Science › Space, time & gravity
E = mc²
1905· Idea
ProvenTested many times; part of working physics.
Einstein's 1905 equation: energy equals mass times the speed of light squared. Mass is a highly concentrated form of energy.
See it on the Science map →How it works
Because the speed of light squared is enormous, a small amount of mass equals a huge amount of energy. One gram fully converted would release roughly the energy of the Hiroshima bomb. In practice, nuclear reactions convert only a fraction of a percent. It also works in reverse: most of your body's mass is the energy of quarks and gluons moving and bound inside protons and neutrons.
Why it matters
It explains why the Sun shines, how nuclear power and weapons work, and where most of the mass of ordinary matter comes from.
Think of it like
Like a property's equity: value locked in the building that can be released by sale or refinance. Mass is energy locked up; nuclear reactions cash some of it out.
How we know
Cockcroft and Walton split lithium in 1932 and the energy matched lost mass. Nuclear reactors and bombs work as predicted. A 2005 test confirmed the equation to better than one part in a million.
Still a mystery
It is settled. Why particles have the specific masses they do is still unexplained.
Connections (6)
▸Conservation of energy was widened by E = mc²Proven
The relationship
Energy conservation said energy is never created or destroyed, while chemistry said mass is never created or destroyed. E = mc² merged the two rules: mass is a form of energy. Only total energy, mass included, is conserved. A hot object weighs very slightly more than a cold one; a nucleus weighs less than its parts.
How the link was found
Conservation of energy was established by Mayer, Joule and Helmholtz in the 1840s. Einstein linked mass to it in September 1905.
Why it's proven
Nuclear reactions show exactly the predicted mass loss as energy release. Particle collisions create new particles from energy and the books always balance.
Open questions and mysteries
In an expanding universe, total energy conservation becomes hard to define; how to account for it cosmically is debated.
▸Special relativity implies E = mc²Proven
The relationship
Einstein asked what happens when a body emits light. Applying relativity, he found the body loses mass equal to the energy carried away divided by light speed squared. So mass and energy are the same quantity in different forms.
How the link was found
Einstein, in a three-page follow-up paper in September 1905.
Why it's proven
Nuclear and particle reactions match the formula; a 2005 precision test confirmed it to better than one part in a million.
Open questions and mysteries
Einstein's original derivation is considered incomplete by some historians, though later proofs are rigorous.
▸E = mc² powers stars in Stars forge the heavier elementsProven
The relationship
When four hydrogen nuclei fuse into one helium nucleus, the helium weighs about 0.7% less than the four parts. That missing mass becomes energy, by E = mc². Because c² is huge, a little mass yields enormous energy. The Sun converts about four million tonnes of mass into energy every second, and has done so for 4.6 billion years.
How the link was found
Arthur Eddington suggested in 1920 that stars run on hydrogen turning into helium. Hans Bethe worked out the detailed reactions in 1938-39 (Nobel 1967).
Why it's proven
Precise atomic mass measurements give the 0.7%. Neutrinos from the Sun's core, detected since the 1960s, match the rates the theory predicts.
Open questions and mysteries
Fusion's energy is proven; harnessing it on Earth for power remains an engineering challenge, with net-energy experiments only since 2022.
▸E = mc² lets energy become matter and AntimatterProven
The relationship
Because mass and energy are interchangeable, enough concentrated energy can become new particles. Electric charge must still balance, so energy produces matter paired with antimatter, such as an electron plus a positron. In reverse, when a particle meets its antiparticle, their whole mass converts back into energy, usually gamma rays.
How the link was found
Einstein's 1905 formula set the exchange rate. Dirac predicted antimatter in 1931; Anderson found the positron in 1932, and Blackett and Occhialini saw electron–positron pairs created from cosmic-ray energy in 1933.
Why it's proven
Pair creation and annihilation are seen daily in accelerators and hospitals. PET scanners detect the two 511 keV gamma rays from each annihilation, exactly the electron's mass times c².
Open questions and mysteries
If energy always makes matter and antimatter in equal amounts, why does our universe contain almost only matter?
▸Albert Einstein derived E = mc²Proven
The relationship
Einstein imagined a body giving off two bursts of light in opposite directions and compared how it looked to a moving observer. Energy bookkeeping only worked if the body lost mass equal to the light's energy divided by light speed squared. He concluded that mass is a measure of a body's energy content.
How the link was found
Einstein, in a three-page paper submitted in September 1905 and published that November, "Does the Inertia of a Body Depend Upon Its Energy Content?"
Why it's proven
Nuclear reactions release exactly the energy matching their lost mass. A 2005 test by teams at MIT and NIST confirmed the equation to better than one part in a million.
Open questions and mysteries
Historians and physicists have debated whether his first 1905 derivation was fully general; later derivations settled the physics.
▸The Higgs field and boson (2012) leaves ~99% of proton mass to E = mc²Proven
The relationship
The Higgs field gives electrons and quarks their mass. But the three quarks inside a proton account for only about 1% of its mass. The rest is the energy of quarks moving near light speed and the gluon field binding them, which counts as mass through E = mc². Most of the weight of ordinary matter is bound-up energy.
How the link was found
Worked out through quantum chromodynamics, the theory of the strong force, developed in the 1970s. Supercomputer lattice calculations computed the proton's mass from it in 2008.
Why it's proven
The 2008 lattice calculations (Dürr and colleagues) reproduced the proton and neutron masses within a few percent using only quark properties and the strong force.
Open questions and mysteries
Proving mathematically why quarks stay permanently trapped inside protons is tied to an unsolved Millennium Prize problem, the Yang-Mills mass gap.