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• 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.

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PROF. MERRIFIELD: Mach's Principle. As in Mach number, as in the speed of sound.

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# Mach's Principle - Sixty Symbols

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林宜悉 posted on 2020/03/30
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