eli5: Why was E=mc2 so revolutionary?

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Relativity has been part of mechanics since the days of Newton. He recognized that you should assume some frame of reference, then do all of your physics calculations from within that frame. If you’re standing on the ground then that presents a convenient frame of reference–just describe how fast things are moving relative to the ground. If you’re in a moving car then that becomes a more convenient frame of reference, describing speeds relative to that car. What Newton found is that as long as you choose a reference frame that isn’t accelerating then all of the laws of physics still work. This is “Newtonian Relativity.”

Towards the end of the 19th century physicists were looking at light. They had found that light doesn’t actually travel at infinite speed–they could measure the time it takes light to get from one place to another. This then proposed the next question: how does that speed vary? For comparison, a pitcher may be able to throw a fastball at about 100 mph. Put them on a flatbed truck cruising at 100 mph and have them pitch forward and the ball will come out at 200 mph. What if you do the same with light?

To set up this experiment they set up two long tracks that they could use to measure the speed of light. One ran north/south, while the other went east/west. The idea was that the east/west track would be going extra fast due to Earth’s rotation. What they found, though, was that the speed was the same in either case. This prompted further experiments, like repeating the trial 6 months later when Earth’s motion was in the opposite side of its orbit around the sun, but try as they might they kept coming up with the same speed for light.

In all of this debate the prevailing belief was that light propagates as a disturbance in the ether, a layer that permeates space without interacting with things. This ether gave a medium for light to travel through, and also gives a single privileged reference frame to the universe. The experiments measuring the speed of light on Earth in different directions and at different times were essentially looking to measure the speed of earth through the ether, but they kept coming back that the speed of light is constant no matter how you’re moving.

That statement is a contradiction in Newtonian relativity, and so in order to square the observations with that framework physicists devised all sorts of band-aid solutions, like considering how massive objects like Earth must pull the ether along with them. Then Einstein came along and explained the whole thing.

The ether isn’t real, and light travels at the same speed for everyone. The flaw in understanding is in how we see space and time themselves: space is not a rigid grid of coordinates through which objects move, and time is not an ever-flowing march forward with constant speed. Distances change depending on how fast you are moving, and clocks tick at different rates. Speed is simply a ratio of a distance over a time, and when neither distance nor time is rigid this gives the flexibility for the speed of light to be absolutely constant.

Einstein’s special take on relativity turned physics on its head with regard to how it treats space and time, but it didn’t stop there. When this new framework is applied to the equations around light the famous E = mc^2 relationship winds up dropping out. This relationship is very simple for people to repeat and recognize, so it wound up being the public image for Einstein’s work. It’s also very deep in what it implies: there is a fundamental equivalence between mass and energy, and the amount of energy contained in only a tiny amount of mass is *enormous*.

That idea is what was behind the race to harness the atom, which of course was done first in the context of the Manhattan Project to develop nuclear weapons. Time dilation and Lorenz Contraction aren’t things that have had an obvious impact on day to day life (though they are required knowledge for things like GPS satellites to work). Nuclear weapons colored the global geopolitical stage from WW2 through the Cold War and are still very relevant today, so E=mc^2 is still the best known result of Einstein’s work.

Weirdly enough, it wasn’t. Kind of.

The idea of mass-energy equivalence had been floating around for a while by 1905. It was understood that there was some link between matter and energy, and *c* had been brought into that (in some cases using ideas about the ether), and ideas about the “fixed” kinetic energy of particles. So things had generally settled down to E = mc^2 or E = 1/2 mc^(2).

In particular, Poincaré was playing around with electromagnetic radiation and in 1900 reached E = mc^2 in that context, but not for all things.

Einstein’s 1905 paper on E=mc^2 is only a couple of pages long. It was an interesting afterthought to his main paper on special relativity, where he does a thought experiment and shows that if a body gives off *L* energy as electromagnetic radiation, its mass must go down by *L/c^2*.

That led him down the path of mass-energy equivalence, and helped explain violations of conservation of mass.

Others built on this, and Felix Klein provided a generalised proof of E = mc^2 in a 1918 paper.

Anyway. As for its uses, E = mc^2 can be used to predict the energy released from certain nuclear reactions. This is pretty important for nuclear energy (both nuclear power and nuclear weapons). The equation doesn’t really explain the huge energies that come out of radioactive decades, but it does let you calculate them if you know the mass changes. But it wasn’t until the 30s that this was put into practice.

In terms of public perception, E = mc^2 became famous due to the [July 1946 issue of Time](https://en.wikipedia.org/wiki/File:Einstein_-_Time_Magazine_-_July_1,_1946.jpg), which featured Einstein, a nuclear explosion, and the equation. The nuclear bombs (both tests and uses in war) were a major demonstration that E = mc^2 calculations could have real-world implications. Einstein used the attention the nuclear bombs (which he wasn’t particularly involved in) received to achieve a level of fame outside the scientific community, which he leveraged for political goals. E = mc^2 – due to its simplicity (and relative importance) became the symbol of that.

It was revolutionary in multiple ways. Probably the biggest was that it provides the relationship between mass and energy, implying that the two are different aspects of the same thing. This led to things like atomic energy and nuclear bombs. It’s also a pretty fundamental understanding of how our universe works.

It also led to the understanding that things we typically think of as immutable such as the flow of time, the dimensions and mass of objects, are in fact not just one thing. They can be different depending on things like relative motion. This is contrary to pretty much all of physics before it, where it is assumed that there is a single objective reality.

One of the things that was so amazing about it was that Einstein basically took the measured fact that the speed of light (in a vacuum) is a constant and deduced the rest.

Run that one by again: The constant speed of light led to understanding that matter = energy. That’s genius.

If a grain of sand was moving at the speed of light squared, the amount of energy it would release would be equal to a 20kiloton bomb.

Alright, imagine you have a really big puzzle, and you’re trying to figure out how all the pieces fit together. One day, a super smart person named Albert Einstein comes along and looks at the puzzle.

Einstein looks closely and notices something incredible. He realizes that a tiny piece of the puzzle, like a little dot, can explain a huge part of the whole puzzle. He figures out that if you take a little bit of matter (that’s the “m” part) and multiply it by a special number (that’s the “c squared” part), you get a crazy amount of energy (that’s the “E” part).

This discovery was like finding a hidden treasure that no one knew was there. Before Einstein, people didn’t really understand that matter and energy were connected in this special way. It was like he solved a super tough riddle about how the universe works.

This equation, E=mc², was revolutionary because it showed that even a tiny bit of matter could create an enormous amount of energy. It changed the way people understood the universe and how things like atoms, energy, and even big things like stars and galaxies work. It’s like Einstein found a key to a door that led to a whole new world of science and knowledge. That’s why E=mc² is considered one of the most important and groundbreaking equations ever!