For hundreds of years, there was an immutable law of physics that was never challenged: that in any reaction occurring in the Universe, mass was conserved. That no matter what you put in, what reacted, & what came out, the sum of what you began with & the sum of what you ended with would be equal. But under the laws of special relativity, mass simply couldn"t be the ultimate conserved quantity, since different observers would disagree about what the energy of a system was. Instead, Einstein was able khổng lồ derive a law that we still use today, governed by one of the simplest but most powerful equations ever khổng lồ be written down,E = mc2.

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A nuclear-powered rocket engine, preparing for testing in 1967. This rocket is powered by... <+> Mass/Energy conversion, và E=mc^2.

ECF (Experimental Engine Cold Flow) experimental nuclear rocket engine, NASA, 1967
E, or energy, which is the entirety of one side of the equation, and represents the total energy of the system. m, or mass, which is related lớn energy by a conversion factor. Andc2, which is the tốc độ of light squared: the right factor we need lớn make mass và energy equivalent.
Niels Bohr & Albert Einstein, discussing a great many topics in the home of Paul Ehrenfest in... <+> 1925. The Bohr-Einstein debates were one of the most influential occurrences during the development of quantum mechanics. Today, Bohr is best known for his quantum contributions, but Einstein is better-known for his contributions lớn relativity và mass-energy equivalence.

Paul Ehrenfest

What this equation means is thoroughly world-changing. As Einstein himself put it:

It followed from the special theory of relativity that mass và energy are both but different manifestations of the same thing — a somewhat unfamiliar conception for the average mind.

Here are the three biggest meanings of that simple equation.

The quarks, antiquarks, & gluons of the standard mã sản phẩm have a màu sắc charge, in addition lớn all the... <+> other properties lượt thích mass and electric charge. Only the gluons và photons are massless; everyone else, even the neutrinos, have a non-zero rest mass.

E. Siegel / Beyond The Galaxy

Even masses at rest have an energy inherent lớn them. You"ve learned about all types of energies, including mechanical energy, chemical energy, electrical energy, as well as kinetic energy. These are all energies inherent to moving or reacting objects, and these forms of energy can be used to do work, such as run an engine, power nguồn a light bulb, or grind grain into flour. But even plain, old, regular mass at rest has energy inherent khổng lồ it: a tremendous amount of energy. This carries with it a tremendous implication: that gravitation, which works between any two masses in the Universe in Newton"s picture, should also work based off of energy, which is equivalent lớn mass via E = mc2.

The production of matter/antimatter pairs (left) from pure energy is a completely reversible... <+> reaction (right), with matter/antimatter annihilating back lớn pure energy. This creation-and-annihilation process, which obeys E = mc^2, is the only known way to create & destroy matter or antimatter.

Dmitri Pogosyan / University of Alberta

Mass can be converted into pure energy. This is the second meaning of the equation, where E = mc2tells us exactly how much energy you get from converting mass. For every 1 kilogram of mass you turn into energy, you get 9× 1016 joules of energy out, which is the equivalent of 21 Megatons of TNT. When we experience a radioactive decay, or a nuclear fission or fusion reaction, the mass of what we started with is greater than the mass we wind up with; the law of conservation of mass is invalid. But the amount of the difference is how much energy is released! That"s true for everything from decaying uranium khổng lồ fission bombs to nuclear fusion in the Sun to lớn matter-antimatter annihilation. The amount of mass you destroy becomes energy, và the amount of energy you get is given by E = mc2.

The particle tracks emanating from a high energy collision at the LHC in 2014. Composite particles... <+> are broken up into their components và scattered, but new particles are also created from the available energy in the collision.

Energy can be used to lớn make mass out of nothing... Except pure energy. The final meaning is the most profound. If you take two billiard balls & smash them together, you get two billiard balls out. If you take a photon and and electron and smash them together, you get a photon & an electron out. But if you smash them together with enough energy, you"ll get a photon, and electron, & a new matter-antimatter pair of particles out. In other words, you will have created two new massive particles:

a matter particle, such as an electron, proton, neutron, etc., & an antimatter particle, such as a positron, antiproton, antineutron, etc.,

whose existence can only arise if you put in enough energy lớn begin with. This is how particle accelerators, like the LHC at CERN, search for new, unstable, high-energy particles (like the Higgs boson or the đứng top quark) in the first place: by making new particles out of pure energy. The mass you get out comes from the available energy: m = E/c2. It also means that if your particle has a finite lifetime, then due lớn Heisenberg uncertainty, there"s an inherent unknowability lớn its mass, since∆Et ~ħ, & therefore there"s a corresponding∆m from Einstein"s equation, too. When physicists talk about a particle"s width, this inherent mass uncertainty is what they"re talking about.

The warping of spacetime, in the General Relativistic picture, by gravitational masses.

LIGO/T. Pyle

The fact of mass-energy equivalence also led Einstein to lớn his greatest achievement: General Relativity. Imagine that you"ve got a particle of matter và a particle of antimatter, each with the same rest mass. You can annihilate them, and they"ll produce photons of a specific amount of energy, of the exact amount given by E = mc2. Now, imagine you had this particle/antiparticle pair moving rapidly, as though they had fallen from outer space, và then annihilated close khổng lồ the surface of Earth. Those photons would now haveextra energy: not just theE from E = mc2, but the additionalE from the amount of kinetic energy they gained by falling.

If two objects of matter và antimatter at rest annihilate, they produce photons of an extremely... <+> specific energy. If they produce those photons after falling deeper into a gravitational field, the energy should be higher. This means there must be some sort of gravitational redshift/blueshift, the kind not predicted by Newton"s gravity, otherwise energy wouldn"t be conserved.

Ray Shapp / Mike Luciuk; modified by E. Siegel

If we want khổng lồ conserve energy, we have to understand that gravitational redshift (and blueshift) must be real. Newton"s gravity has no way to trương mục for this, but in Einstein"s General Relativity, the curvature of space means that falling into a gravitational field makes you gain energy, & climbing out of a gravitational field makes you thua thảm energy. The full & general relationship, then, for any moving object, isn"t just E = mc2, but that E2 = m2c4+ p2c2. (Where p is momentum.)Only by generalizing things to include energy, momentum, và gravity can we truly describe the Universe.

When a quantum of radiation leaves a gravitational field, its frequency must be redshifted to... <+> conserve energy; when it falls in, it must be blueshifted. Only if gravitation itself is linked khổng lồ not only mass but energy, too, does this make sense.

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Vlad2i & mapos / English Wikipedia

Einstein"s greatest equation, E = mc2, is a triumph of the power & simplicity of fundamental physics. Matter has an inherent amount of energy khổng lồ it, mass can be converted (under the right conditions) khổng lồ pure energy, và energy can be used lớn create massive objects that did not exist previously. Thinking about problems in this way enabled us lớn discover the fundamental particles that biến hóa our Universe, to invent nuclear power & nuclear weapons, & to discover the theory of gravity that describes how every object in the Universe interacts. And the key to lớn figuring the equation out? A humble thought experiment, based on one simple notion: that energy và momentum are both conserved. The rest? It"s just an inevitable consequence of the Universe working exactly as it does.


I am a Ph.D. Astrophysicist, author, and science communicator, who professes physics & astronomy at various colleges. I have won numerous awards for science writing since 2008 for my blog, Starts With A Bang, including the award for best science blog by the Institute of Physics. My two books, Treknology: The Science of Star Trek from Tricorders to lớn Warp Drive, Beyond the Galaxy: How humanity looked beyond our Milky Way and discovered the entire Universe, are available for purchase at Amazon. Follow me on Twitter