It is perhaps the most famous equation in the world, and also one of the most elegant. Einstein’s legendary equivalence between mass and energy, given the simple formula E=mc^2, is familiar even to schoolchildren.
At times, it simply stands as a placeholder for science — like in cartoons where writing E=mc^2 on a chalkboard signifies there’s some serious physics going on. But the relationship Einstein’s equation alludes to underlies fundamental properties of the universe itself. Mass is energy, energy is mass; the equation builds a bridge between two seemingly disparate domains.
The physics underpinning the equation are appropriately heady and complex. But for the rest of us, the significance of Einstein’s formula boils down largely to one thing: There’s a huge amount of energy bound inside the matter surrounding us. The equation equates the energy of a body in its rest frame, the E on the left-hand side of the formula, to an object’s mass multiplied by the speed of light squared.
As you probably already know, the speed of light is very fast. Photons zip along at around 300,000,000 meters per second (or around 186,000 miles per second). Now multiply that by itself, or square it, and the number gets astoundingly large. The speed of light squared is 8.98755179 × 10^16 m^2/s^2 (That’s 8.9 with 16 zeros behind it.)
A common misconception surrounding Einstein’s formula is that mass can be converted into energy. That’s not actually quite true, nor is it what Einstein meant when he set down his revolutionary idea. Instead, his equation shows that a change in the mass of an object requires a change in its energy. It’s the reason why the end products of nuclear reactions together weigh less than their parent atoms. When protons and neutrons split off from atoms during nuclear fission, they release energy. And as we know from Einstein, that’s equivalent to mass.
It’s easy to see that even tiny amounts of matter represent very large amounts of energy. Humans got a taste of that frightful energy when we invented the atomic bomb. The enormous amount of energy released by the Little Boy nuclear weapon was equivalent to the mass of less than a gram of its radioactive fuel. That’s less than half the weight of a dime.
You don’t need an atomic weapon to turn mass into energy, of course. You extract energy from matter every time you light a candle (though the mechanism there is a chemical reaction, rather than a nuclear one.) But the light and heat that comes from a candle is but a sliver of the energy contained within. A single candle might light up a romantic dinner, but the energy equivalent to all of the mass inside would be sufficient to level an entire city.
The Photon Paradox
Though the energy-mass equation might appear simple, there are some special cases that appear to challenge its assumptions. Take the case of photons, for example. These particles, which represent packets of light, have zero mass, but still contain energy. Taking Einstein’s equation at face value, that appears to be impossible. If mc^2 is zero, then E must be zero as well. But we know that’s not the case.
The paradox is resolved with a slightly expanded, lesser-known version of the equation. This formulation adds in momentum, or p, and also multiplies it by the speed of light. Written out, the equation is: E^2=p^2c^2 + m^2c^4. In the case of a photon, for which m=0, the equation boils down to E=pc. Because photons move at the speed of light regardless of where we view them from, they have momentum, and therefore energy. It’s a result that’s borne out by experiments in particle physics, which return results that are only consistent if the energy-mass-momentum equation holds true for photons.
The Power of an Equal Sign
Setting E equal to mc^2 enabled the most powerful and influential physics of the 20th century. But it was also a kind of logical leap for the field of physics. Prior to Einstein’s work, scientists viewed energy and mass as two entirely separate things. Energy, whether as light, heat or other forms was its own category, and mass, something held by all matter, was another. Though mass and energy could interact with each other, there was never an equivalence between them.
But with two simple strokes of a pen, Einstein set mass equal to energy, metaphorically destroying the wall between the two. Seen in this light, it’s possible to understand that objects with more mass also have more energy, and that adding (or subtracting) mass also changes the amount of energy it represents.
Einstein’s equation prefaced not only the atomic bomb, but to other ways of harnessing nuclear energy as well. Nuclear power plants today utilize the same fundamental scientific principles as nuclear weapons. Small nuclear “batteries” power the Voyager spacecraft — still running after more than four decades — and larger-scale nuclear powerplants could one day provide energy to lunar astronauts. And should humanity ever crack the daunting scientific challenge of sustaining nuclear fusion, we’ll again have Einstein’s work to thank.
FAQs
Einstein went on to present his findings mathematically: energy (E) equals mass (m) times the speed of light (c) squared (2), or E=mc2. The secret the equation revealed—that mass and energy are different forms of the same thing—had eluded scientists for centuries.
What is Einstein's famous equation What does it mean? ›
E = mc2. It's the world's most famous equation, but what does it really mean? "Energy equals mass times the speed of light squared." On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.
What is the famous formula E mc2? ›
E = mc2, equation in German-born physicist Albert Einstein's theory of special relativity that expresses the fact that mass and energy are the same physical entity and can be changed into each other.
What does the c in Einstein's famous equation of E mc2 stand for? ›
In the equation, E = m c2, E stands for energy, m stands for an object's mass, and c2 represents the speed of light ( 186,000 miles per second ) multiplied by itself.
Why is Albert Einstein famous for E mc2? ›
The implications of E=mc2 are profound. For centuries, scientists had considered energy and mass to be completely distinct and unrelated to each other. Einstein showed that in fact, energy and mass are different forms of the same thing.
What is the full equation for E mc2? ›
It just describes objects that have mass and that aren't moving. The full equation is E squared equals mc squared squared plus p times c squared, where p represents the momentum of the object in question.
What equation is known as Einstein's big idea? ›
Over 100 years ago, Albert Einstein grappled with the implications of his revolutionary special theory of relativity and came to a startling conclusion: mass and energy are one, related by the formula E = mc2. In "Einstein's Big Idea," NOVA dramatizes the remarkable story behind this equation.
Who proved E=mc2 is right? ›
GAITHERSBURG--Albert Einstein was correct in his prediction that E=mc2, according to scientists at the Massachusetts Institute of Technology (MIT), the Commerce Department's National Institute of Standards and Technology (NIST), and the Institute Laue Langevin, Genoble, France (ILL) who conducted the most precise ...
What is an example of E mc2 in real life? ›
When you drive your car, E = mc2 is at work. As the engine burns gasoline to produce energy in the form of motion, it does so by converting some of the gasoline's mass into energy, in accord with Einstein's formula. When you use your MP3 player, E = mc2 is at work.
Do people still use E mc2? ›
They are metamorphosing mass into energy in direct accordance with Einstein's equation. We take advantage of that realization today in many technologies. PET scans and similar diagnostics used in hospitals, for example, make use of E = mc2.
“Einstein mass–energy equivalence equation E=mc2 is wrong because does not contains Dark Matter”. Einstein in 1905 did not formulate exactly the equation E=mc2 but he said: 'if a body gives off the energy L in the form of radiation, its mass diminishes by L/c2'.
What is E mc2 for dummies? ›
(Energy is related to mass by Einstein's famous E = mc2 equation, so it takes energy to create a particle.) They may have existed in the early universe, but as the universe cooled off and energy spread out after the big bang, these particles would have collapsed into the lower-energy states that we observe today.
What is E-mc2 in the human body? ›
But E=mc^2 is the equation for mass-energy equivalence. The protons and neutrons, and the atoms that are made out of them, are made out of energy. Their mass is proportional to the amount of energy they contain. So the human body cannot be converted into energy, because it already is energy!
What was Albert Einstein's IQ? ›
The IQ of Albert Einstein remains a subject of speculation since he never took an IQ test. However, based on historical records, Einstein's estimated IQ is around 160. Despite the absence of concrete data, Einstein's genius is undisputed, given his profound contributions to science.
Does e-mc2 apply to everything? ›
Yes — in short, this is true for all forms of matter and energy, including dark matter and dark energy.
What is the meaning of Einstein's special relativity equation? ›
Einstein went on to present his findings mathematically: energy (E) equals mass (m) times the speed of light (c) squared (2), or E=mc2. The secret the equation revealed—that mass and energy are different forms of the same thing—had eluded scientists for centuries.
What do Einstein's field equations mean? ›
What Does It Mean? The Einstein Field Equations are ten equations, contained in the tensor equation shown above, which describe gravity as a result of spacetime being curved by mass and energy.
What is the meaning of Om mc2? ›
This concurs with modern science which says that every atOM and molecule is formed out of energy vibration. Einstein's equation, E=mc2, states that matter (m) is an expression of energy (E). OM as the sound symbolizes that all material objects, all phenomena, and all thought patterns are states of energy vibration.
What does Einstein's famous equation say that all matter is quizlet? ›
Einstein's famous equation, E=mc2, shows mathematically that energy and matter are one and the same when paired with the speed of light. E stands for energy, m for mass, and c for the speed of light. According to this equation, all matter is concentrated energy that has condensed into the atoms.
