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.
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