The theory of relativity was developed by Albert Einstein in the early 1900s. There are two theories of relativity. The first is special relativity and the second is general relativity. E=mc² is the Special Relativity Equation.
Einstein spent 10 years trying to include acceleration in the theory and published his theory of general relativity in 1915. In it, he determined that massive objects cause a distortion in space-time, which is felt as gravity.
Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels. As a result, he found that space and time were interwoven into a single continuum known as space-time. Events that occur at the same time for one observer could occur at different times for another. (14.1)
If you're traveling North at some speed for some amount of time, you go some distance North. Likewise, going East at the same speed for the same amount of time makes you go the same distance East. But if you go NorthEast at the same speed for the same amount of time, you don't go quite as far North as you did when going purely North, and you don't go quite as far East as you did going purely East.
Time and space work the same way. Imagine, instead of North and East on a graph, time and space. The more you travel through space (the faster you go), the less you travel through time. Which agrees with the Theory of Relativity: the closer you get to the speed of light, the slower time moves for you. Also, the less you travel through space (the slower you go), the more you travel through time- that would only make sense.
The most important piece of information that one needs to understand in order to understand the theory of relativity: gravity and acceleration both have the same effects on an object in terms of time. If you go really fast, time moves slowly for you. Likewise, if you're experiencing a lot of gravitational pull, time moves slowly for you. You could even think of gravity and acceleration as the same thing.
Say you're in an elevator in space: If the elevator starts accelerating in some direction, you will be pushed up against a wall and experience an illusion of gravity.
To further explain how gravity and time are related would undermine the fact that you're explaining this to someone who doesn't really get this sort of thing. (14.2)
This Sciencemag interactive post will give you a better understanding of the Theory Of Relativity. (14.3)
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