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Special RelativityPosted 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
Before that I'll have to explain the
And before --- 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 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
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, 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
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
What this all means is that you and the person on the sidelines will
come up with 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
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. |