Okay. I’ve been teasing doubly special Saturday and (especially this year) since last Monday (and planting hints along the way). If you haven’t figured it out by now, today is Albert Einstein’s birthday. It’s also pi day, and how cool is it that a guy like Al was born on pi day?
So: Happy Birthday Albert! The (especially this year) part is because it’s extra-special pi day (3/14/15) and because this year I’m finally going to do what I’ve been wanting to do here to commemorate Einstein’s birthday since I started this blog back in ought-eleven.
I’m going to write — at length — about Special Relativity!
But wait! Before you all hit [Unfollow], I promise you it won’t be that bad.
No really; it won’t. In fact, if you stick with me, I’ll take you on a journey that will blow your mind. And you may come away actually understanding Special Relativity (SR). Just imagine how you can impress your friends at your next party!
I know some of you are working on being science fiction authors, and you folks especially might get some value from the topics I’ll cover. In particular, what happens when you travel extremely fast and why FTL (faster than light) travel is probably impossible.
This all begins on Monday (right now there’s birthday cake to eat). In the meantime here are some of the interesting topics I’ll be covering:
¶ According to SR, going really fast causes your length to contract along your direction of motion.
There is a thought experiment involving a high-speed train that is longer than some tunnel (assuming you line them up side-by-side). If the train passes through the tunnel at high speed, due to length contraction, it can fit entirely within the tunnel.
This means an observer watching this could momentarily close gates located at both mouths of the tunnel. For a brief instant, the train is enclosed by those gates. And yet the train is physically too long for this to occur.
Worse, from the perspective of the train (where the train seems normally long), the tunnel is moving and therefore contracted. Not only is the tunnel too short to begin with, now it’s even shorter!
This leads to the question: WTF?!
¶ According to SR, the concept of simultaneity goes out the window when one person is traveling fast and the other is standing still.
There is a thought experiment involving an observer watching that high-speed train pass by. As it does, two lightning strikes simultaneously hit the ground, one right at the front of the train, the other at the back.
At least that’s what the observer on the ground sees. The observer on the train sees something quite different: the two lightning strikes are not simultaneous.
A reverse version of this involves blinking lights on the train. To the observer on the train, they blink simultaneously. But to the observer on the ground they do not.
Again: Huh?! What??
¶ According to SR, when you go fast your clock goes slower compared to someone watching you zip past.
You can take a fast spaceship to a nearby star, turn around, and come back. When you arrive home, you find that your twin sibling has aged more than you have (because you went fast and your clock slowed compared to your sibling’s clock).
But wait! From your point of view, it’s equally correct to say you sat in the spaceship while the Earth zipped away from you and then came back. From that perspective, the Earth twin’s clock should be the slower one.
So why isn’t it the Earth twin who’s younger? (This is called the Twins Paradox. I’ll hint right now that the resolution involves the fact that you turned around halfway through the trip.)
¶ If FTL is possible, then either SR or causality has to be false. But we’re pretty sure causality is true (the universe would be a weird place if it weren’t), and SR is one of the most thoroughly tested theories in science.
Essentially, you get:  causality;  SR;  FTL. Pick two.
These are the main things I’ll be trying to explain. There’s a fair amount of preliminary groundwork necessary to make the explanations of these things make total sense (and they do), so we’ll take it slowly.
I expect this to be a (possibly longish) series of (hopefully fairly short) posts. In each one I’ll try to address a single topic in detail so you have time to digest it before moving on. (I can’t guarantee daily posts; we’ll see how it goes. It might actually be better for everyone involved if I space them out.)
No math is required. I’ll show you a bit of math, but you can ignore it if you wish. And it’s not really hard math — nothing worse than a square root (and just one of those).
Speaking of math, I want to introduce you to Emmy Noether, who is one of the most influential and ground-breaking mathematicians ever. (Please take a moment to read the Wiki link and get to know her.) She’ll be assisting Albert in our demonstrations (where they’ll go by the nicknames “Al” and “Em”)
Incidentally, Emmy Noether’s birthdate is March 23 (1882), so she’s celebrating later this month. The Vernal Equinox is the 20th, so once you get done celebrating that, raise a glass to Emmy!
Usually Al will be the observer on the ground — the one who is “not moving” — and Em will be the one in the fast train or spaceship. Just remember that, from Em’s point of view, she seems to be standing still while Al (and the ground on which he’s standing) are zipping past.
A lot of the fun comes from comparing their points of view!
School starts Monday!