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Special Relativity
Posted January 6, 2002

Hello, you're listening to Mostly Mozart on CJLY 93.5fm in Nelson, Kootenay Coop Radio. My name is -- and Mostly Mozart is sponsored by -- Tom Clegg.

I'm going to talk about relativity again today. I'll tell you about the problem that Einstein solved by inventing special relativity, and the new problem that he created by inventing special relativity, and maybe even how he solved that problem few years later by inventing the general theory of relativity.

Before that I'll have to explain the principle of relativity, which is a different sort of thing than the theories of relativity.

And before that, you will be listening to some Mozart.


This is CJLY 93.5fm in Nelson and you're listening to Mostly Mozart, which is sponsored by Tom Clegg. I am your host, and I am telling you about relativity. I've done it before, and I'll probably do it again, but this time is probably somewhat different from the other times, so it's not a total waste of time.

The principle of relativity is an approach to thinking about physics. The idea is that if you do an experiment in one place, then you do exactly the same experiment in another time and place, then you should get the same result. This assumption appears to be true, which is a good thing -- if the Universe behaved differently at different times and places, then the whole idea of science wouldn't work very well. People wouldn't be able to replicate each other's results, for one thing. Of course, the results wouldn't be much use anyway, because you couldn't assume that anything would ever happen the same way twice. Fortunately, the universe does seem to follow one set of rules at all times and places.

For example, Newton's laws of motion seem to be true: whether you live in the 18th century or the 21st century, whether you're in England or in Canada or on the moon, if someone runs away from you at 20 km/h, and you run in the opposite direction at 20 km/h, you can look over your shoulder and see him moving away from you at 40 km/h.

That seems pretty obvious, but in the late 19th century it was discovered not to be true after all. It turns out that light always travels at the same speed, which we can call light speed; and as far as anyone can tell, nothing can move faster than light speed.

That doesn't seem like such a big revelation at first. But there's a huge problem with adding the idea of a speed limit to Newton's laws of motion. The problem comes when you run away from a beam of light. According to Newton's laws, if the person running away from you is also pointing a flashlight at you, then you should be able to look over your shoulder and see the light moving toward you at the speed of light, minus 40 km/h. And if you both turn around and run toward each other, you should see the light coming toward you at the speed of light, plus 40 km/h.

But you won't. You'll see the light coming toward you at exactly the speed of light. The other runner will see it going away from him at exactly the speed of light. A third person, who is watching from the sidelines, will also see the light move at exactly the speed of light.

This is nice and symmetrical, and (better yet) it agrees with experimental results, but it causes some pretty annoying problems. For example, let's say that third person on the sidelines measures the distance between you and the other runner when you're exactly one kilometre apart, and also measures the time it takes for a light wave to cover that distance. By the time a light wave can travel that distance, of course, you will be a little more than one kilometre from where it started, because you're running away from the light. So in order to get to you, it would have to travel one kilometre, plus a little bit, at the speed of light.

Now let's say that you measure the same thing at the same time. You see that the person with the flashlight is running away from you, and is exactly one kilometre away. The light will approach you at exactly the speed of light, and it has to cover exactly one kilometre. It doesn't have to cover a little more than a kilometre, like it did when someone was watching from the sidelines, because now the light is moving at exactly the speed of light from your point of view; and you're not running away from yourself.

What this all means is that you and the person on the sidelines will come up with different answers when you measure the distance between you and the other runner. There are similar setups for equally disturbing results. Two people, who are equally sane but travelling at different speeds, can disagree on which order things happened in. One person can see A and then B, while a different person sees B and then A. Which one is right? According to the principle of relativity, they're both right. The order in which things happen... depends on your point of view.

Einstein's solution to this problem is simply to define distance and time differently. The only way to accomodate the constant speed of light is to accept that distance and time are influenced by motion. To make a long story short, if you watch an object move past you at extremely high speed, you will see two strange things: distances are smaller, and time moves more slowly. If a train goes past you at something near the speed of light -- which is extremely unlikely, by the way -- it will appear contracted, like an accordion. If you look closely at the passengers in the train, you'll notice that their watches are moving slowly. Their hearts are beating slowly. They're talking slowly. And when they talk, the resulting sound waves move more slowly than yours.

For the people in the train, of course, things seem completely normal. Unless they look out the window, and they see you all squished up like you've been crushed from the sides. They'll notice that your wristwatch is moving slowly, your heart is beating slowly, and so on. And this isn't just Einstein seeing this; that's really what happens. Nobody noticed that it was happening until Einstein figured it out in his head -- but that's is only because light speed is so much faster than trains and planes and rockets. That means that these length contraction and time dilation effects are extremely small. But they do always happen, and in high speed environments like particle accelerators, they're quite evident.

So that's Einstein's solution to the light speed paradox, and it's called the special theory of relativity. All we have to do is give up the idea that distance and time are constant, and accept that they look different from moving points of reference. The same laws still apply everywhere, so the principle of relativity still holds; the big difference is that the laws no longer agree with our intuition as well as Newton's laws did.

I mentioned that special relativity created a problem. The problem is pretty simple: if you're on the train, and I'm on the ground, I see your heart beating slowly; if time is passing very slowly for you, then I can safely predict that you will live longer than me. Meanwhile, you see my heart beating slowly, and you conclude that I will outlive you. Who's right?

This is called the twin paradox; it is a seemingly fatal contradiction that arises from the special theory of relativity. Of course, it's not really fatal. But it took Einstein to figure it out, just like it took Einstein to create the problem in the first place.

I'll probably tell you how he figured it out on a future episode of Mostly Mozart. But I'm not making any promises.