This version of Einsteins equation is often used directly to find what value?

How would ten tiptop physicists—two Nobel Prize winners among them—describe Einstein's equation to curious non-physicists?

Nima Arkani-Hamed
Theoretical Physicist
Harvard Academy

When showtime encountering relativity, what actually struck me about it more than annihilation else was actually how incredibly simple the underlying ideas were. The big betoken wasn't hidden in some minutiae of some deep mathematics, or these stunning, very striking assumptions—that the speed of low-cal is constant and that physics looks the same in all frames of reference—and from these two seemingly innocuous assumptions come this incredibly different worldview than the standard Newtonian picture of the world.

But now that we understand information technology, the more profound lesson is that things that seem incredibly different tin really be manifestations of the same underlying phenomena. Earlier Einstein, before Eastward = mc² , there was no even possible thought that just a hunk of material, whatsoever old hunk of fabric, was pregnant with enormous quantities of energy that yous could release if only you could harness it. That was not something anyone even thought nigh, that only whatsoever piece of textile has so much energy in information technology that if y'all could harness all of it, it could power an entire city. And all the same these amazing facts almost the world can just be sitting all around the states waiting for the correct eye, for the right angle to empathize them properly. Then that's the legacy that theoretical physicists are trying to conduct on today.

Janet Conrad
Experimental Physicist
Columbia Academy

Eastward = mc² is a very central statement about the idea of what mass is, and that mass can be equivalent to energy. And nosotros tin actually convert mass into energy. But the thing that I wanted to say is that Eastward = mc² is not the whole of the equation that Einstein wrote downwards. And it'due south worth talking about what the whole equation looks like, considering it's very related to what kind of research I really practice. The research that I do is on a particle called the neutrino. And for a long time nosotros thought that neutrinos were massless particles. And when I started, my sis said how is it possible that a particle can exist massless? Because when she thinks about a particle she thinks nearly a little speck of grit or something similar that. Whereas when I think about a particle I think nigh a little packet of free energy coming out of this equation from Einstein, E = mc^two . And, in fact, the whole equation is E is equal to mc² , the amount of energy the particle would take if it was sitting still, plus the extra energy that it would have if information technology has whatever motion. And if you think about it in that equation, if you at present say E is equal to mcⁱⁱ plus this energy of motion, you could set the mass equal to zero and yous still have free energy. And so every bit far every bit a particle physicist is concerned, at that place's all the same a particle at that place. It's just a particle that can't ever stop. It always has energy of motion. It'southward always going the speed of light. So for me there's a lot more to the equation than Eastward = mcⁱⁱ . It matters a lot to my field.

Sheldon Glashow
Theoretical Physicist
Boston University

This is the 100th anniversary of Einstein's development of the special theory of relativity and and then, of course, I went dorsum and looked at his original papers, at to the lowest degree translated into English language. And information technology actually is astonishing. The paper that he wrote in September of 1905 developed a bones idea of E = mc² , except it was more M=e/c² , same equation. But he argued in this paper that when an object emits low-cal, say a flashlight, information technology becomes lighter, that the decrease in mass would exist equal to the amount of energy radiated, divided by the square of the speed of light. And that was kind of a separate development in add-on to the theory of relativity, and it is central, considering what I'd similar people to understand is that once upon a time in that location was a law of conservation of mass. Lavoisier, in the 1700s, showed that when you have chemical reactions, the mass of the reactants is the aforementioned as the mass of the final products. That was a keystone to science, and a 2nd keystone was the police force of conservation of energy developed in the 19th century.

And what E = mc² does is tell us that both of those laws are incorrect—mass changes. When I combine hydrogen and oxygen to brand water, the mass of the water is not equal to the mass of the hydrogen and oxygen. It's a little fleck less. And when you take water apart into hydrogen and oxygen, the mass of the hydrogen and oxygen is a little tiny flake greater than the mass of the h2o, and that difference is the amount of free energy that you supplied to accept the water molecules apart. So this is a pretty trivial event. Lavoisier couldn't mayhap know this, because it occurs in the 10th decimal place commonly. If you burn a ton of fuel, peradventure a few micrograms of matter disappear and are converted into energy, so y'all don't notice information technology. You do notice information technology at nuclear reactors. There, a meaning fraction of the mass is converted into energy. And you certainly notice it at particle accelerators, where we convert energy into mass.

Brian Greene
Theoretical Physicist
Columbia University

Eastward = mc² is certainly a simple equation to write down, just it's a very subtle equation in some ways. You actually take to continue your head on straight to recognize what the symbols mean in whatever given situation. With exercise information technology's not difficult to keep it straight, but it certainly is not an equation that reveals all its subtlety in the few symbols that information technology takes to write it down.

Einstein'southward primary goal throughout much of his life was to unify concepts in physics that at first sight seemed completely separate, merely through his genius he realized that they're actually unlike facets of the aforementioned thing. This is what he did in special relativity. He showed that space and fourth dimension, 2 ideas that we had since the days of Newton and have long thought to exist completely separate ideas, he melded them together into something called space-time and showed that they were actually ii sides of the same coin.

After he united space and time together with special relativity, he realized a couple of months after that an result of that was to merge together two other ideas that had been around for a long fourth dimension but had also been thought to be different. He put together the concept of mass and the concept of energy and showed that they are actually the same thing when you retrieve almost them correctly. So his equation, East = mc² , the E is for energy and the m is for mass, and he showed that given a certain amount of mass yous could calculate the amount of energy information technology contains. Or, alternatively, given an amount of energy, yous can make up one's mind how much mass you lot can create from it. So mass and energy, he showed, are the ultimate convertible currencies. They are different carriers of some fundamental stuff that you tin call free energy, with mass simply being one manifestation of energy. But in that location are other manifestations: oestrus and light, radiation, and so forth. These are now recognized to all be different facets of one idea, one entity called energy.

Alan Guth
Theoretical Physicist
MIT

It's very difficult for me to recall when I beginning heard the equation E = mc² . I e'er have regarded it as something that, at to the lowest degree equally a phrase, is familiar to simply virtually everybody. Probably it's easiest to explicate past explaining how things looked from the point of view of Newton before we knew about E = mcⁱⁱ . In that context energy and mass were two completely dissimilar things. What Einstein showed is that the thing that Newton called mass really was just a reflection of the total energy of the object. The very existence of the object had a certain energy associated with it called the rest energy or rest mass. So instead of having energy and mass we at present simply had one conserved quantity, which we usually telephone call energy.

Of course, energy and mass themselves have nothing whatever to do with light, so information technology is a picayune peculiar to notice c, the speed of lite, sitting in this earth-shaking formula that relates energy to mass. What I judge is the easiest way of describing the alibi for that is that c in special relativity is non only the speed of a certain object that's chosen light. C is the limiting velocity of any motion in special relativity. And then information technology's very fundamental to the very structure of motion itself. Co-ordinate to special relativity, if y'all try to advance an object that was initially at rest it would commencement to go faster and faster and as it went faster it'due south effective mass would also increment. And what you'd discover is that no matter how difficult you pushed on information technology and no matter how long y'all pushed, it would keep going faster and faster, just only approaching this limiting velocity of the speed of light. And information technology would never, ever reach the speed of light or go beyond it.

Tim Halpin-Healy
Theoretical Physicist
Barnard Higher, Columbia University

As physicists, you go hitting upwards in a bar. Somebody wants to know, if they're not request y'all or reminding you virtually that terrible course in physics that they took manner back when, they often want to know about special relativity and Einstein and things like that, which is really great. When I try and explain Eastward = mc² I accept to footstep back and effort to explain the fact that moving clocks run deadening, moving meter sticks are shortened—how does that happen? And that ties in and is a result of the continuance of the speed of calorie-free.

The speed of lite is contained of your frame of reference. So if I'm moving on a train, the train is moving at 100 miles an 60 minutes, and I throw a baseball as difficult as I tin can at 80 miles an hour in the direction the train is moving, then with respect to the people on the basis, who are wondering what I'thousand doing on the train, the ball seems to be moving at 100 plus 80—simple velocity addition—180 miles per hour with respect to the ground. That simple velocity addition formula just doesn't work at all when information technology comes to light. If I shoot a light beam off a moving train, and so the speed of light is the same in both frames of reference.

At present, a speed is a distance over a fourth dimension. Because if I'm going 60 miles per hour, what that means is that if I travel 300 miles, that's a distance, in five hours, it works out: 300 miles divided by the five hours, gives me the 60 miles per hr. Speed is always a altitude over a time. So if I'm in a state of affairs where I accept two frames of reference, ane moving with respect to the other, and somehow the speed works out to be the same in both frames of reference, the only mode it can happen is, well, if the distance is altered and the time is contradistinct.

And so the constancy of the speed of light basically means that in different frames of reference the notions of time intervals and distance measurements are fundamentally altered. Moving clocks basically will run more slowly in their own frame of reference, and lengths are shortened. Meter sticks are shortened. So that'south the merely way that it can basically milkshake out. The denominator and the numerator take to modify in a way that conspires in some cosmic fashion to give a ratio—velocity, the speed of light, which remains constant.

Lene Hau
Experimental Physicist
Harvard University

To some extent in that location's a lot of myth around the equation, yous know, this equivalence of mass and energy, and y'all tin can turn ane into the other. I mean, the existent fascinating matter is that before that y'all had actually idea of masses, particles with mass, being one entity, and free energy, like heat, existence a completely different entity. Only now you really had to first to recollect of the two as being equivalent. And you can transfer one to the other. That means, for example, that yous tin annihilate one particle with its anti-particle, and poof, a lot of energy comes off. All the mass of those two particle/anti-particle pairs will come off as energy. Yous have this idea you are really moving into a completely new government of nature where you tin do things, get access to parts of nature, yous had never been able to get access to before. And yous tin start saying, well, gee, that tin can be used for different purposes if you want to think of applications peacefully and non then peacefully, considering in that location'southward an enormous amount of energy stored in the masses of the universe.

Michio Kaku
Theoretical Physicist
City University of New York

E = mc² is the hush-hush of the stars. It is the cosmic engine that drives the entire universe. It means that even a few tablespoons of matter, if fully burned, tin release the energy of an atomic bomb. It's the reason why the stars shine, and why the sun lights up the World. Affair and energy are, in some sense, the aforementioned thing, and can turn into each other. Even a stone can plow into a low-cal ray if the rock happens to exist uranium and the light ray is a flare-up of atomic radiation.

I first became conscious of Eastward = mc² when I was in sixth form. That'south when Walt Disney came out with the moving picture Our Friend the Atom. I got the book. I read every single folio, every single line of the volume, had the book practically memorized. And then to me it was no mystery that thing and energy really are the same thing, because even before then I had decided that I wanted to become a theoretical physicist. That was my goal in life when I was most 10 years of age.

Neil deGrasse Tyson
Astrophysicist
American Museum of Natural History

What I like about E = mc² is not only its simplicity just [in] how many different environments in the universe the equation applies. It applies to what's going on inside of stars, inside of our ain lord's day. It applies to what's going on in the center of the galaxy. It applies to what's going on in the vicinity of black holes. Information technology applies to all the events that took identify at the big blindside. Our cardinal cognition of the formation and evolution of the universe would exist practically nada were it non for the existence and understanding of that equation. And, as a recipe for converting thing into energy and dorsum into matter, it's something that doesn't happen in your kitchen or in everyday life, because the energies required to brand that happen fall far outside of anything that goes on in everyday life.

Considering, for example, visible light that you use to illuminate the page yous read, you can summate how much energy that calorie-free has. It's not enough to make any particles with. Y'all need more than energetic light than visible light, than ultraviolet. You gotta get into X-rays. If you go high enough energy X-rays passing past your room, spontaneously, unannounced, unprompted, unscripted, they will brand electrons. The whole suite of particles you learn nigh, all of those can be manufactured simply past inbound a pool of energy where that energy is above the mass threshold for that particle.

We are fortunately non bathed in that level of free energy, because we would showtime get sterilized, and then information technology would mess with our Deoxyribonucleic acid, and then nosotros would die. So nosotros should be glad we don't see E = mc^two happening in front of the states. It would be a dangerous environment indeed. In that location are places in the universe where this equation is unfolding moment by moment. How else do you think the universe tin be equally big as it is at present but start out with something smaller than a marble? East = mc² is cranking, converting matter into energy and back again. When you're energy y'all don't have to take up much space. You tin can become very small when you're a pocket of energy. So I was in one case asked what exercise I recall is the greatest equation ever. There are a lot in the running but I would accept to put E = mc^two at the height. If you sit back, look at the universe and say, what equation holds all the cards, that would exist E = mc^two . That's all I gotta say.

Frank Wilczek
Theoretical Physicist
MIT

E = mc^two famously suggests the thought that you can get a lot of energy out of a small amount of mass. But that's not what Einstein had in mind, really, and you won't observe that equation in the original newspaper. The way he wrote it was 1000 = e/c^two and the original paper had a title that was a question, which was, "Does the inertia of a body depend on its free energy content?" So correct from the beginning Einstein was thinking well-nigh the question of could you explain mass in terms of energy. It turned out that the realization of that vision, the understanding of how not simply a trivial bit of mass but most of the mass, ninety percent or 95 percent of the mass of matter as we know information technology, comes from energy. We build it up out of massless gluons and almost massless quarks, producing mass from pure energy. That'south the deeper vision.