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