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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
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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
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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
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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,
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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
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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
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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,
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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
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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
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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
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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.
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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,
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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
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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
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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
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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
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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,
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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
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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