rest mass. So instead of having energy and mass wenow only had one conserved quantity, which we usually call energy.

^{2}Of course, energy and mass themselves have nothing whatever to do with light,so it is a little peculiar to find *c*, the speed of light, sitting inthis all-important formula that relates energy to mass. What I guess is theeasiest way of describing the excuse for that is that *c* in specialrelativity is not just the speed of a certain object that's called light.*C* is the limiting velocity of any motion in special relativity. So it'svery fundamental to the very structure of motion itself. According to specialrelativity, if you try to accelerate an object that was initially at rest itwould start to go faster and faster and as it went faster it's effective masswould also increase. And what you'd find is that no matter how hard you pushedon it and no matter how long you pushed, it would keep going faster and faster,but only approaching this limiting velocity of the speed of light. And it wouldnever, ever reach the speed of light or go beyond it.

**Tim Halpin-HealyTheoretical PhysicistBarnard College, Columbia University**

As physicists, you get hit up in a bar. Somebody wants to know, if they're notasking you or reminding you about that terrible course in physics that theytook way back when, they often want to know about special relativity andEinstein and things like that, which is really great. When I try and explain*E = mc ^{2}* I have to step back and try to explain the fact that movingclocks run slow, moving meter sticks are shortened—how does that happen?And that ties in and is a consequence of the constancy of the speed of light.

The speed of light is independent of your frame of reference. So if I'm movingon a train, the train is moving at 100 miles an hour, and I throw a baseball ashard as I can at 80 miles an hour in the direction the train is moving, thenwith respect to the people on the ground, who are wondering what I'm doing onthe train, the ball seems to be moving at 100 plus 80—simple velocityaddition—180 miles per hour with respect to the ground. That simplevelocity addition formula just doesn't work at all when it comes to light. If Ishoot a light beam off a moving train, then the speed of light is the same inboth frames of reference.

Now, a speed is a distance over a time. Because if I'm going 60 miles per hour,what that means is that if I travel 300 miles, that's a distance, in fivehours, it works out: 300 miles divided by the five hours, gives me the 60 milesper hour. Speed is always a distance over a time. So if I'm in a situationwhere I have two frames of reference, one moving with respect to the other, andsomehow the speed works out to be the same in both frames of reference, theonly way it can happen is, well, if the distance is altered and the time isaltered.

So the constancy of the speed of light basically means that in different framesof reference the notions of time intervals and distance measurements arefundamentally altered. Moving clocks basically will run more slowly in theirown frame of reference, and lengths are shortened. Meter sticks are shortened.So that's the only way that it can basically shake out. The denominator and thenumerator have to change in a way that conspires in some cosmic fashion to givea ratio—velocity, the speed of light, which remains constant.

**Lene HauExperimental PhysicistHarvard University**

To some extent there's a lot of myth around the equation, you know, thisequivalence of mass and energy, and you can turn one into the other. I mean,the real fascinating thing is that before that you had really thought ofmasses, particles with mass, being one entity, and energy, like heat, being acompletely different entity. But now you really had to start to think of thetwo as being equivalent. And you can transfer one to the other. That means, forexample, that you can annihilate one particle with its anti-particle, and poof,a lot of energy comes off. All the mass of those two particle/anti-particlepairs will come off as energy. You have this idea you are really moving into acompletely new regime of nature where you can do things, get access to parts ofnature, you had never been able to get access to before. And you can startsaying, well, gee, that can be used for different purposes if you want to thinkof applications peacefully and not so peacefully, because there's an enormousamount of energy stored in the masses of the universe.

**Michio KakuTheoretical PhysicistCity University of New York**

*E = mc ^{2}* is the secret of the stars. It is the cosmic enginethat drives the entire universe. It means that even a few tablespoons ofmatter, if fully burned, can release the energy of an atomic bomb. It's thereason why the stars shine, and why the sun lights up the Earth. Matter andenergy are, in some sense, the same thing, and can turn into each other. Even arock can turn into a light ray if the rock happens to be uranium and the lightray is a burst of atomic radiation.

I first became conscious of *E = mc ^{2}* when I was in sixthgrade. That's when Walt Disney came out with the movie

*Our Friend theAtom*. I got the book. I read every single page, every single line of thebook, had the book practically memorized. So to me it was no mystery thatmatter and energy really are the same thing, because even before then I haddecided that I wanted to become a theoretical physicist. That was my goal inlife when I was about 10 years of age.

**Neil deGrasse TysonAstrophysicistAmerican Museum of Natural History**

What I like about *E = mc ^{2}* is not only its simplicity but [in]how many different environments in the universe the equation applies. Itapplies to what's going on inside of stars, inside of our own sun. It appliesto what's going on in the center of the galaxy. It applies to what's going onin the vicinity of black holes. It applies to all the events that took place atthe big bang. Our fundamental knowledge of the formation and evolution of theuniverse would be practically zero were it not for the existence andunderstanding of that equation. And, as a recipe for converting matter intoenergy and back into matter, it's something that doesn't happen in your kitchenor in everyday life, because the energies required to make that happen fall faroutside of anything that goes on in everyday life.

Because, for example, visible light that you use to illuminate the page youread, you can calculate how much energy that light has. It's not enough to makeany particles with. You need more energetic light than visible light, thanultraviolet. You gotta get into X-rays. If you get high enough energy X-rayspassing by your room, spontaneously, unannounced, unprompted, unscripted, theywill make electrons. The whole suite of particles you learn about, all of those can be manufactured simply by entering a pool of energy where thatenergy is above the mass threshold for that particle.

We are fortunately not bathed in that level of energy, because we would firstget sterilized, then it would mess with our DNA, and then we would die. So weshould be glad we don't see *E = mc ^{2}* happening in front of us.It would be a dangerous environment indeed. There are places in the universewhere this equation is unfolding moment by moment. How else do you think theuniverse can be as big as it is now but start out with something smaller than amarble?

*E = mc*is cranking, converting matter into energyand back again. When you're energy you don't have to take up much space. Youcan get very small when you're a pocket of energy. So I was once asked what doI think is the greatest equation ever. There are a lot in the running but Iwould have to put

^{2}*E = mc*at the top. If you sit back, lookat the universe and say, what equation holds all the cards, that would be

^{2}*E= mc*. That's all I gotta say.

^{2}**Frank WilczekTheoretical PhysicistMIT**

*E = mc ^{2 }*famously suggests the idea that you can get a lot ofenergy out of a small amount of mass. But that's not what Einstein had in mind,really, and you won't find that equation in the original paper. The way hewrote it was

*M = e/c*

^{2}^{ }and the original paper had atitle that was a question, which was, "Does the inertia of a body depend on itsenergy content?" So right from the beginning Einstein was thinking about thequestion of could you explain mass in terms of energy. It turned out that therealization of that vision, the understanding of how not only a little bit ofmass but most of the mass, 90 percent or 95 percent of the mass of matter as weknow it, comes from energy. We build it up out of massless gluons and almostmassless quarks, producing mass from pure energy. That's the deeper vision.