字幕表 動画を再生する 英語字幕をプリント PROF. MERRIFIELD: Mach's Principle. As in Mach number, as in the speed of sound. Well, let's start off, back up a little bit. I want to talk about centripetal force and centrifugal force 'cause they're kind of sources of much confusion and amusement. People commonly talk about centrifugal force, and then you learn a little bit of physics, and then you get told actually there's no such thing as centrifugal force; there's just a thing called centripetal force. And then, if you go a little bit further down the line, maybe you think, "Well, maybe there's both." So we should talk about them both actually. So, a bit of latin: Fugo, fugare means "to flee". So you're fleeing the center. Centrifugal force is fleeing the Center. Centripetal Force: Peto is "I seek", so it's actually seeking the center. So one is fleeing, the other seeking. And so one is going away from the center, the other is coming towards the center. Let's start with a simple thought experiment. What I want is a cylindrical room, with you standing in it, and let's put you on a pair of rollerskates, just to make life simple. And then I'm going to start the room rotating around its central axis. So what's gonna happen? Well, what's gonna to happen is that as the room rotates you're gonna start moving around as well. But remember, unless the force is being applied to you, your natural tendency is you'll carry on in a straight line. So if you're on rollerskates, then that's probably not much by way of friction, which means you'll just slide on the floor, so, as the thing starts to rotate around, you start traveling as the thing rotates, but you'll travel along in a straight line, so you'll head off in this direction. You're going in a straight line. BRADY HARAN: Till I whack into the wall? MERRIFIELD: And then you're gonna hit the wall, and that's the interesting thing that, actually, at the point where you hit the wall, suddenly you're kind of pressed against the wall as the thing rotates, and as it rotates faster and faster you'll be pressed to the wall harder and harder. And that's why people think about centrifugal forces, because actually they're being pressed to the wall, so, from your perception, in this rotating room, there is a centrifugal force where you're being pushed outwards and you're being pressed against the wall and clearly, there's a centrifugal force. Whereas somebody who's just watching the room from above, as we are here, will say "Actually, no, there isn't a centrifugal force at all. What's going on "is that you wanted to travel in a straight line, but then this wall stopped you," "and that's actually a centripetal force." "The wall is pushing you towards the middle all the time." "And so, actually the force there is, you know, is pushing you inwards, there's a centripetal force," "which is keeping you going around in a circle as you're pressed against the wall." HARAN: Sounds like centripetal was right, then? MERRIFIELD: It is, kind of. Because that's the kind of the bigger picture view when you're outside the rotating reference frame. Whereas, you know, if you're in the rotating reference frame then centrifugal force is what's going on, but, in some sense, what's more fundamental is the rest of the universe, that's actually looking down on this thing seeing it rotate. HARAN: We do learn that for every force, there's like an equal and opposite, though, so doesn't it make sense that both are happening at the same time at that point? MERRIFIELD: Indeed. By the time you're pressed to the wall, you're neither being accelerated away from the wall or towards it, so there's kind of a balance of forces there. You can think of the centrifugal force is pushing you out, while the centripetal force is pushing you in, well, it all comes to the same thing. As you said, in some sense, that centripetal force is kind of more fundamental. In the centrifugal case, you're kind of being fooled: you think you're in a non-rotating room, right? And actually you're suddenly flung to the wall, and that's why you interpret it as a centrifugal force, and therefore you're being fooled because, although the things in the room around you don't appear to be rotating, because they're all rotating at the same speed you are, somebody looking down on this from above could say, "Actually, you know," "the whole thing is rotating and therefore the centripetal force is fundamentally what's going on." But that's where we get to Mach's Principle. Because the question you could ask is "How do you know you're rotating?" How do you know it's just not the rest of the universe rotating the other way? All the time when we were doing Relativity things we would always say, "you can't tell whether it's you moving forwards and something else stationary," "or you stationary and something else moving backwards;" "there was this kind of relativity there." So the obvious question is why isn't there a relativity here? Why isn't it equivalent to saying either the room's rotating and the rest of the universe is stationary, or the room stationary and the rest of the universe is rotating the other way? Because they both look the same to an outside observer. You know, they're both, one thing's rotating relative to the other. HARAN: I can answer that! MERRIFIELD: Okay... HARAN: If you created that scenario for me there, the person on the rollerskates wouldn't move. With the rest of the... but how does the universe know, right? You're right! You're absolutely right! But it means in some sense rotation is absolute, right? That actually you can tell the difference between whether the room is rotating and the rest of the universe is stationary, or whether the room is stationary and the rest of the universe is rotating by the fact whether or not on your rollerskates you get pushed to the outside. And that's what Mach's principle says, is that, "actually, the physics of the small scale depends on the large scale." That actually the entire universe is somehow influencing this room. So that you actually know that it's the room that's rotating and the rest of the universe is stationary, rather than the rest of the Universe that's rotating and the room's stationary. Somehow the two are talking to each other. HARAN: They're talking to each other and one's saying, "I'm the big guy here and you're the little guy, so you're the thing spinning, not me." MERRIFIELD: Exactly. Although, you know, in principle, you could make the entire universe rotate if you want to do. It'd be a lot of effort, but actually, you know, you could do it. But somehow they know which is the thing that's really rotating which is the thing that isn't. And that means somehow the physics of the large scale is affecting what's going on on the small scale. The reason why you know you're rotating is only by reference to the entire universe around you. And another statement of Mach's principle, which is kind of the same thing, is that if you actually made the entire universe rotate, including this room... you wouldn't be able to tell. Because then there's nothing for it to be rotating relative to. HARAN: Coming back to just the room in the universe, the simple version, MERRIFIELD: Yep. HARAN: Has has anyone got any idea how this... through what medium this information is communicated between the room and the Universe? MERRIFIELD: Not in detail. I mean, that's why this is a principle rather than a law, is that actually it's just something which we know has to be happening because we can tell when we're in a rotating room or when we're not, but what the mechanism is, is not entirely clear, at least in detail. This very much influenced Einstein when he was moving on from Special Relativity to General Relativity, 'cause clearly he was kind of thinking about reference frames, 'cause he'd done all that with Special Relativity. Then you come to this General Relativity case where he knew perfectly well, that actually if you're in a rotating room you know you were in a rotating room because you get flung to the walls. And that was what made him think that actually whatever is going on in General Relativity has to somehow have Mach's Principle imprinted in it. And, indeed, the laws of General Relativity say that what kind of effects the motion on the small scale depends on the distribution of mass all over the Universe. Because actually the curvature of space, the way that space is distorted on small scales, depends on the distribution of mass throughout the Universe. So actually in some sense sort of has Mach's Principle built into it because the what's going on on a very small scale in terms of particles being accelerated around by gravity, depends on how space has been distorted, which in turn depends on the distribution of mass throughout the Universe. So I think he was very much inspired by Mach's Principle to think about the things which then led to General Relativity. HARAN: I find it deeply disturbing that the Universe is talking to itself like this, and we have no idea how! [Cheesy Ringtone Plays] MERRIFIELD: It is! Somehow that information on the big picture of the Universe is somehow being communicated to the small scale. So Einstein got very excited. He was able to show, within General Relativity that there is this strange effect. That if you have, like, a pendulum just swinging here, and you put a sphere around it, and make the sphere rotate, that actually makes the pendulum start to process around. And so, because actually, effectively the rotating mass is kind of dragging space with it and that affects what's going on. So he was quite excited that actually he could show mathematically that actually f the universe really is rotating around an object it actually does have an influence on the object. So again there is this tie between what's going on on a large scale and what's going on on the small scale. But beyond those kind of very specific cases, I don't think anyone's tackling the big picture question of why Mach's Principle is true in general. HARAN: Thanks for watching this video. If you'd like to help the Sixty Symbols that little bit more, you can actually contribute on Patreon, just like the people whose name you're seeing on the screen at the moment have. 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