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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-t1274.36 | x6YWpe9xHMg | it's defined by where it is. A field is everywhere, but it's defined by how big it is at every single | 1,274.36 | 1,281.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1281.96 | x6YWpe9xHMg | point. So something like this formula we have for the kinetic energy minus the potential energy | 1,281.96 | 1,288.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1288.8400000000001 | x6YWpe9xHMg | seems not up to the task because it's a function of x and v, the position and velocity, whereas here, | 1,288.84 | 1,296.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1296.04 | x6YWpe9xHMg | we can work with phi, which is itself a function of position and time, and we can also work with | 1,296.04 | 1,302.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1302.04 | x6YWpe9xHMg | various derivatives of phi. So we can work with the, what we call the partial derivative. This is | 1,302.04 | 1,308.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1308.84 | x6YWpe9xHMg | sorry, too much math here, but now that phi depends on both space and time, rather than just saying | 1,308.84 | 1,314.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1314.04 | x6YWpe9xHMg | the derivative of phi, we have to say the derivative of phi with respect to space, and the derivative | 1,314.04 | 1,320.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1320.4399999999998 | x6YWpe9xHMg | of phi with respect to time, etc. And so we use these weird curly D's, I think that it was lignets | 1,320.44 | 1,326.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1326.76 | x6YWpe9xHMg | who invented these to let you know that we're doing a partial derivative of derivative in one | 1,326.76 | 1,331.32 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1331.32 | x6YWpe9xHMg | particular direction at a time in space time. So we have a whole bunch of things that we can work | 1,331.32 | 1,336.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1336.44 | x6YWpe9xHMg | at, and every single one of these is a function of both space and time. So the reason why this works, | 1,336.44 | 1,344.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1344.2 | x6YWpe9xHMg | so nicely in field theory, is the action s is given by, in our old formula, or go to a way of | 1,344.2 | 1,353.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1353.0800000000002 | x6YWpe9xHMg | doing it, the integral of something called the Lagrangian. So we wrote kinetic minus potential, | 1,353.08 | 1,359.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1359.08 | x6YWpe9xHMg | and that was a particular form, but this function, kinetic energy minus potential energy, is what | 1,359.08 | 1,367.32 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1367.32 | x6YWpe9xHMg | is called the Lagrangian. And that was for a point particle, it looks like I've written POH, | 1,367.32 | 1,376.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1376.12 | x6YWpe9xHMg | but I really haven't. Potential. In field theory, the Lagrangian itself L is going to be an integral | 1,376.12 | 1,388.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1388.36 | x6YWpe9xHMg | of some function, some function of space over all of space. So at every point in space, | 1,388.36 | 1,403.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1405.24 | x6YWpe9xHMg | I take these quantities, the field and its derivatives, I construct some function, I multiply the field | 1,405.24 | 1,411.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1411.3999999999999 | x6YWpe9xHMg | together, I multiply the derivatives of the field together, I do all these things that I want to do, | 1,411.4 | 1,415.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1415.56 | x6YWpe9xHMg | and then I integrate over all of space, call that the Lagrangian, and then I integrate over all | 1,415.56 | 1,421.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1421.08 | x6YWpe9xHMg | time the Lagrangian, I call that the action. So this function is called the Lagrange density, | 1,421.08 | 1,426.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1430.28 | x6YWpe9xHMg | but because we are always lazy, and because we literally are always working with the Lagrange | 1,430.28 | 1,434.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1434.6799999999998 | x6YWpe9xHMg | density, we just call the Lagrange density the Lagrangian. So the technical, careful thing is | 1,434.68 | 1,442.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1442.44 | x6YWpe9xHMg | that the Lagrangian is the thing you put and integrate over time to get the action. Lagrange | 1,442.44 | 1,448.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1448.1200000000001 | x6YWpe9xHMg | density is the thing you integrate over all of space to get the Lagrangian, but we actually just | 1,448.12 | 1,452.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1452.52 | x6YWpe9xHMg | use the terminology informally that the Lagrange density we call the Lagrangian. So the point is, | 1,452.52 | 1,458.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1458.68 | x6YWpe9xHMg | all of this is to say, the Lagrangian to a particle physicist with quantum field theorists, | 1,458.68 | 1,465.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1465.96 | x6YWpe9xHMg | oops, yeah, I had it right, Lagrangian. Curly L, it is often written, and it is a function of | 1,465.96 | 1,475.32 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1475.32 | x6YWpe9xHMg | phi and its derivatives, the derivative of phi with respect to space, derivative of phi with | 1,475.32 | 1,480.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1480.3600000000001 | x6YWpe9xHMg | respect to time, and also the derivative of other fields, because there's more than one field in | 1,480.36 | 1,486.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1486.52 | x6YWpe9xHMg | the world, right? So maybe you have a field psi, I don't want to call it a psi because that's the | 1,486.52 | 1,491.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1491.88 | x6YWpe9xHMg | quantum wave function that gets confusing. Ada is a field, and Ada has derivatives with respect to | 1,491.88 | 1,498.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1498.0400000000002 | x6YWpe9xHMg | space, and Ada has derivatives with respect to time, and there's a large number of fields, | 1,498.04 | 1,502.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1503.88 | x6YWpe9xHMg | and they're derivatives, okay? So Lagrangian is a function of many, many things, but it's just one | 1,503.88 | 1,510.76 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1510.7600000000002 | x6YWpe9xHMg | function, it's just one particular combination of all those different fields. If you have a huge | 1,510.76 | 1,517 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1517.0 | x6YWpe9xHMg | collection of fields, then if you just wrote down Newtonian looking equation of motion, | 1,517 | 1,522.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1522.52 | x6YWpe9xHMg | every field would have its own independent equation of motion, whereas in the Lagrangian | 1,522.52 | 1,528.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1528.52 | x6YWpe9xHMg | way of doing things, you take all the fields, you combine them into some function to make a | 1,528.52 | 1,533 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1533.0 | x6YWpe9xHMg | Lagrangian, you calculate from that Lagrangian the action, you minimize the action, where to go, | 1,533 | 1,540.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1540.68 | x6YWpe9xHMg | delta s equals zero, right? There you go, you minimize this action, and that's all of your | 1,540.68 | 1,545.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1545.56 | x6YWpe9xHMg | equations of motion, because you're minimizing it with respect to field one, phi, and then field two, | 1,545.56 | 1,551.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1551.1599999999999 | x6YWpe9xHMg | Ada, and then field three, omega, or whatever it is, you separately minimize this function, | 1,551.16 | 1,556.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1556.2 | x6YWpe9xHMg | the action, with respect to all the fields, and all those separate minimizations give you | 1,556.2 | 1,561.72 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1561.72 | x6YWpe9xHMg | different equations of motion. So if you go down here, what you would say is that delta s, delta phi | 1,561.72 | 1,570.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1570.36 | x6YWpe9xHMg | equals zero, delta s, delta Ada equals zero, dot dot dot. So from one function, the Lagrangian, | 1,570.36 | 1,579.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1579.9599999999998 | x6YWpe9xHMg | you get all the different equations of motion, that's an enormous increase in simplicity and power, | 1,579.96 | 1,587.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1587.1599999999999 | x6YWpe9xHMg | and so what that means is when you're guessing new theories of nature, when you're being a | 1,587.16 | 1,592.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1592.84 | x6YWpe9xHMg | modern particle physicist or quantum field theorist, the thing that you're doing is writing down | 1,592.84 | 1,597.72 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1597.72 | x6YWpe9xHMg | new Lagrangian. So you're inventing new fields, and you're inventing new ways for them to interact | 1,597.72 | 1,602.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1602.3600000000001 | x6YWpe9xHMg | with each other. If you talk about the Higgs boson, what did Higgs and his friends, Angler, | 1,602.36 | 1,607.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1607.88 | x6YWpe9xHMg | and Brout, and others actually do, they wrote down a new Lagrangian for a new field, and they showed | 1,607.88 | 1,613.4 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1613.4 | x6YWpe9xHMg | that this new Lagrangian would lead to certain new features of the world, like breaking of symmetries | 1,613.4 | 1,619 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1619.0 | x6YWpe9xHMg | and things like that, and then many years later, that actual prediction that there was a particle | 1,619 | 1,624.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1624.04 | x6YWpe9xHMg | associated with that field was discovered in the Large Hadron Collider. So one of the reasons why | 1,624.04 | 1,630.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1630.28 | x6YWpe9xHMg | Lagrangians and therefore actions are so important is that the job of the modern quantum field | 1,630.28 | 1,637.8 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1637.8 | x6YWpe9xHMg | theorist is to write down the right Lagrangian of the world, at least to the extent that quantum | 1,637.8 | 1,645.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1645.1599999999999 | x6YWpe9xHMg | field theory is the right description of the world. So far we think it is, but there's some hints | 1,645.16 | 1,649.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1649.08 | x6YWpe9xHMg | from gravity and other things that maybe it's not complete. But anyway, this is how modern cutting | 1,649.08 | 1,654.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1654.1999999999998 | x6YWpe9xHMg | edge field theorists think. They think in terms of Lagrangians. That's what I wanted you to know. | 1,654.2 | 1,658.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1658.84 | x6YWpe9xHMg | So sorry about, you know, this got Matthew. Sorry about that. I don't want to get too Matthew. The | 1,658.84 | 1,663.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1663.1599999999999 | x6YWpe9xHMg | point is the least action principle is not just a cool twist on Newtonian mechanics. It's an | 1,663.16 | 1,670.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1670.4399999999998 | x6YWpe9xHMg | extraordinarily powerful tool in modern physics, so we use it all the time. There's another reason, | 1,670.44 | 1,676.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1676.92 | x6YWpe9xHMg | I'm not going to go into it too much right now, but the other reason why the Lagrangians and the | 1,676.92 | 1,680.52 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1680.52 | x6YWpe9xHMg | action are great is because they let you implement symmetries very, very simply. If you have symmetries | 1,680.52 | 1,687.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1687.16 | x6YWpe9xHMg | like remember Galilean invariance, right, it doesn't matter where you are or how fast you're moving, | 1,687.16 | 1,692.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1692.28 | x6YWpe9xHMg | you can write down the Lagrangians that respect those symmetries and then the equations of motion | 1,692.28 | 1,696.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1696.92 | x6YWpe9xHMg | will respect them automatically. So again, just because this single function of Lagrangian is a | 1,696.92 | 1,701.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1701.96 | x6YWpe9xHMg | much simpler thing than a long list of equations of motion, it's a much more compact powerful way | 1,701.96 | 1,707.48 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1707.48 | x6YWpe9xHMg | of thinking. Okay, another question was quantum mechanics because look, when I'm drawing pictures | 1,707.48 | 1,717.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1717.56 | x6YWpe9xHMg | like this, which I've now drawn over and over again, x, t, point, point, path, but then also other | 1,717.56 | 1,726.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1726.12 | x6YWpe9xHMg | paths. There's another path, there's another path, okay, many, many little paths doing different things. | 1,726.12 | 1,732.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1734.4399999999998 | x6YWpe9xHMg | That's the picture that you draw associated with the principle of least action. And then the thing | 1,734.44 | 1,739.24 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1739.2399999999998 | x6YWpe9xHMg | that you say is the there's only one of those actual paths that is taken, the one where the | 1,739.24 | 1,744.2 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1744.1999999999998 | x6YWpe9xHMg | action is minimized, but you've probably heard of Feynman, Richard Feynman, | 1,744.2 | 1,749.64 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1749.64 | x6YWpe9xHMg | some over histories. What Feynman realized was that in quantum mechanics, you know, in quantum | 1,749.64 | 1,761.48 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1761.48 | x6YWpe9xHMg | mechanics, what we talk about in the traditional way of talking about it is forget about particles, | 1,761.48 | 1,766.04 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1766.0400000000002 | x6YWpe9xHMg | forget about positions, we have a wave function, Schrodinger's wave function, we evolve it forward | 1,766.04 | 1,771.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1771.0800000000002 | x6YWpe9xHMg | or backward in time, those of you who are not familiar by my book, something deeply hidden, | 1,771.08 | 1,775.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1775.96 | x6YWpe9xHMg | I'll write that down, something deeply hidden, you can read about this. Ah, but I have to write | 1,775.96 | 1,782.44 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1782.44 | x6YWpe9xHMg | the word correctly, my own book, right? Something to be honest, I think that the sum over histories | 1,782.44 | 1,788.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1788.68 | x6YWpe9xHMg | is only mentioned very, very briefly, I don't try to explain it in this book, but quantum mechanics | 1,788.68 | 1,792.84 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1792.8400000000001 | x6YWpe9xHMg | and wave functions, the traditional way of doing it, I definitely do explain it great length. | 1,792.84 | 1,797.64 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1798.44 | x6YWpe9xHMg | So if you want the traditional way, read that book. The sum over histories way is, you know, | 1,798.44 | 1,802.68 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1802.68 | x6YWpe9xHMg | even though what we care about is the wave function, let's pretend that what we care about is a | 1,802.68 | 1,809 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1809.0 | x6YWpe9xHMg | particle, okay? Let's care about their, let's pretend there really is a particle, let's pretend | 1,809 | 1,813.56 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1813.5600000000002 | x6YWpe9xHMg | the particle really has a location in space as a function of time, and let's pretend that there's | 1,813.56 | 1,818.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1818.3600000000001 | x6YWpe9xHMg | all these different paths it could take. And let's say, let's imagine that, because it's now quantum | 1,818.36 | 1,824.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1824.28 | x6YWpe9xHMg | mechanics, not classical mechanics, that it takes all of the paths, that the actual quantum evolution | 1,824.28 | 1,831 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1831.0 | x6YWpe9xHMg | of the particle is that all of these paths are actually taken. But when we take all these paths, | 1,831 | 1,837.96 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1837.96 | x6YWpe9xHMg | what we do is we calculate not the, we calculate the action to all those paths, but we're not done | 1,837.96 | 1,843.88 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1843.88 | x6YWpe9xHMg | yet, we don't just minimize the action, we add up a contribution, and again, this is a little | 1,843.88 | 1,849.16 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1849.96 | x6YWpe9xHMg | more math than you need, we write down a contribution e, the number e, to the power i, the square root | 1,849.96 | 1,858.36 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1858.36 | x6YWpe9xHMg | minus one times the action, this is the number that we integrate over all paths. We sum them up, | 1,858.36 | 1,868.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1868.12 | x6YWpe9xHMg | that's what sum means integral and sum are the same thing, and integral is just a continuous version | 1,868.12 | 1,872.92 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1872.9199999999998 | x6YWpe9xHMg | of the discrete sum. So this is an integral over all paths of this number e to the i times the action. | 1,872.92 | 1,879.72 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1879.7199999999998 | x6YWpe9xHMg | And what this means is that when the action is near a minimum, right, when it's near this location | 1,879.72 | 1,885 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1885.0 | x6YWpe9xHMg | that is classically allowed, the least action path, paths that are almost least action path, | 1,885 | 1,892.28 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1892.28 | x6YWpe9xHMg | but not quite, will give almost the same action, right? If it's, if the derivative of the path of | 1,892.28 | 1,900.12 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1900.12 | x6YWpe9xHMg | the action is zero, that means that nearby paths have almost the same action. So near the classical | 1,900.12 | 1,907.08 |
https://youtu.be/x6YWpe9xHMg | The Biggest Ideas in the Universe | Q&A 3 - Force, Energy, and Action | 2020-04-12T15:32:41Z | x6YWpe9xHMg-t1907.08 | x6YWpe9xHMg | path, this number s is almost the same for nearby paths, and therefore when you add them up, they | 1,907.08 | 1,913.32 |
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