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https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t0.0 | x6YWpe9xHMg | Hello everyone and welcome to the biggest ideas in the universe. This is one of our Q&A sessions. | 0 | 6.24 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t6.24 | x6YWpe9xHMg | I'm your host Sean Carroll and today we're going to be doing the Q&A associated with idea number three, | 6.24 | 12.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t12.040000000000001 | x6YWpe9xHMg | force, energy, and action. So as I go through these Q&A videos, I am moving away more and more | 12.04 | 19.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t19.56 | x6YWpe9xHMg | from the idea of specifically going down question by question and more and more toward a theory of | 19.56 | 24.72 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t24.72 | x6YWpe9xHMg | using the questions to inspire me to elaborate on things that maybe I glossed over or simply forgot | 24.72 | 32.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t32.2 | x6YWpe9xHMg | to talk about when I did the original video. This is the downside of having a very casual, | 32.2 | 36.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t36.76 | x6YWpe9xHMg | non-polished, non-rehearsed approach is that sometimes there are things I wanted to say and | 36.76 | 41.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t41.4 | x6YWpe9xHMg | I just forgot to say them. Also in this Q&A I'm going to use the opportunity a few people have asked | 41.4 | 46.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t46.56 | x6YWpe9xHMg | how I actually make the videos. So I will be at the end of this Q&A talking a little bit about the | 46.56 | 52.48 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t52.48 | x6YWpe9xHMg | setup and the technology that goes in to actually making the videos. If you want to stick around for | 52.48 | 56.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t56.44 | x6YWpe9xHMg | that, I thought I was sticking at the end because many of you couldn't care less. So clean up. In | 56.44 | 61.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t61.919999999999995 | x6YWpe9xHMg | other words, what are the things that I didn't talk about in the actual video that I want to talk | 61.92 | 66.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t66.96 | x6YWpe9xHMg | about? The most important thing is nothing very profound that I have to say, but remember we were | 66.96 | 72.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t72.4 | x6YWpe9xHMg | talking about the Newtonian versus Laplacian paradigms, right? So here is a particle at some point X. | 72.4 | 79.8 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t79.8 | x6YWpe9xHMg | This is X0 equals 0. That was another question that was healthfully answered. 0 is just a way of | 79.8 | 91.24 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t91.24 | x6YWpe9xHMg | saying 0 and T0. Then at some other time T1, the particle is located at X1. In the least action | 91.24 | 102.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t102.84 | x6YWpe9xHMg | way of doing things, we say of all the paths you could traverse between X0 and X1 and between time | 102.84 | 109.48 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t109.48 | x6YWpe9xHMg | T0 and T1, what is the one that minimizes this quantity called the action? And all I wanted to do | 109.48 | 116.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t116.28 | x6YWpe9xHMg | was to sort of highlight the question, how does it know? This is the big issue with the miraculous | 116.28 | 125.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t125.88 | x6YWpe9xHMg | feeling that we have about the principle of least action. So we're saying that I don't tell you the | 125.88 | 133.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t133.16 | x6YWpe9xHMg | initial velocity of the particle. I don't tell you the final velocity. I just tell you where it starts | 133.16 | 137.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t137.4 | x6YWpe9xHMg | and when it ends. I tell you when it starts and when it ends. And somehow the procedure for figuring | 137.4 | 145.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t145.07999999999998 | x6YWpe9xHMg | out all of the different ways of getting from here to there is that had I gone on another path | 145.08 | 152.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t152.12 | x6YWpe9xHMg | that is not the actual physical one. The action, this quantity that we defined, action is an integral, | 152.12 | 163.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t163.16 | x6YWpe9xHMg | if that's okay, the sum over all the different moments of time of kinetic minus potential energies. | 163.16 | 169.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t173.0 | x6YWpe9xHMg | Over time, okay. So, and then you minimize the action, you get the least action to get the actual | 173 | 179.32 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t179.32 | x6YWpe9xHMg | path. It seems like precognition is going on here, right? It seems like the particle leaves at point | 179.32 | 187.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t187.88 | x6YWpe9xHMg | X0 at time T0 and it immediately has a velocity, right? Like there's some velocity that the particle | 187.88 | 194.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t194.28 | x6YWpe9xHMg | actually has right at that moment and following that velocity in the Newtonian paradigm, we would | 194.28 | 199.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t199.95999999999998 | x6YWpe9xHMg | say at every moment we chug forward using f equals m a and we get to the final point. But in this | 199.96 | 205.24 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t205.24 | x6YWpe9xHMg | picture, we say, well, it could have taken other paths. It could have gone on other velocities and | 205.24 | 210.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t210.20000000000002 | x6YWpe9xHMg | done other things. But then the this integrated quantity called the action would have been higher. | 210.2 | 216.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t216.36 | x6YWpe9xHMg | So it didn't take those. It took the one with the least action, even though the action is this | 216.36 | 220.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t220.92000000000002 | x6YWpe9xHMg | non local quantity, this quantity that can only be evaluated by already knowing what the path is, | 220.92 | 227.48 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t227.48 | x6YWpe9xHMg | right? How did it know? What to do? So I don't want to, there's no answer to this in a simple way. | 227.48 | 235.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t235.16 | x6YWpe9xHMg | It's just to point out that the question is badly phrased. You know, it didn't know. The particle | 235.16 | 241.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t241.07999999999998 | x6YWpe9xHMg | didn't guess. The particle doesn't think about every single path ahead of time and then choose | 241.08 | 247.24 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t247.23999999999998 | x6YWpe9xHMg | to go on the path of least action. There is a way the particle moves and that way can be specified | 247.24 | 254.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t254.36 | x6YWpe9xHMg | by saying of all the paths, it is the one with the least action. So one way of thinking about this | 254.36 | 259.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t259.56 | x6YWpe9xHMg | is, you know, I said in words that minimizing the action gives us the same path as the Newtonian | 259.56 | 268.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t268.04 | x6YWpe9xHMg | way of doing things starting with f equals m a, but it's more specific than that. So let me talk | 268.04 | 273 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t273.0 | x6YWpe9xHMg | about minimizing a path. What does it mean to minimize something? Minimize the action. | 273 | 278.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t278.84 | x6YWpe9xHMg | Minimize in math terms, how do we find the minimum of any function? Okay, so let's imagine | 278.84 | 287.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t287.88 | x6YWpe9xHMg | the much simpler function f of x as a function of x. So this is not x, the position is just x | 287.88 | 295 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t295.0 | x6YWpe9xHMg | sum variable, we don't know what it is. And someone has a function that does something like this. | 295 | 298.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t299.55999999999995 | x6YWpe9xHMg | How do we know where the minimum of that function is? Well, you can see it. There it is. You and I | 299.56 | 304.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t304.92 | x6YWpe9xHMg | can see it just by looking, but math can't see it or a computer can't see it. How would we | 304.92 | 310.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t310.84000000000003 | x6YWpe9xHMg | mathematically figure out where the minimum is? Again, I should have said this a long time ago, | 310.84 | 315.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t315.56 | x6YWpe9xHMg | but the point is we know that the slope of that curve is the derivative, the change in f as we | 315.56 | 324.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t324.68 | x6YWpe9xHMg | change x. And the point about the minimum is that at the minimum, the slope d f dx equals zero. That's | 324.68 | 335.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t335.08 | x6YWpe9xHMg | the mathematical way of saying where the minimum is. The minimum is the point, if it's a minimum, | 335.08 | 341.32 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t341.32 | x6YWpe9xHMg | then at the minimum, the slope is zero. So the derivative is zero. So to solve for the minimum | 341.32 | 346.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t346.76 | x6YWpe9xHMg | mathematically, you take the function f, you differentiate it, you find its derivative, you set | 346.76 | 352.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t352.52 | x6YWpe9xHMg | the derivative equal to zero, and then you solve that equation. That's an equation, some expression | 352.52 | 356.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t356.84 | x6YWpe9xHMg | in terms of x, the whole thing equals zero, you solve it, you find the minimum. So that is what | 356.84 | 362.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t362.52 | x6YWpe9xHMg | you do up here, of course, for the least action principle, you take the action, but the action | 362.52 | 368.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t368.03999999999996 | x6YWpe9xHMg | is not a function of one variable, like x. It's a function of all the different paths you could | 368.04 | 372.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t372.68 | x6YWpe9xHMg | go on, right? Here's another path you could have gone on. So you have to do a much more complicated | 372.68 | 379.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t379.16 | x6YWpe9xHMg | integral. This is the subject called the calculus of variations, the idea that you have an infinite | 379.16 | 385.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t385.08000000000004 | x6YWpe9xHMg | dimensional space, the space of all possible paths. But nevertheless, you can find one path and then | 385.08 | 390.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t390.76000000000005 | x6YWpe9xHMg | take the derivative of some quantity, like the action, as you change the path by a little bit. In | 390.76 | 396.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t396.28000000000003 | x6YWpe9xHMg | fact, the mathematically rigorous way to define it is to basically turn that infinite dimensional | 396.28 | 401.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t401.16 | x6YWpe9xHMg | thing into a finite dimensional thing, where you just change the path in one direction at a time, | 401.16 | 406.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t406.68 | x6YWpe9xHMg | and set that equal to zero everywhere. So you can do this little bit of calculus, this little bit | 406.68 | 412.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t412.2 | x6YWpe9xHMg | right here. Look at this, I'm learning to change colors. So this little bit of calculus can be done | 412.2 | 418.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t418.12 | x6YWpe9xHMg | on the space of all paths, not just on individual curves. So that's how you find the path of least | 418.12 | 424.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t424.76 | x6YWpe9xHMg | action. But then the way that we do this, how do we, there is a cute mathematical way of | 424.76 | 430.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t431.64 | x6YWpe9xHMg | letting you know that we're differentiating with respect to an infinite dimensional thing, | 431.64 | 435.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t435.56 | x6YWpe9xHMg | rather than a finite dimensional thing, which is that rather than using the letter D for derivative, | 435.56 | 440.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t440.44 | x6YWpe9xHMg | we use the Greek letter delta, the lowercase delta. So the functional derivative, as we call it, | 440.44 | 446.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t452.04 | x6YWpe9xHMg | of the action is written d s s is the action. I don't know if I said that. I don't know again, | 452.04 | 460.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t460.04 | x6YWpe9xHMg | why is the letter S used? There's probably some reason lost to history, but d s and I'm not going | 460.04 | 466.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t466.28000000000003 | x6YWpe9xHMg | to delta s rather, delta path. So for path, I was going to write the word path, but that's a little | 466.28 | 472.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t472.84000000000003 | x6YWpe9xHMg | bit too casual even for me. Let me write x of t. Okay, this is a fancy language for simply saying | 472.84 | 482.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t482.12 | x6YWpe9xHMg | we differentiate with respect to all possible paths, that number called the action, we set that | 482.12 | 486.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t486.92 | x6YWpe9xHMg | equal to zero. And the point is we get an equation, okay, we get an equation, and that equation turns | 486.92 | 494.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t494.04 | x6YWpe9xHMg | exactly into Newton's laws. That's how you prove the equivalence between the least action way of | 494.04 | 501.8 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t501.8 | x6YWpe9xHMg | doing classical mechanics and the Newtonian way of doing classical mechanics. You have this | 501.8 | 506.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t506.20000000000005 | x6YWpe9xHMg | formalism that sounds very abstract, you have all these paths and infinite dimensional space of all | 506.2 | 510.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t510.68 | x6YWpe9xHMg | the different possible paths, you figure out how to differentiate with them, there's a lot of math | 510.68 | 514.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t514.68 | x6YWpe9xHMg | involved, you take math classes, good for you, but at the end, the equation that comes out from | 514.68 | 520.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t520.76 | x6YWpe9xHMg | minimizing the action is the statement that at every single point along the trajectory, the particle | 520.76 | 527.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t527.0799999999999 | x6YWpe9xHMg | obeys Newton's laws of motion. Okay, so that's a way of easing your anxiety about the fact that | 527.08 | 534.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t534.8399999999999 | x6YWpe9xHMg | the particle seems to know ahead of time which path to take. It's not that it thinks about every | 534.84 | 539.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t539.96 | x6YWpe9xHMg | single path and chooses the right one, it's that the condition that follow, that the path you follow | 539.96 | 545.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t545.4000000000001 | x6YWpe9xHMg | be the least action one is the same as the condition that you're obeying Newton's laws at every moment. | 545.4 | 551.32 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t551.32 | x6YWpe9xHMg | Okay, that's one thing to keep in mind. Here's another thing that you're probably thinking already, | 551.32 | 557.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t557.5600000000001 | x6YWpe9xHMg | as you watch me write these things, sure, the minimum of this function has the feature that | 557.56 | 565.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t565.16 | x6YWpe9xHMg | its derivative is zero, but guess what, a point where the function is a local maximum also has that | 565.16 | 572.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t572.28 | x6YWpe9xHMg | feature where the slope is exactly zero. So the condition that the action have zero derivative, | 572.28 | 580.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t580.04 | x6YWpe9xHMg | zero slope in the space of all possible paths, doesn't pick out the minimum uniquely, it just says | 580.04 | 586.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t586.68 | x6YWpe9xHMg | it's a place where the function isn't changing instantaneously momentarily, it could be a minimum | 586.68 | 592.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t592.28 | x6YWpe9xHMg | or a maximum or in higher numbers of dimensions, it could be what we call a critical point where | 592.28 | 597 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t597.0 | x6YWpe9xHMg | in some directions it could be going down, in other directions it could be going up, but it's | 597 | 601.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t601.4 | x6YWpe9xHMg | momentarily stationary. So sometimes this is called a saddle point, if you think of literally a saddle | 601.4 | 607.64 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t607.64 | x6YWpe9xHMg | that is sort of this kind of shape in two dimensions, right, then if you're right here, you're at a | 607.64 | 614.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t614.04 | x6YWpe9xHMg | critical point where everything is flat, you're at a flat location on the surface, but in this | 614.04 | 618.6 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t618.6 | x6YWpe9xHMg | direction things are going up, in this direction things are going down, right, so you're at a mixed | 618.6 | 625.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t625.16 | x6YWpe9xHMg | point where in some directions it's up, some directions is down, but momentarily everything is flat. | 625.16 | 629.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t630.44 | x6YWpe9xHMg | How do you know that the actual path you're going to take is not just some extreme, some | 630.44 | 636.2 |
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