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Wondrous Wednesday 03: Constancy of the Speed of Light

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Summary

Explains what it means for the speed of light to be constant using train thought experiments. Discusses how this differs from naive expectations about relative velocities.

Transcript

0:00 Welcome to "Anna in the Air - Wondrous Wednesdays" where I talk about something
0:05 wondrous. Today I will talk about the constancy of the speed of light. So the
0:13 main goal is not to actually talk about the consequences or anything like that
0:18 or derive it, but simply to try to explain what it actually means. So I'll
0:27 first give you the example that seems intuitively clear but is wrong. Namely,
0:36 you're on a train, okay, and it's moving at 10 miles an hour, slow train, but it's a
0:45 really long train, like 200 miles long, okay, and it's all one smooth thing so
0:53 you can actually drive a car along it. Right, so you've got one person at the
0:58 end of the train
1:01 just kind of standing there and then another person in the car driving and it
1:10 goes at 60 miles an hour for an hour and then it comes back. So it's traveled a
1:17 total of 120 miles and it has taken two hours to do that and everything's fine.
1:26 This is all from the perspective of the train. So you're just in this train, you
1:31 don't know anything about the outside world, it's all smooth going, the person
1:36 at the end hasn't moved, the car person has gone and come back. Constant speed of
1:41 60 miles an hour. Good, wonderful, and that's perfectly fine. That never changes
1:47 like anything that you're sort of not moving with respect to, we'll see the
1:55 kind of same kind of stuff. All right, now you and the next picture, this is the
2:06 wrong one, is you have somebody outside of the train and what they see is the
2:14 train moving at 10 miles an hour and they see the car going six, you know,
2:19 going along and then coming back and so when the car is going away from from the
2:26 end of the train at 60 miles an hour it's also going an extra 10 miles an
2:31 hour from the outside of the train because it's moving along with the train
2:35 so that's 70 miles an hour and then when it's coming back you subtract the motion
2:42 of the train to get 50 miles an hour so from the perspective outside the train
2:47 it's going 50 miles an hour so like if you measure the distance that's actually
2:51 traveled outside of the train after one hour will have gone 70 miles and then on
3:00 its return trip it would have traveled 50 miles and so it will have gone at a
3:04 total of 20 miles which is also what the person at the end of the train has
3:08 traveled after two hours because the train is going 10 miles an hour that
3:14 makes perfect sense hopefully and it's completely wrong well at least if the
3:22 car is actually a light photon going at the speed of light so the speed of light
3:30 is a very fast very large number I think it's like 670 million miles per hour
3:37 but you can still just think of it as like the 60 miles an hour kind of thing
3:43 in the train so the trains may be going a six to the speed of light and then
3:49 you're talking about the speed of light it's fine whatever so anyway using the
3:54 smaller numbers the idea that the constancy of the speed of light is that
4:02 so this picture I just talked about where it's going 70 and then 50 from the
4:09 external perspective it's not it's going 60 from the external perspective and
4:13 that is weird because it's not so the person inside the train sees it going 60
4:20 and 60 person outside the chain sees it going 60 and 60 but the person inside
4:25 the train is actually moving towards the car from the external perspective right
4:32 so and that's that's the bizarre bizarre thing about the whole thing now the
4:43 basic resolution of this well first of all the reason the speed of light is is
4:50 constant why we take that is it basically comes out of the
4:54 electromagnetic wave equations that you have this constant speed and then they
4:59 verified it with experiments and lots of experiments so fairly fundamentally
5:06 accepted fact by this point in time and and so you know there's some
5:15 consequences of this basically the way we measure things depends on kind of the
5:23 motion of stuff so basically the motion of things length contracts and time gets
5:34 slower and it's a reciprocal perspective so that you know person on the train
5:41 will see the things outside going slower and being contracted and the people
5:47 outside the chain will see stuff in the train being contracted and going slower and so
5:54 you know there's lots of computations you can do a nice setup for like deriving
6:03 the say the time dilation is you have a kind of a bouncing clock mirror but
6:10 instead of going along in the same direction as the train it's just sitting
6:14 on the train and then because there's no nothing funny going about the vertical
6:20 direction you actually get kind of a triangular path and you can compute the
6:25 time dilation from that if you want to see it you can look up time dilation on
6:33 Wikipedia it's cool and then because a horizontally laid clock would you know
6:46 also have to kind of click in the same way the vertical I mean now that doesn't
6:53 have a vertical thing and so now the length contraction gets involved and so
6:57 that's kind of how you can derive both the length and the time factors yeah
7:04 usually involved a whiteboard I don't have one for a podcast so anyway that's
7:09 the setup of the constant CS speed of light that's what that means next time
7:13 I'll hopefully talk about the notion of simultaneity what is at what is happening
7:21 at the same kind of instant from a person's perspective that has a great
7:27 deal of importance and relativity and then that ties up with in quantum
7:32 mechanics how you you might think there is a universal now because of various
7:39 things and that conflicts with this relativity and I'll talk about that
7:44 maybe in two weeks all right so that was your wondrous Wednesday just the most
7:52 important thing is probably to accept that you know the the going forward and
7:59 backwards from the naive perspective that that makes sense and then you can
8:04 appreciate how weird it is that the speed of light is constant