Bob Somerby keeps asking for an understandable explanation of the theory of relativity. In this post, I shall try to oblige him in less than 500 words. Note, however, that I am taking an, um, nontraditional approach.
- Until 1905, everyone thought that velocities added up. That is, if you're walking at 2 mph and you get on an escalator that's moving 2 mph, your total velocity is 4 mph. Simple.
- Simple but wrong. In fact, your total velocity is a little less than 4 mph. It turns out that our intuitive sense of how the universe works is incorrect. Here is the actual formula for adding up velocities, where c is the speed of light:
- Once you have this, the rest is just arithmetic. If you take this formula and apply it to objects in motion, all the weird predictions of relativity pop out: lengths get shorter as velocities increase; time slows down; nothing can go faster than the speed of light; and e=mc².
General Relativity (Gravity)
- Until 1916, everyone thought that normal Euclidean geometry described how the universe worked.
- It doesn't. Once again, our intuitive sense of how the universe works was wrong.
- In fact, in the presence of mass (the earth, for example), geometry becomes non-Euclidean, or slightly "warped." Here is the Einstein field equation that describes the shape of space and time in the presence of mass:
- This equation is even more complicated than it looks, but it basically says the curvature of spacetime (the curvature tensor Gαβ) equals the distribution of mass/energy (the metric tensor Tαβ).
- The rest, as Einstein himself said, is just (very advanced) arithmetic. When you work through the consequences of warped spacetime, it turns out that time slows down in the presence of mass. Another way of saying this is that motion through time decreases.
- Another consequence is that objects accelerate toward the mass. In other words, motion through space increases.
- This is gravity: in the presence of mass, motion through time decreases (slightly) and is converted into motion through space.
You will notice that both cases have two things in common. First, the rules of how the universe works turn out to be a little more complicated than we thought. The old rules of Isaac Newton are almost right, but not quite.
Second, once you have the rules the rest is just working through the math. This might seem a bit like cheating, but it's nothing new. An ordinary freshman physics textbook spends hundreds and hundreds of pages working through the consequences of a few rules set down by Isaac Newton. But if you discover new rules, then you have to work through the math all over again and you'll come up with different results. That's what college textbooks on special and general relativity do for hundreds and hundreds of pages.
You're disappointed, aren't you? You really want to know what it all means. Sorry. There's really no deep philosophy here. For reasons no one entirely understands, we live in a universe ruled by the iron fist of mathematics.
In other words, once you know the rules, it's all just math, baby.