16 December 2016

BOOK REPORT: Einstein's Relativity

Man, this book was over my head.

And yet, it drove me to Wikipedia. So let me share a few of the things I learned.

Einstein developed his theory of Special Relativity first. It’s mostly about space and time. And it says that any two events which are separated by a spacetime interval (a 4D distance) will have variance based on the viewer’s inertial point of view.

What! Yeah, it’s dense. Here’s a down-to-earth example.

Say you have two perfectly accurate atomic clocks. One stays on earth, sitting on the ground right next to where you are now. The other goes up to the International Space Station, which is zooming along at 17,136 mph! After two years of these clocks traveling at different speeds, the one in space will be about 0.02 seconds behind the one next to you on the ground. So the faster one moves relative to the other, the greater this discrepancy becomes.

No, this isn’t just a crazy theory. This actually happened to Sergei Vasilyevich Avdeyev, who spent over two years in space zooming along at insane speeds, and when he came back he was 0.02 seconds younger than he ought to be.

Einstein’s second big theory was called General Relativity, and it’s about gravity. It says that spacetime gets curved by the energy and momentum of matter. General Relativity actually says that the closer you are to a source of gravity, the slower your time will go.

So let’s go back to our two atomic clocks. This is another actual experiment they’ve done. You put one atomic clock on a mountaintop, further from earth’s center of gravity, and you leave the other on the couch next to you. The one next to you will tick slightly slower than the one on the mountain. Because of this same effect, they’ve calculated that the core of the earth is 2.5 years younger than the crust where we live. More gravity means slower time.

Of course, these are all relatively small numbers. But scifi geeks known that as you go faster and heavier, the effects become greater, like you see when Ender travels at lightspeed (Ender’s Game) or when Murph’s dad lands on Miller’s Gargantua (Interstellar).

Einstein also says that it’s impossible to say in an absolute sense that two distinct events separated by space occur at the same time. Meaning if the speeds and distances are just right, to one person A might happen before B, and to another B might come before A. See this chart:

You’re thinking that’s pretty weird. But it gets crazier.

Imagine you’re in Spaceship X and out the window you see Spaceship Z come zooming by at something close to lightspeed. And let’s say you can see a clock inside the other ship as it passes. To you, in Spaceship X, it would look like your watch is ticking just fine and the clock in Spaceship Z is ticking really slowly.

Now, common sense would tell you that if his watch looks slow to you, then your watch would look fast to him. But relativity is relative. Meaning it doesn’t matter whether you think your ship is moving at light speed and the other one is parked or if you’re the one parked and the other is moving. The only thing that matters is how you seem to be moving in relation to each other. And you’re each moving fast in relation to the other. So that means if someone in Spaceship Z saw your watch, it would look, to him, like it was also ticking really slowly!

This blew my mind. It doesn’t seem to fit. Or didn’t, until I read this metaphor.

Imagine you had a clone. And you magically shrunk this clone so he was about as big as a sylphe. (That’s a thumb-sized being, if you haven’t read SONG OF LOCKE). He seems very small to you. And when he looks at you, you seem very big, even though your size hasn’t changed. This example shows a literal change of scale.

Now imagine you have another clone, and he’s still your same size, but you order him to climb to the top of that mountain in the distance. To you, he now looks very small. But does that mean you will look very large to him? No. Because he is also seeing you across the same vast distance.

In short, you appear large if seen within handshaking range, but you appear small if seen from a great distance. It’s not actually a paradox then, is it?

If I’ve piqued your curiosity for more of this stuff, take a look at the Ladder Paradox, which will teach you about length contraction at high speeds!

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— J