Around 9:30 when the narrator begins listing the reasons why this is worth knowing, the reason that kept popping into my head was (while closely related to reasons 1 and 2) is that it shows that the Newtonian methodology is not necessary. I think finding a separate way of solving these equations shows that while they are both extraordinarily accurate, they are both inventions, and that other inventions that solve these problems might still yet be more useful and powerful, and maybe even simpler than either. To me that is the most exciting thing about a first encounter with the principle of least action, is it can make a person realize that our descriptions are provincial, and the possibility of a great discovery, even in the realms we think to have mastered, seems to still be possible.

Why does that graph remind me of the Jaws poster from the 70's?

Hi Physics Help. I really enjoyed this video and compliment you on your style in presenting the information. I can not believe that I never came across this Principal (not in high school or Engineering school) until I read that book "The Theoretical Minimum". As Jared points out above it ties nicely into Relativity and QM (I have not tackled String Theory yet). I am looking forward to viewing your other videos.

Hey thanks for the feedback. This is just the first video of a playlist (still in progress right now). In the "Finding the path of least action" videos, you'll find the equivalence to Newton's 2nd law is addressed. You're right about quantum, but I'm waiting until I actually cover the Hamiltonian to allude to quantum mechanics since that's what's more commonly used in quantum.

Principle of Least Action? Kinda sounds like my social life dude. :(

this is the first of your videos i have watched and oh god you're amazing. would love to be your subscriber

Been reading quantum mechanics and path integrals but couldn't figure out what s was. Thanks man!

All right, I see great confusion in this comment section, thanks to the misleading title. In mechanics, this principle should be called stationary action, not least action, since it isn't that. The easiest example is a hatmonic oscillator, you can easily sgow that for given boundary conditions staying still has less action than the actual motion of the object. THIS IS NOT THE PRINCIPLE OF LEAST ACTION, BUT THE PRINCIPLE OF STATIONARY ACTION. And there isn't a deep phylosophical depth behind why this works. It just turns out to be mathematically equvivalent to newtons laws. It actually has a connection with quantum mechanics, you can basicakly derive the stationary action from quantum mechanics, but that is a pretty advanced topic.

Answered exactly the questions I had about this concept.

Thanks for the simple explanation, brah

S, i believe, because historically this intergral was associated with length (ds) and that was denoted as ds, integrated S. And the idea of shortest path comes from Hygen's principle that light travels shortest distance. But its also L or H.

Thank you for posting these videos. They are extremely helpful.

Your video was very informative. Thanks!

Very well explain and helpful, Thank you !

Great informative video!

Really good introduction!

Thanks for the informative video! Can you please clarify something. From the equation I can conclude that having a small kinetic energy and high potential energy does not really describe the behaviour of the equation. However it is the average DIFFERENCE between them that is important. So average difference should be as small as possible. I.e. both of the energies can be very large or very small, the minimum average difference is the one that wins. What am I missing? (obviously with the assumption that "Action" scalar is always positive)

Thanks for the explanation of Feynman's Principle of Least Action.

another way of saying "minimize action" is to: maximize potential energy for a given initial kinetic energy (the speed at which you throw the rock)?

Physics University student here, love this video.

Assuming the item were launched from h=0 in a consistent field of gravity, wouldn't this equation always = 0?

thanks you saved my year

Has anyone told you you talk just like Sal Khan from Khan academy?? Thanks ...these vids are helping me prep for my upcoming QFT class ...cheers!!

Hello! Not using Newton's F = ma, allow me ask: 1 - Where does the { Action = Integral (K - U)dt} come from? 2 - Where does the {Lagrangian (K - U)} come from? 3 - Can I deduce that I must minimize the Action integral equation from minimizing the potential energy U? 4 - Can you elaborate? Thanks!👋

@05:26 We use the letetr 'S' for action for some reason? I think the fact that S = T - U, may give us a clue why at least two f these letters were chosen : )

Richard Feynman wrote his PhD thesis on this for QM in 1942

Thank you!

Thank for this video, there arent videos on youtube about this, and they do not say exactly the same shit and do not add anything new, thanks bro

Something bugs me all the time: if i let a rock free fall, it accelerates (increase in T) down (decrease in U). More generally systems tends to minimise their U. Moreover, in relativity, a particule chooses the geodesic with the maximum proper time, and action is essentially the proper time (length along geodesic). So shouldn't that be called the principle of maximum action and reverse your discussion ? I am probably wrong because it's still called the principle of least action, i just don't understand why.

Is there any relation between this and the Lifeguard's Calculation? I've come across both concepts separately, but they both seem to be ways of illustrating the same broader concept.

so helpful thank you!!

How did they conclude that the action should be the integral of T - U,?(or, in other words the Lagrangian) ? I don't quite understand where the T-U comes from and if there could be any other definition and we use this one as it is the simplest one. ( I know that it works as i've solved problems using this concept, but it is this theorical aspect in particular that I couldnt find the answer to.)

Question: "What is the point?!" 8:41 Answer: QUANTUM MECHANICS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! LoL

Amazing brother.. I like your teaching process

Big LIKE!

It must be called the principle of least energy because action is a force. can we arrive at this principle starting from the forces applied instead of the energies?

@8:00 is that mean that if start point and final point is fixed, then only middle path is possible?

Unless I am significantly misunderstanding, the way in which the narrator describes action at around 8:00 implies that it is impossible to throw a ball higher or lower than a fixed path. I'm assuming that the reason that this is not true is because we're setting the initial kinetic energy by throwing the ball at a fixed speed, and ergo kinetic energy. I still get the point, but it does feel like a slightly unclear description...

Good video. The pace was a bit slow for me but no problem I just speed up the video to 1.25x

You are absolutely right that it's interesting (no doubt) and useful (again, no doubt)...I think you should ALSO mention the fact that ALL modern physics is based on this principal, from Relativity to Quantum Mechanics to String Theory. Although this doesn't necessarily "prove" it's correct, it shows how it is actually used (likewise you never really proved that Newton's Laws are equivalent to Hamilton's Principle).

Thanks

then matter prefers rest to movement, why?

Why would you want T to be small and U to be large? Wouldn't you want them both to be small if you're trying to minimize your differences... a small number subtracted by a large number is still a large difference? Or by a minimum of "S" do you mean negative values as well? ( I guess I'm thinking of absolute differences)

This is actually God's Way, if there is a god. But Leibniz called it Sufficient Reason. I don't know who invented calculus first. But Newton's Inverse CUBED law explains the wave/particle duality of quantum mechanics, if anyone had bothered to read Newton properly. Fancy Fields Medal maths isn't/wasn't necessary; the solution was staring us in the face all this time. I deserve a medal for pointing it out!

Principle of least action. The name sound great! Why things go this way in this world? I feel the deep philosophy in it, don't you.

U are so smart where did u get all this information from

damn leonardo dicaprio getting some action

this is impressivly good. only 1:40 in

The Principle of Most Action is moshing your way around a nightclub or stadium.

U saved my brain 🧠

He sounds like Steve Carell :D

So the Universe is like me - tries its best to half-ass it

Iunder stand thankyou

I'm not sure your depiction of why it works is right. It should not be too hard to visualize.

i first read least action in 1983-- but i under stood today-- thank u

thought you were going to solve it

LoL...I wonder if ROCKpeople ever throw STICKS

oops. it's about AVERAGE over the path.

Great stuff, however, I have a comment to make: Please speed up the past of your videos. Thanks :)

Letter S is used because it's from German, where this came from.

I think the comment about the shallow path having a small kinetic energy is wrong. To go just as far while subjected to the same gravity, it must be thrown quite hard. Bullets take a pretty flat trajectory.

It won't look like a parabola: it's an ellipse. -- Kepler.

Why T-V ?

4:15 a mistake here, if we add up all the points from t1 to t2 of the difference of KE and PE, that would be infinity for sure, it is because there are infinitely many points. So the correct way to say this is draw another graph with T-U to be the y-axis and time to be the x-axis, and calculate the area of it.

this is awesome. Maybe "Action" in French starts with an S.

NO, IF YOU THROW IT HIGHER it will take longer to come back down. your graph shows it moving faster then returning in the same time.

There's something philosophically wrong with the narrator's approach: 1) The narrator defines action formally. 2) The narrator reveals the path taken is that of least action. 3) The narrator appeals to our intuition; it makes sense that you take the path that makes you do the least. The philosophical issue is that while the intuition in step 3 is sound, there is no reason to believe what is called "action" in our case has anything to do with the intuitive notion of "action." I mean, one could replace the curious label of "action" with "number of debt collectors" and rename the principle to "The law of taking the path with the least number of debt collectors." Why should I believe there's anything intrinsically sensible in referring to what has been defined as "action?"