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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
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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-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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