In "The Principle of Least Action" ("The Feynman Lectures on Physics", Vol. II, Ch.19), Richard Feynman discusses how his high school physics teacher, Mr. Bader, introduced him to this Principle.

I honestly think that Paul is the best You Tuber who can present these kind of brain-melt concepts in a way that at least gives my brain a brief illusion of dim comprehension.

There is beautiful aspect to Physics that sends chills down my spine. Truly understanding Physics and these relationships at the fundamental level is exciting and gives one an appreciation for the way the universe works like nothing else can. Okay, I'll admit that I am a Physics nerd, but who cares, Physics is beautiful and exciting.

Being a lazy person I approve of the principle of least action.

SUBSCRIBED!!! Always wanted to study higher level physics but was not able to afford college so high-level explanations like this help someone who was unable to formally study, the ability to at least understand the tie-points. Thanks!

Greetings from Brazil. I've been listening to your podcasts for quite a while and honestly it's the best podcast I've ever encountered. It's idealistic, well explained, enthusiastic, smart, and also made in a way that is easy to ordinary public to digest these hard topics related to space science. You were born to do this, to present science to a broad range of ordinary people that like me weren't formally initiated in science. Congratulations!

Great topic! Why haven’t I heard famous physicists talk about the least action principle before?

Sometimes a problem can be solved using simple energy relationships like roller coaster problems, or trajectory problems a staple of introductory Physics courses. However, when the problem gets complicated, Lagrangian and Hamiltonian Physics is the best and simplest method. We usually don't get into those methods until advanced Mechanics courses, like third year, fourth year, or graduate level classes. The principle of least action is a very powerful and useful concept that should be in every graduate Physics student's toolbox.

Thank you Mr.P.M Sutter for explaining to all who tune in, and hopefully don't drop out-about such subjects with a intense yet fun and creative way, without losing me when most prof. might perhaps whip out the dreaded chalk and blackboard. Love your channel and the subjects discussed

This principle comes closest to what is called a universal theory. The best part of it is that for any given problem, you can chose coordinates and apply respective coordinate transformations so that the formulation of the promlem gets easiest. And in order to find solutions, it‘s also easier because the resulting differential equations are of first order and not of second order like for example F=ma=m*(d2x/dt2).

Paul explains it all. Loved this episode. Thanks

This was an excellent presentation. Thank you!

This episode put a great deal of information into a new perspective for me. Thank you!

F=ma: acceleration is change in velocity over change in time, and velocity is a change in position over change in time. F = (dp/dt)

BRILLIANT, and brilliantly explained! What an eye opener! Wow, just.. WOW!!! Thank you.

Awesome explanation…you’re a great teacher .. thank you for your interesting, insightful, helpful talk (:

On a constant force-field "wind", 4 particles are "started" from the exact same point: 1 has position, but no velocity; 1 has velocity; 1 has acceleration; 1 has hyperacceleration. As you can see, your "principle of least action" expression is already incomplete by neglecting hyperacceleration. Each is released; each trajectory is plotted. How should any know that their definition of Natural action differs from your definition of least action. Now let any of them have charge, such that they radiate field. Now there is an entropy loss to the force-field "wind". Now add universal background field with constant variances. Niw add energy exchanges between temperate modes, kinetic to vibration to rotation to spin; except for translation, these are not accounted for in your wave-based least-action model.

You have all these physicists creating all new theories trying to find the answers to life, universe and everything, and along comes Paul saying. "Come on people! 42 = the least action taken."

Eye opening video! Thank you so much 🙏🏻

Great video, thank you!

Here is something fun for me. Engineering vs pure physics. What is practical for a specific purpose and what is the real underlying physics. Do we have a specific problem to solve? Then use what which will solve that specific problem. Do you want to look beyond a specific application and find what will solve any and all specific problems. Forget what will solve specific problems and look for that which solve all problems. We have not yet found that. Let us keep on looking.

Wow, first notification I've got from this channel in months. Funny thing is I was wondering about you yesterday. If you were still uploading.

Great video sir, thanks

Very interesting how you chose to explain this

Ayyy great breakdown mate

a mind blowing explanation

Very difficult topic to discuss to a general audience and yet so important, too. I'm very happy you tried. Enjoyed.

Excellent teacher!!!!

Paul, I watch and I am always learning, but where did you buy that chair, fantastic hugging factor!!

Thank you for reading (and maybe answering) this. When black holes merge, don't you create a naked singularity for some time as their gravitational fields overlap, causing the net gravity and many places to be low enough for light and matter to escape?

So from that design battery for anything with a reaction produce an energy with how we can capture right now that only 1st edition time will bring

great video ,

I wondered why the ball was getting bigger. Then it hit me!

I remember a couple of problems we had in graduate Mechanics, one on the midterm exam and the other on the final exam. The midterm was a spring pendulum, not too bad. The final was a different story, it was a wheel connected to a spring which rolled without slipping as it moved with SHM, a rod of length L and mass m, was connected to the rim so that it could swing like a pendulum as the wheel rolled. The problem was to write an equation of motion for the end of the rod. In one problem we had SHM, rotation, and pendulum motion. I think he was a sadist. LOL One other problem was the trajectory of a relativistic projectile. To be honest, it has been so long since I solved problems like these two that I could not do it without many hundreds of hours of study and review.

That was awesome

I study physics lightly as a hobby. I came to some understandings of possibilities in regards to physics both Newtonian, atomic, and quantum, but what this man just said I swear for me is or was a Epiphany like no other. A grand epiphany, but now I have to watch this video like maybe 10 times to have it sink in and then dwell into I believe Newton's calculus, clearly Maxwell's equations, Einstein of course and there's others too many. Either way outstanding outstanding! 🎉🎉🎉🎉🎉 somebody buy this man a drink okay,put it on my tab.

But aren't the Lagrangian formulation and the Newtonian formulation as fundamental as each other, where you can go both ways between them: Derive the E-L EOM to get F = ma. Then go the other way from F = ma where the potential energy and kinetic energy are expressions ultimately related to F = ma which we put into the Lagrangian in that nice form. Unless you're saying the minimisation of the action is inherently more fundamental. But is it.

If this is the way to construct physical theories, this is also the way how physics should be taught at school instead of blind memorization of equations. Train the kids to think like a scientist, not like a slave.

Awesome stuff! If you're into Eastern philosophy you will also recognise this as Wu Wei, the core principal of Daoism.

Given that the Lagrangian approach can help determine the necessary physics equations, I assume scientists have tried to apply this approach to quantum gravity. Can you explain that approach and the difficulties involved in getting out the final physics equation from that? Is it just that they don't know how to properly define the kinetic and potential energies in that case?

It always struck me that the alternative to a universe in which things follow the path of least resistance is one in which things did not, but in trying to picture such a universe the only result I could see is one where the universe self destructs from asymptotic run away energies.

Taoism core principle is "The Principle of Least Action" It is named Wu Wei.

But, then, why not have the action, A, be sqrt( (KE)^2 + (PE)^2) / ( (KE/PE)^4 + 1) and then minimize THAT? I wrote A specifically so that is dimensionally consistent and has dimensions of energy. I'm just making the point that: you asked "Why F=m*a?" "Why the Einstein field equations?" "Why Maxwell's equations?" AND NOT SOME OTHER rules/differential equations, and proceeded to explain how they get derived from minimizing the action given by A = KE - PE. But that just moves the question back to: why A = KE-PE and NOT SOME OTHER expression? Why even energies? Why not momentums? Why not velocities? Why not the absolute temperature divided by the lumens emitted?

About 05:15 _...the core of LAGRANGEian physics is just kinetic minus potential energy. Now, where do we go from there?_ This is onlythe second question I have. My first is: How do we get there in the first place? Why is it the difference rather than e.g. the sum?

I am very happy with kinetic energy. I am very happy with potential energy. They are in a sense, the first integral of Newton's equations. I am happy with the principle of least action. What I have never understood is why, in combining these two energies, Lagrange SUBTRACTS one from the other. That is not at all obvious. Lagrange might as well have started from specifying his inside leg measurement.

07:42 _...it follows a parabola._ As long as you can neglect air resistance and wind. However, in this case, NEWTON's law F=ma is not more complicated.

My dude, you are so underrated.

I said this in a crude way to teach my 5 year old to ride on two wheels, maybe im wrong but i thoight and told her once you go a little fast keep peddling and its easier for the bike to go forward then fall over........ It didnt help, we still had to practice just as much

If you have to use math to calculate where to step each time you take a step, you could never move. So this means that the least action to see the ball and calculate each motion required to catch it, is exactly why we can prove life. The attempt to prove how to SIMULATE and execute each movement we make being totally ignorant of any math at all. Yet it is assumed that we are Quantitive. Amazing that we try to quantify everything. Even life. Fascinating. It also appears to me ,that the least action calculation is valid with controlling of objects through quantitive calculation, but that AI will never be able to function as our brains do in that we need no math to catch a ball. We can determine it’s path instantly. That would be the least action required, yes???

4:48 How is 'the kinetic minus the potential energy' an equation?

Got me interested because it' kind of overlaps with taoism.

If you throw a ball straight up and it comes down to the place from which it was thrown, is that also a parabola?

Best physics book ever on the PoLA - “Variational Principles of Mechanics” - Cornelius Lanczos

So if we have a single lagrangean equation that covers both General Relativity and Quantum Physics, don't we already have a Grand Unified Theory? So what's the holdup?

i have a question, is this real or just a represntation. for example, a river if the least action principle is truly a rule the river should just go 1 path but on reality take aloot of path even create lakes, waterfalls, and alot sort of things i know the most of water should run on th mainl path but are aloot other than just ignore that, it that is true for a riven can be for particles or another things ? like watch a weird path that just violate the least action ?

sorry to pic at nits, but didn't you literally call the second law of motion (f=ma) the third law of motion at 1:24?

The tortures of maths and physics give you an approximation of reality. Conceptual understanding does without that maths structure and produces another description. People who know physics, such as Richard Feynman, have cognizance of concepts that are representative of maths, and vice-versa. Gravity on earth changes the numbers and the concepts. I have a feeling that the reason for cosmology’s obsession with long distances in space and infinitesimally small particles in colliders has to do with avoiding this terribly confusing aspect of the universe. Without gravity calculations are as nearly precise as can be found, and the maths simplified greatly for presentation purposes (papers, written formulae and scripted equations, speaking events, teaching). Then there are of course the conditions on earth Somewhat unfortunately, a model of any terrestrial event loses its appeal for physicists almost completely. I think that not only do maths and physics help greatly with reckoning on earth, the languages of chemistry, biology and meteorology can subtly modify theoretical constructs because there isn’t a vacuum and without one a further study of axioms, principles and ongoing perhaps modified stresses. In any event, the commonly-accepted presuppositions of the irrelevance of gravity and the negligibility of expansion as a contributor to tiny objects and motions will have to be reviewed. “Sensitive dependence on initial conditions”, as referred to frequently (SDIC) in chaos theory, remains largely overlooked in absolute theory. We ought to prepare ourselves to recognize the implications of Planck Length’s precision at unheard-of negative factors. It may be too hot to improve on, but the tiniest of the tinies may represent more (particularly in its extended influence on) of a demonstrable difference in the calculation of much larger actions and objects. Just how “sensitive” is our dependence on initial conditions when we don’t have a precise measurement or understanding of those initial conditions? Conceptual “reckoning” of reality might improve or possibly replace maths reckoning when data or numbers aren’t available. Or we could relentlessly keep extending the design and production of telescopes and colliders. I don’t think maths or traditional physics are going to get us to a theory of everything when expansion and microscopy can’t be precise. With an additional conceptual framing of reality it might work. What deduction can’t prove, induction can render manageably understood. All of this is an hypothetical extension of Feynman’s intuition that “everything” might be expressible as a few words in a readily understood prose sentence or so. He was responding to his own astonishment at the amounts of calculation there are within the smallest area of space, which left him briefly skeptical of putting “everything” in math and physics terms. Conceptual induction may reveal more, unshackled by the constraints of numbers, which, we remember, paint only an approximation of reality. The Standard Model is also “only a model”. If it should turn out that a conceptually-based and linguistically-expressed “model” does describe everything acceptably, we should also consider its applications in earth science and day-to-day existence. If telescopes and colliders are the treble and bass voices of harmony, the world as we know it might provide the tenor and alto voices. And all of their harmonies overtones and undertones…analogously speaking, of course. ❤️. Sincerely, Jeff.

This video could have been half its length!

So is this Occams Razor in practice ?

My takeaway is that nature likes efficiency.

F=ma shows up EVERYWHERE! Just like the Pythagorean theorem can be derived in many ways and shows up equivalently in places you wouldn't immediately consider.

B R A V O ! Hands down, your best video ever.

At 1:15 Newton's F = ma is not the "... classic third law of motion ..." F = ma is Newton's Second Law *Newton's Third Law is the action/reaction law

Wow, how mind blowing!! "Why F=ma"? Love it.

Can mass of a proton be derived from the principle of least action ?

The universe is efficient, saves time and energy, almost like its a simulation…

If what you say is true, then why is this principle accepted as THE theory of everything, the holy grail of physics?

You should sell that t-shirt 🤔. You could then wear all of physics

What i really want to know..is how fast is the universe travelling, and how is that affecting our time dilation. Does it flow like water (in which case there may be time slipstreams we can travel with, ..think that weird acceleration some space craft suffer..that would be the angle of ascent/descent in relation to the universal speed no?) Also given all the evidence of nature, the universe has to be rotating around something as well as possibly traveling in a linear direction. Which would suggest the microwave background is just a veil/limit and the universe continue far beyond it, possibly circling back on us. I would laugh if we got a quadruple gravity lens and saw earth in the distance 🤣 There is no correct until the final quark. Its all relative

But why are the formulas for kinetic and potential energy correct?

I dont quite see how lagrangian can generate physics, because it needs the potential energy and you need F=ma or Maxwell or relativity to calculate the potential energy......so this seems like circular reasoning

What does it mean to apply the least action principle?

What about the principal of the probability of self revealing reality...

Could have gone to, Occam's razor..., states that the simplest explanation is preferable to one that is more complex. Simple theories are easier to verify. Simple solutions are easier to execute. Sir William of Ockham as a Catholic priest. "In the beginning was the Word and the Word was made flesh. and dwelt among us." ...It's the simplest explaination.

Right, but almost no one explains the insight as to WHY we invented kinetic minus potential energy.

The ball follows an ellipse with the center of mass of earth at one focus. It would be a parabola if earth was flat.

The universe created out of nothing sounds like me trying to start a business with no money😂😂😂

Como podria una persona perde su voluntad de alguna manera o como disen labarles el serebro para que agan lo que tu les digas como un casco

wow

Isnt this the same as the path of least resistance

Sounds like a theory of everything to me, or at least a parameter in it.

It sounds very simple in this situation, sitting on the Earth

How can such a smart person repeatedly say "exact same" thing? Don't mathematicians and physicists learn basic English grammar?

Principle of least principle is like "wu wei" in the Dao of physics.

What happens when you kick a ball? That's answered by classical physics. What happens when you kick a dog? That's answered by cybernetics. (Unless you kick very hard, in which case, go ahead with the physics).

I mean... when I look at a "physical situation," I call the police

What is action?

Thats Sir Isaac‘s s e c o n d law.

Una cosa solo dios es corecto los umanos cuando buscamos algo nunca se encuentra de la primera pero tu que saves resuelve este asunto de llasavemos para que sevaya trankilo el espiritit

The shortest path is the path of least resistance. It is the path that nature chooses all around us. It's the only way.

Never much liked the phrase "laws of physics". The entire use of "law" in physical science goes way back and is influence by religious beliefs. A better, IMO, way to think of these things is that we humans have discovered some traits of the universe that we, using our language abilities, have put into coherent descriptions.

You say that the parabola is the path with the least action, but you didn’t solve all infinitely many possible paths. And calculus of variations can only tell you that you have a locally optimal solution. I claim that you don’t know that you have a global solution.

…you’re obviously Kevin Spacey lol

In other words, you cannot create something from nothing.

If the universe take it nice and easy… why won’t you ?

Your lampshade is crooked. Please fix it by first finding the shortest path.

Wow. Physics principles don't get any bigger and broader than this. This will take some contemplating. I'd say it puts us much closer to what religious people would call the mind of God.

You're a brilliant teacher but you needed a visual aid and/or a bigger definition of what the principle is, you gave excellent examples but didn't lay down enough foundation It's on a graph you say? Tell me more, and more than one way

AHa! Cigarettes cause cancer, what causes cigarettes?

Newton is the man 😁. I think he held back into, read where he tried to teach the sight of the unseen. Ever hear of that?