The Closest We Have to a Theory of Everything
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- เผยแพร่เมื่อ 5 พ.ค. 2024
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In the diagram at 4 minutes 30 seconds, the labels for h_1 and h_2 are mixed up. Sorry about that!
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Everything I am talking about here is standard material of undergrad physics textbooks. My personal favorite is good old Goldstein en.wikipedia.org/wiki/Classic...)
On variational principles more specifically I quite like this textbook: link.springer.com/book/10.100...
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0:00 Intro
0:45 Optimization
1:35 Shortest Path
3:20 Least Time
5:36 Least Action
10:27 Quantum Mechanics
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My son, like the rock, somehow intuitively knows and applies the principal of least action to everything he does.
As an experienced parent, I can confirm that this law applies to all children.
Look up Active Inference and the Free Energy Principle in neuroscience! It applies these ideas to biological organisms, including teens.
Love ❤️ the analogy. 💪😘
Actually had to come back. Tell him/her get off hiss/her ass, and go to work! 🤬😡
Kick his/her ass out!
AHUM’M’@
Like you back. I don’t have kids.! But I used to be one.
At 52 years old. I know better. 🤪
The word "Action" (in Latin: "Actio") was taken in the meaning of "Evolution" (of movement of a body) into a final state named "Stationary": that could be a minimum, a maximum, or a kind of equilibrium. Maybe because Hero used the Greek word "Αγωγή" (agogí, "aghojee") in his works on the same subject.
The "Stationary-action Principle" is the official title since 17th century in scientific and philosophical papers. "Principle of least action" is a more popular title mainly during the popularization of Physics after WWII.
The word "Stationary" (in Latin: "Stationarius" or "Stabilis", in Greek: "Σταθερός" (statherós, "statherohs") or "Στάσιμος" (stásimos, "stahsimos") ) is the origin of letter "S" for action by decision of French and German Physicists and Mathematicians on that century. Letter "A" was already overtaken for many other uses such as acceleration. "S" as in "Section" (in Latin: "Sectionem") for Sectional Area came later in replacement of "A" despite this vowel still in use in some fields.
The same happened with "Momentum", "Impetus" or "Quantity of Motion", the last one used until few years ago in schools of some Latin language countries, mainly the Portuguese speaking ones to make distinction between the (dynamic) "Momentum" as Mass x Velocity (Q = p = m × v) of a body and the (static) "Momentum" as Force x Distance (M = F × d) of a lever.
The small letter "p" came from the etymology of word "Impetus", a Latin word meaning force, from "impetere" where "in-" (or "im-" before "b" and "p" in Latin languages) means "into" and "petere" means "to seek".
On the same century and by the same Scientists above, the small letter "i" or the capital "I" were overtaken mainly for "Inertia" as "m" or "M" for mass, the decision was for the small "p" for "petere".
It shall not be confused with the Greek letter "ρ" (rho) mainly used for density (or specific gravity) to describe the "ratio" (same in Latin) between the mass and the volume of a matter.
In Greek, γ is never pronounced as a 'j'.
@Michael Sommers I also had this doubt, however I tried in more than one Greek translator and all of them pronounce just like the Latin rules: "g" before the equivalent vowels "e" and "I" are pronounced as "jhe" and "jhi" and not as "ghe" and "ghi", making this sound exclusive for vowels "a", "o" and "u" as in other Latin languages... and Greek as well (???)... Modern Greek maybe (???)... I really don't know... but I considered these machine translations acceptable with these "happy" coincidence between Greek and Latin... maybe you right... however these are the only sounds I could confirm.
@@alexdemoura9972 I'm virtually certain (I'm no expert) that Hero(n) would have used a hard 'g'. Perhaps modern Greek is different.
@@michaelsommers2356 yeah, I think attic Greek was always hard g, except in certain combinations - e.g. gg was pronounced ng (two separate consonants, rather than as in English sing).
wow this was an amazing comment tysm
I'm so glad you touched on the idea that those "shortest paths" aren't future dependent. The concept, as you and others illuminated it, always bugged me: Every ray of light takes the shortest path, and which ray of light coming from A reaches B, doesn't need to know it's going on the correct path to B. If you imagine an infinite number of rays coming from point A at all possible angles, Most of them miss B, but the one ray that does not miss B, doesn't know it's headed to B. It just takes the path of least action. The "How does it know what the shortest path is?" question, is an artifact of human perception. It doesn't. All rays just go shortest, always. There is a ray that exists which connects A to B in the shortest possible path, and the ray which leaves at that angle makes it. Shortest is the causality of the whole thing.
I just wish you'd expounded on it a little bit more, and especially went into more detail about the wrench you threw into my entire concept there at the end, with the Quantum Mechanics actually needing future information.
I'm not a physicist, and I understand opinions differ here, but I don't think QM necessarily has a future dependence either. The wave equation *really does* describe the evolution of the system forward in time, and the fact that we only see one result is because we happened to get entangled with one "branch". So under the Many Worlds interpretation it works the same as it does classically, which makes me feel better about it, anyway.
@@incongruousa Yeah I would really appreciate some clarification on that whole thing, because I thought I had a grip on the classical side of the mechanics, but QM still throws me for a loop.
Also did I accidentally double comment the same thing? YT Threw an error when I tried to post the comment initially so it wouldn't surprise me.
You'll want to look up Sabine's work on superdeterminism. In her paper on a superdeterministic toy model, she describes how that model might be modified to accommodate a suitable optimization function for least action.
@@naasking I'm sure I saw her video about it once but I'll go back and check it out again, thanks!
@@neilhopwoodsjugband That's pretty deep! Thanks for the thoughtful response.
I'd imagine Sabine would say something to the effect of that there are none of those isolated systems being created, the universal wavefunction has always existed and those isolated systems were predictable from the dawn of time, if you had sufficient information.
To my understanding, for free will to exist, we must be able to impact the universal wavefunction in a way not predictable from prior conditions in that wavefunction. This does not seem so far fetched to me. I can't figure out how to test it though, as anyone who favors superdeterminism can simply claim "We never had sufficient starting information" if an experiment shows that free will exists.
Sabine, I can’t claim that I always understand every aspect of your videos. But they always leave me with this intense feeling of wonder and awe at this extraordinary universe that we live in. Thank you for this precious gift.
Well put.
@@Brucebod Thank you!!
Dark matter /energy paradox SOLVED
m.th-cam.com/video/ZQNWVQc5sNI/w-d-xo.html
me too
Yes
A couple of years ago I saw a great video of a lecture by Richard Feynman in which he proved, using quantum mechanics, that angle of incidence equals angle of reflection. He demonstrated how the principle of least action arises, in that case, from interference.
The most interesting part was that some of the students at that time were not yet convinced quantum mechanics was correct. While it was a pretty mature field at the time, it was new enough that not everyone in the room was convinced it had a real advantage over classical optics in dealing with light.
The part that convinced people was when one of his students pointed out that if you remove part of the mirror, not in the center, the light woild get brighter. And Feynman confirmed that not only was this correct, but the experiment had been done and it works.
woaaaa what's the video?
Yes link please
@@pmcate2 It's an 8 hour lecture series, but worth the watch:
th-cam.com/play/PL9s_vYCJclAYXFwhuMynZz8CNnoUAG5mr.html
@@mayabartolabac Only a few of his lectures were recorded and posted on TH-cam so it should be easy to find if you search for it. If you want more most of his lectures are transcribed and posted publicly for free. They are not recorded but I think they are still interesting enough to read through without getting burned out.
@@Sam_on_TH-cam thx dude
Langransian mechanics completely blew my mind as a student. I loved it.
And Nöther's theorem is probably the most beautiful thing my mind ever encountered. What a beautiful mind she was.
She was amazing, the mother of glorious abstract algebra.
Emmy is so amazing, her cursive writting is also so beautiful 🌹🕊
It definitely blew your mind because you've forgotten how to spell Lagrangian LOL
A small point: it's Noether, not Nöther; there is no umlaut, even though it looks like there ought to be one.
Lagrange (Like ZZ TOP's La Grange), and it's Lagrangian...
Structural engineering also uses Euler-Lagrange paths to minimise a structure's strain energy! It is always amazing to see the ubiquous uses of such brilliant mathematical developments
You are "the teacher" we all dreamt to have . Thank you for your clear explanations🙏🙏
It's interesting how Fermat could come up with his principle. Just a few decades before Rømer had discovered that the speed of light is finite at all, and the speed of light in media could only measured using Foucault's method invented in 1849 (even the Fizeau method required too large distances to fill with water etc.).
It may just have been an idea that turned out to make a shocking amount of sense. Einstein (to use the main source of this channel...) predicted the effect of gravitational fields on light before that could be measured (or was observed).
@@HaukeLaging But Einstein derived that from what he already knew - he knew about the quantization of light (that's part of what his Nobel was for, how that explains the photoelectric effect), and he had his theory of relativity, so he could ask "how would this effect light". That's why he could predict this. It was *not* "just an idea that ... made sense".
@@HaukeLaging äF6NTMYF6NTMY
@pyropulse I thought what Einstein predicted was gravitational redshift, not simply gravity bending light. I don't think gravitational redshift exists in Newtonian gravity.
@pyropulse My sister Jeannie Lee predicted gravity bent light just before she whacked my half-brother Randy Lee over the head with one of those tall, skinny floor lamps.
I started watching your videos a year before I got my abitur, which facilitated my interest in physics. Now I am in my second semester and I actually understand what you are talking about! :)
I spent the first half of the video wondering if we were trying to paint the target around the arrow in a causality-busting maneouvre, but was genuinely relieved when you explained the Euler-Lagrange formulation. Thank you for this video, Sabine. My layman brain highly appreciates the challenge!
This is the most remarkable principle that I have encountered in physics, and I will study it further until the end of my life.
I‘d like to add that if you construct the Lagrange density T-V for a free particle and apply the principle of least action, you end up with the Dirac equation. This is so beautiful.
Thank you so much for this most inspiring video.
My new Best physics video. Can’t recommend high enough. It never ceases to amaze me how optimization using calculus of variations and functional analysis explains “almost” everything around us.
This is a great little video Sabine. I'm glad you didn't dumb down the equations and showed them in their full beauty, regardless if everyone understood. You left the details up to the reader, and focused on the main points in a straightforward manner. Thank you.
Arrogant comment.
This mesmerised me when I read it in "The Feynman Lectures on Physics" when I was a student. It opened a new way to look at physics for me. Nice video.
Just found your channel yesterday now it’s one of my fave physics channels.
Awesome work
'How does the light know it will enter a medium before it gets there, so that it can pick the right place to change directions? It seems like the light needs to know the future.'
Even before the Euler-Lagrange equations are brought up, this seems like mere slight of hand to me. The destination of the light, ie. the supposed 'future', is already observed/given/assumed right from the beginning, so really it is already in the past.. The principle of least action simply deduces the path the light already took to get from A to B. If I see wet concrete one day, and paw prints in the now set concrete the next, I don't ask 'how did the concrete know to be depressed in just such a way to resemble a paw?' Similarly, it doesn't make sense to ask 'how did the light from point A know to enter the medium at just such a place to reach point B?' We already know the light went from A to B, which we can then combine with our knowledge of the speed of light in the medium and the principle of least action to deduce where it must have entered the medium.
Sabine calls out this sort of mystification in more complicated situations (eg. the delayed choice quantum eraser), so of course she already knows this, I just take issue with the framing in this otherwise interesting video.
When you start assuming the future destination is known to the source of light in the past, you have already lost on several levels. Humans get it, but how did the light know?
Yes, I agree, this is unnecessarily mystical. Look at diagram at 5:30, the initial conditions are A and Theta1, given that, B is a consequence.
Along the light path, the proper time is zero for the photon, so the start and end points are simultaneous in the photon frame.
@6:27 the action is abbreviated "S" because it is short for "Stationary action". I do not know why it is an "action" but the same etymology problem arises with most derived physical quantities. It's a decent name since the root "act" is from Latin (“register of events”), plural of (“decree, law”). That's the best you can say, whoever coined it (Leibniz?) choose well.
In German that thing is called "Wirkung". Maybe this makes a bit more sense. 🤔
The etymology of "action" is not what you say. It's simply from the verb agĕre which means (guess what) "to act".
Do you have any sources that say the lettece of letter "S" for the action functional comes from the word "stationary"?
your latin makes no sense .... action is from actio, the noun form of "agere" "to DO / to MAKE" + "-tio" suffix, and as such even as a noun only means "A instance of doing or making X" which then can be applied about anything you talk about. a judge/advocat will refere to a process, an instance of doing _it_ in the court, an actor about doing _it_ on stage, a roleplay. but the latin word itself, "actio" linguistically can NOT be a plural form of anything . . . .
@@eyeofthasky: I am Italian. We study Latin in high school for 5 years. The form agĕre is obviously the infinitive. The paradigm of the verb is ăgo, ăgis, egi, actum, ăgĕre [The little wiggles that you see are called quantities and are often omitted in writing]. Yes, the noun actio comes from the verb ăgĕre. As it often happens in any language, a word may be translated in many ways into another language, depending on context. But the one meaning that you chose ("register of events") is definitely not the right one in this context.
The meaming that you refer to in your second comment (to do, to make, to act) sounds way more appropriate to me.
It's properly called Hamilton's Principle. I'm not sure who called it the principle of least action. It was probably a physicist and not a mathematician. The least action doesn't even necessarily give the minimum of the functional, it just gives an extrema
1. The path integral has a dependences on the future because you tell the particle what point it's going to. If the particle has a particular trajectory, there will be some action for which that path is optimal. That is it's a feature of the analysis, not of the universe.
2. The future dependences of the action becomes the dependence on the derivative in the Lagrangian. To see this replace the action integrall by a summation over actions of points infinitesimally close together. Over the infinitesimal paths, the 2 endpoint degrees of freedom becomes equivalent to the value and the derivative degrees of freedom.
Currently using Euler-Langrange to formulating models for control systems in robotics. It kind of seemed like like magic to me. This finaly put some perspective on things. Thank you for this video!
This is the version of QM that made the most sense to me. Somewhat analogous to how lightning forks off into multiple directions but the real flash occurs through the main line once it makes contact with the "leader" on the other end. I'm sure the mechanics are entirely different, but I think it's a good analogue to explain it to a layman.
I never understood Langrangian mechanics. This is the best explanation I've ever seen. Thank you.
When somebody explains why it should be obvious that the form is T-V will be a great day tho!
Amazing video, Sabine! I believe the Principle of Least Action is indeed the Theory of Everything. As both a mathematician and physicist - and also a singer/artist, I understand everything you say and also touched quantum mechanics quite a lot in my PhD 6 years ago. That one was about time-dependent density functional theory based Ehrenfest (mean-field quantum-classical) dynamics.
I keep learning more with these clear explanations.
Thank you
When I first derived the electrodynamic action I put down my pencil and was just amazed. I think it brought a tear to my eye, it was so beautiful.
How did you derive it? From my experience, it's found by trial and error until it gives Maxwell's equations and the Lorentz force.
Man..... I really dig this channel. ....
And, since 99 and a half percent of the content is Sabine speaking, I guess that's saying quite a bit then. Most of the topics she picks right up my alley of interest, and how she goes about explaining anything just works really well for my brain.
I wish my professor had explained this topic like you did. This seemed so arbitrary back in my undergrad, you really have a talent for teaching!
A quite brilliant presentation. It was a joy to watch. Thank you!
Wow, this is really great! That was a dense yet perfectly paced and fascinating 13 minutes! If it's not too much to ask, I'd really appreciate a follow up that tries to provide a conceptual understanding of how Lagrange equations eliminate future dependence. If I could wrap math deficient mind around that, I feel it would be enlightening. Thanks!
Here’s my take. It’s not that there’s anything completely reality breaking about the future dependence. If you split the path in half, the optimal paths for each of the two segments would still be the same. You can keep splitting into more and more segments until they’re tiny and local, and that’s how you get the Euler-lagrange equations.
It’s also not that the rock knows where it’s going to be in the future. By picking a future position, you’re fixing the current velocity of the rock. If you fix both the current position and velocity, then you can’t just pick an arbitrary path for the future, you have to know where it’s going to go already. It’s okay that reality is able to do that, because these equations already predict the full trajectory of the rock into the future and the past.
correct me if i'm wrong, but i'm pretty sure it is because you not integrating from TA to TB anymore and only considering TA
I agree! I hadn't seen it explained that way before. Thanks.
Michael Kreitzer -"eliminate future dependence" There is no future dependency. Light does not have to predict the (future) properties of the medium in which it will refract, because it is the refraction angle and therefore the position of point B that depends on the angle of incidence and the place where the light will refract, not the other way around. Mrs. Sabine suggests to us inverse causation, and some magical quality of light and other objects - the anticipation of the future conditions of the processes taking place. Nothing of the sort is needed here
Always fascinating and well presented. I am often struck by the possibility that the universe is more simple than we suspect but that the explanation for that simplicity is quite complex!
Your explanations are very clear and comprehensible. Excellent work.
Easily the clearest explanation of least action, and its importance, I’ve come across. Thanks!!
A new classic right here. Really fantastic 👏🏼👏🏼👏🏼
I’ve always felt this is the physics version of “syntactical sugar”. That nature somehow optimizes without trial and error is mystifying until you realize V is essentially a free variable, something that we’ve made up precisely so that the equation works.
This is not quite true, because not every differential equation is the Euler-Lagrange equation of some action. This is why these phenomena are astonishing. You're quite right though: if for every differential equation I could cook up some action for which that differential equation is the Euler-Lagrange equation of the action, then this would just be syntactic sugar and entirely unsurprising nor insightful nor deep (but of course this isn't the case!)
the trial and error was done on a quantum level with all available paths
The reason nature "knows" the optimal path without trial and error is simply because nature imposes it.
It's called *_determinism._*
It's not about magically "knowing" the future. It's simply about factually *_having_* one.
@@TechnoEstate Agreed...math is a cute little tool we use to describe and approximate behavior in our reality...but, our reality is not based on math or fundamentally built on complex concepts. I would be my life that there are a few very very simple basic concepts which all of these seemingly complex concepts arise from. We are blackbox testing trying to reverse engineer reality without even being able to probe the entire "box" (system) due to our own limitations of senses. When building our own systems such as computers, you realize that there are VERY few operations being done at the hardware level that get abstracted from 1's and 0's by 8+ layers of abstraction of what are simple transistors and logic gates. Imagine giving that to someone from the 1700s and being like, "yea, figure out how this youtube video is playing." They'd come up with some really interesting and complicated theories and without the right tools, they'd never discover the true simplicity that make up the building blocks of it all. From what we observe life on our planet, we observe how perfectly efficient and extremely complicated life is now based on the basic building blocks it evolved from.
I see no reason why we aren't just chasing emergent properties in physics and probably will never know what the simply unifying theory of everything is because of our limitations on observation, but that's probably fine as we have most of what we need to live within reality.
@@Dr.FeelsGood I agree with a lot (if not virtually all) of what you're saying.
One point I like to make to illustrate the role of our own limitations and biases as human beings is that of what we call *_"randomness."_*
The truth is not only that there is no such thing as a *true* "random" number generator -- although we all "know" a "random" number/sequence when we see it, right?
Or to put it another way: EVERY number/sequence is as random as the other. Even if I write a "random" number generator consisting of exactly 1 line of code such as , I can *prove* that the resulting sequence of 1s is just as random as any other -- simply by virtue of me, a being fully subjected to "random" quantum mechanics, just having arbitrarily created it. 😌
And from there, I like to keep with Einstein and argue that the fact we believe certain quantum-mechanical processes to be "perfectly random" is our BEST HINT that we actually have not fully understood quantum mechanics yet. Because as with number generators, *_there is no such thing as "random"._* Only things that *_appear random_* simply because we haven't figured out their algorithm yet.
Thank you for this presentation. As a geophysicist trying to understand laser interferometry the breakdown was really helpful.
Thanks! I learned the Feynman path integral formulation before I learned about the Principle of Least Action, so the motivation of the former didn't make much sense until I learned the latter. But as a result, I always thought of the "knowing the future" aspect of least-action as feeling natural, because the Feynman formulation conditioned me to think that way.
However, until watching this, I didn't see the possible connection between the hand-wavey measurement postulate, and the knowing-the-full-world-line-ahead-of-time aspect that seems to be baked into the equations. Food for thought...
This is the best video on physics yet, I remember all these equations, pitty my year 1 and 2 notes were all destroyed in a flood.
I'm not sure I get this point of the"intention" of the particle. It's not like we tell particles (or rocks) "go to point B" and they find the most optimal way of doing so. We just watch things moving and them retroactively evaluate where they landed.
I think what she means is that particles travel along trajectories that optimize the action no matter what the endpoint is: you can imagine the rock at a fixed point P with a fixed velocity V (think of it as a direction), how is the rock going to move in the future given that initial condition?
Well, suppose that you are considering the movement of the rock for a very short time interval, say from 0 to T seconds. Then the rock somehow CHOOSES among ALL the possible trajectories that start at P and have direction given by V the one that minimizes the action for the time interval from 0 to T. And this is true no matter what T is. So you can say that the rock is always looking "infinitesimally" ahead in the future and choosing the optimal path.
@@DanielAlvarez314159 Or it could be doing the opposite and instead be looking an "infinitesimal" amount of time into the past and we wouldn't be able to tell the difference.
Now I'm confused. What variable is it looking into the future for?
@Google user I just watched th-cam.com/video/MIBfKJHMWHU/w-d-xo.html and it's pretty good (it kinda answer that at 5:40)
@Daniel Álvarez - if it starts at P with velocity V, wouldn’t it have just ONE possible path already? Noob question maybe.
Thank you! Everything I've read regarding Lagrangian mechanics has failed to explain the rationale behind the Lagrangian itself. I appreciate you finally explaining this!
Your explanation about action is clear and didactic. Thank you so much.
The principle of least action (where action should rather be read as ‚effort‘ (see my earlier comment)) is by no means a candidate of ‚a theory of everything’, but it is one of the crucial criteria, any eventual theory of everything, has to satisfy
Thanks Sabine. This time I have to watch several times with pauses to consider.
Ah! I see! This was a fantastic new insight into the measurement problem! Thank you!
Great video. I've not come across the principle of least action summarised in this way before. Will watch again!
I realize the social utility of adding the "spooky" element to this discussion. However, in a way that detracts (in my view) because there isn't anything spooky about it. We have derived our formulas to explain how things work after we know how they work. The light beam or the rock don't need to know their outcome. They react to the forces acting upon them from the first instance of their action, and those forces eventually produce the outcome. The outcome may then be explained by us, retrospectively, according to our formulas. Anyway, your talks are fun.
That's literally what she later said though, that each action equation is associated with a set of differential equations called Euler Lagrange equations, and in the case of the rock they are just Newton's laws. And so the rock indeed does not need to know the future and moves according to the forces acting on it from moment to moment, following the differential equations.
Sabine would be the last person to pull such bullshit, not that any of the other science yt channels worth their salt do it either. The spookiness is created precisely to dispell it with a scientific explanation later
@@l1mbo69 If you don't find her last remark about the measurement postulate spooky, then I don't know what is 🙂
A lot of these action principles seem to be constructed only after the equations defining the phenomenon are already known. This makes them and the associated teleology somewhat factitious. The action principles would be more convincing if they had come first, as the means by which the defining equations were originally discovered.
@@l1mbo69 The issue was about the "spooky" part. Was that not clear?
@@johnbarbuto5387 "..that detracts because there is nothing spooky in it"
She already agrees with you. What you said implies that it was left at just being spooky because that's the only way it could detract from anything, since it's not giving any false impressions
And then, you proceed to explain something she already did to prove your point as if you're educating the misled people
It's not actually weird that the particles 'know about the future', you're putting in information about the future by insisting that it ends up at point B.
I think what she means is that particles travel along trajectories that optimize the action no matter what the endpoint is: you can imagine the rock at a fixed point P with a fixed velocity V (think of it as a direction), how is the rock going to move in the future given that initial condition?
Well, suppose that you are considering the movement of the rock for a very short time interval, say from 0 to T seconds. Then the rock somehow CHOOSES among ALL the possible trajectories that start at P and have direction given by V the one that minimizes the action for the time interval from 0 to T. And this is true no matter what T is. So you can say that the rock is always looking "infinitesimally" ahead in the future and choosing the optimal path.
it is tho: imagine you have point B marked, and you shine a laser at the surface of the water. You move the laser around until it hits point B. At that point, it happens that the angle of refraction is such that the light travels the fastest path. How did it know that the point it would hit by this trajectory had no faster path to it?
@@vibaj16 Exactly, as you move the laser around until it finds point B, it is not in the future any more, it already hit point B.
@@jccklh but it refracts before it hits B, so it has to know what angle to refract at
@@vibaj16 Any light that doesn't take the correct path to reach point B because it "doesn't know the future" will simply not reach point B, it will go to C instead. And when it gets there, it's not the future anymore. The path taken, and how it interacts with the environment determines the destination. Except at quantum scale, then things get weird.
Once again, a great video Sabine. As someone pointed out below, please do show the equations. I had to take quite a bit of math at university and our lecture on quantitative financial analysis was taught by a math professor who was so free of any passion and willingness to really explain the background - it was purely abstract. We were only 10 taking his class and given the German system really never spent any time with the students and his assistants had a personality like the rock you described. All your videos are really well done, just keep them coming. Beste Gruesse aus London, John
How cool, a riddle in form of physics. Thank you Sabine
This is my favorite explanation of "principle of least action" yet
If in classic physics objects already follow optimized paths, and in quantum mechanics objects do all possible paths and then settle on the optimal when "measured", does this mean that classical objects actually DO trial and error for optimization but only on the quantum level so that by the time we're measuring them at the classical level they're already optimized?
If so, that actually makes quantum mechanics not particularly mysterious. It's just the level of reality where the universe tests for optimal paths.
How many movies have explored this possibility? More and more by the day. The problem is, what counts as optimal? Are you optimal? Are your parents? You can't even begin to talk about this without defining optimal.
@@MrTonypace it was already defined within the video - the shortest time to get to another location
@@simanolastname2399 But this completely fails to deal with the implication of predestination/multiverse. How are you doing trial and error on the shortest path from a single event without knowing where you're going?
@@MrTonypace this was also discussed in the video. Did you watch it?
This was the best video I've watched in a long time! Thank you!
Very insightful presentation. The macroscopic view of objects "knowing" their optimal least action route fits perfectly within GR's Block Universe description. The issue is linking QM to Block Time. Or rather the measurement problem. Though it can't really be a problem when considering a measured particle is merely an excitation in the underlying fields of macroscopic reality. The act of measurement is simply part of GR's block time.
I only understood about 1% of this but I can tell it's really important for understanding physics.
wow, i feel smart cuz i understood everything except those integrals (which i have not studied about yet)
Will it make you feel better to know that only Einstein understood it, partially :)
No the ray of light doesn't need to know the future because it is not aiming at B. You picked a ray that went through B after the fact. If the Point source A was sending out light all directions there are many other rays that crossed the medium boundry but simple never came close to point B.
This also occurred to me. Would be interested in Sabine's response.
That's depends on the view point. If you see the principle of least action as fundamental then it kinda looks in the future, because otherwise why would the rays even go in radial lines, they could also all go in one direction and never hit the point. It's important to highlight that at this level of abstraction one does not assume any forces and also ignores the wave nature of light.
However, I think you're still correct, because it is imho flawed to assume the principle of least action as fundamental, it's just an extremely useful mathematical formulation of the laws of physics. As Sabine herself told, the Lagrange Equation are closer to real physics, as they yield differential equations that respect locality.
Was looking if someone wrote this to like it. Especially knowing that there is a local differential form to the minimization principle (Euler-Lagrange).
Edit : she actually mentions it after the 9:40 mark, very briefly
The thing is, any ray that passes through point B has bent so that it took the least amount of time to reach it.
If point B moves randomly, then the least time can only be known when the (eg) photon reaches it. You can't know future random motions. Even weirder, suppose a photon leaves a Quasar 13 billion years ago, and hits a point at the bottom of a pond on earth. Earth didn't even exist when that photon left the Quasar, yet that particle took the least time to reach the bottom of the pond. It seems to me that equations that explain the Principle of Least Time involve calculating the position of Point B, or involve treating (eg) photons only as wave functions, not as particles. The explanation that you can explain it by considering the photon as a wave function spreading out in all directions, that collapses when it first touches something, seem cheating. It has to collapse along the entire path it took, instantly.
This is an amazing realisation... Thanks. Many.
It is insightful the way you understand and explain physics I would have loved learn physics from your lectures when I studied Physics at my undergraduate courses. Thank you for your videos, greetings from Ecuador.
I disagree heavily with this characterization. The ray of light doesn't "choose" or "know" anything. If *you* were to point a photon beam at water, it will go to the point of least action based on where *you* aim it. Same for the rock, etc. We should avoid implying autonomy.
The action principle isn't formulated in terms of where you "aim" it, it is formulated in terms of where you end up. It minimizes action, subject to the *constraint* of the given starting and ending configurations. It does not involve any other final configurations. That is just how that principle works.
Btw, I don't mind attributing the same level of "choice" to light as I attribute to ourselves, since we're just a wet bag of biomolecules. As you may infer already, I don't subscribe to the existence of free will. We are just governed by fundamental physical laws like a photon is. Choice is an illusion.
Those kind of statement amazes people that don't know enough about physics but unfortunately does not provide any insight into what is really happening. It is in fact highly mislmiseading to say the least.
But the point is that you can reverse this logic. You don't choose anything, the principle of least action means that the point you aim at was chosen. You need a new principle that works better to disprove this implication of predestination. You are making your own implications without evidence.
MrMetra101: I agree. I left a similar comment. The location of 'B' is not an independent, its location is entirely *dependent* based, in the case of the light, on the initial angle the non-diffuse light is aimed and the amount of time elapsed, and, in the case of the rock, on its initial velocity vector and the amount of time elapsed.
For the light or rock to hit a pre-assigned location 'B', then an outside controller must know the *information of point B's location at time 0* and then use that information to control (aim) the light accordingly, or else project the rock (with the right velocity vector), in order to hit location 'B' at time b.
You've completely missed the point then. There is no "you" in the physics, you've just been confused by the presenters casual language. This principle of action is foundational to all of physics. It forms the basis of QED.
I don't understand why we are supposed to be intrigued by what light does when changing mediums. Point A, point B, and the point where light changes mediums are all chosen by us; and the light ray's angle at the medium change point is fully deterministic. The light ray does not "choose" anything, and most certainly it does not need to know about "what's coming" to do what it does; the light ray is simply passively reacting at all times to what came before.
Well isn't it at least a tiny bit interesting that the laws of refraction just so happen to produce the paths of least travel time? There is literally no obligation for it to on the sufface level.
@@dsdy1205 But they don't even do that, though. If they did, light rays would travel in a straight line from any medium to any medium and there wouldn't be any refraction at all.
Correction: We choose only two of the three points you listed. For example, we could place a laser at point A and aim it at the point where it will change mediums (and place a wall of detectors in the medium, and record which point on the wall detects the light). For another example, we could put at point A something that emits light in random directions, and put a detector at point B (and record both the detection events at B and the orientations of the emitter, to observe the correlation).
@@brothermine2292 You don't need to put a wall of detectors, you already know what Point B will be. Point B is a function of Point A and the Point of Incidence. By choosing Point A and the Point of Incidence, you are also already choosing Point B.
@@RandomHandle120 : You don't know that before empirically confirming the theory using a wall of detectors.
You missed my point. The OP claimed you "choose" B. In fact, you *deduce* B based on your choices of the other two items that the OP listed.
6:46 Sabine, S is usually used to denote path or trajectory, it's the space that the object moves through.
What an interesting and clear video! Thank you!
“Except it doesn’t” was precisely my thought as you were saying “it goes to all points”. No intercepting measurement required, only observation of where and how the action terminated.
I believe observing counts as measuring in this case, though i know very little of quantum mechanics.
@@diegoscb And, for that matter, there's exactly where "many worlds" would come in: it does indeed go to all points, and (assuming you still exist in all of those worlds) you observe all of them, but those are, essentially, "copies" of you, and each only knows about the one measurement. So it _looks_ as if it only goes one place.
@@KaiHenningsen But the Many Worlds interpretation comes with one major problem. The "other worlds" would have to affect our world because we know the paths interfere with each other. Given that the collapse of gas clouds to make planets and stars is chaotic, there should be phantom gravity wells all over every solar system. In fact, matter should be so evenly disturbed across the many worlds that any long distance force should be impossible; both gravity and the electromagnetic would be short range like the weak and strong nuclear force.
@@Amir_404 I certainly don't claim how GR and QM can be unified. And it sounds like that's necessary for your point.
@@Amir_404 Lustro upadku człowieka
To naprzykład dialog wewnętrzny człowieka z osobowości który napotyka dźwięki punktowe naprzykład gdy Człowiek jest w dialogu wewnętrznym i usłyszy trzask gałęzi drzewa pod swoim butem lub odskoczy mu kamyk na drodze po ruchu nogi człowieka który idzie i toczy dialog wewnętrzny. Człowiek winien być uważny na punkty dzwięku z otoczenia i punkty dialogu wewnętrznego w nim samym. Dźwięki oznaczają że Błąd dialogu osobowości człowieka jest Błędem człowieka. Błąd jest pozytywny co znaczy potwierdzony że wystąpił występuje .I człowiek winien odejść od ściężki tego dialogu wewnętrznego naprzykład ze ścieżki osądu lub rozwiązywania problemów w uczuciach złości gniewu obniżonego poczucia wartości. Lub stanów uczuciowych naprzykład po odrzuceniu odpowiedzialności za własny upadek co jest uczuciem pragnienia samouznania się po sytuacji gdy zrozumiał że kierował uczucia niskie złe w sobię samym wobec innych ludzi osobowości osobowości ludzie to tacy którzy kreują
Swój neurotyczny obraz własny do oceniania się Tłem środowiska w którym żyją i pragną wymagają od siebię lub innych ludzi .Powrócę teraz do lustra upadku od Boga które jest żeczywistością w której żyjemy każda osobowość + Lustro upadku =upadek gdy osobowość jest myśleniem o sobię samym i innych ludziach bez zatrzymania się w Zero Myśli i miłości jedności z Bogiem i ludźmi.
Nie ma człowiek osobowości niezmiennej w czasie A mimo to człowiek ocenia się w czasie jako osobowość swoją osobowścią używając z teraźniejszej osobowości zranionych uczuć myślami o sobę samym co pobłebia utrwala w czasie zranione uczucia i nie pozwala w stanie trwania zranionych uczuć rozwiązywać własnych problemów. Tak trzaski z lustra upadku naprzykład dzwiek wyłaczającego się nagle czajnika lub trzask okna grzejnika aluminiowego dźwięki jak stygnie lub nagrzewa się głównie chcę zwrócić uwagę na dźwięki w otoczeniu człowieka te które są dzwiękami punktowymi z dialogiem wewnętrznym aby sobię przyznawać że się jest w błędzie. Sytacja dodatkowa to zrozumienie wieloznaczności i kierunków czy dotyczy mnie to dla osób zewnętrznych czy mnie samego tak odpowiedź na te pytania można uzyskać tocząc dialog wewnętrzny sontanicznie z zaskoczenia. Konflikty są również wyraźnie widoczne w w strąceniach przedmiotów własnymi rękami lub układzie przedmiotów w taki sposób że Człowiek sam sobię przeszkadza coś zrobić nie należy planować stanowiska pracy prywatnie w domu lepiej się uczuć z błędów powstających z obecnej w sobię woli dla siebię samego lub z woli w sobię dla innych ludzi. Ludzie lubią szybkie decyzje w kilka sekund lub minut w ich życiach nie testują nowych decyzji takich nad którymi pracuje się w sobię przez tygodnie miesiące. Ludzie nie pracują w pielęgnowaniu obiektów wewnętrznych uczuć idealnych w swoich osobowościach uczucia idealne pięknie są używane jako zasób do zwrócenia się do myśli od których uczucia pięknie giną ranią ludzie uczucia pięknie myślami lub pracują w uczuciach trudnych do zniesienia nad swoimi relacjami z bliskimi rodziną w tych uczuciach nie rozwiązują problemów lecz przekonują się wrogo wobec innych ludzi.
Czasem doprowadzają się do cierpienia i nastepnego dnia ich organizmy mają zamiast uczuć odbicia od dna na którym byli czują się lepiej lecz pamiętają co mysleli i kontynuują proces myślowy na poziomie niedekwatnym niszcząc w sobię lepsze samopoczucie którego nie wypracowali w przekonaniach. Uzupełniają obraz negatywnymi informacjami dla wzmocnienia szkodliwych przekonań. Dotyczy to mniej lub bardziej ciągle lub czasami każdego.
5:19 The ray hits B beause you aimed your laser appropriately, i.e. not aiming exactly at A. The ray doesn't magically search for A and the ray does not look into the future, it follows some local rules like propagating wave fronts of different speeds. And if you aimed right it will hit A. Let's not pretend weirdness exceeds that of QM which you qualify as not weird. 😆
The variation principle says that any physical law can be reformulated as an optimization problem. So if you say ds=0 is the Weltformel it's like saying there are physical laws. But it isn't saying what it is, so we are no further. 😆
Aiming at a point on the surface interface added a constraint. The new angle is optimal in the constrained new system.
@@Quroxify Sure you can phrase it as an optimization problem. But she is saying that the light "knows" that it will hit a medium in the future and therefore aims at a different location on the surface (versus to when there is no medium). That is nonsense. No light aims anywhere itself. It either shines in all direction or the experimentalist is aiming. In both variants there is nothing the light "knows".
@@tnb178 When it hits the surface, how does it know where to point? It doesn't continue in a straight line (unless it hits at 90 degrees), it changes so that any point it hits will have no faster path to it. How does the light know this without checking all other possible paths? This is what she is talking about.
@@vibaj16 What do u mean by "a faster path"? A Faster path from what point to what point?
Its great to see the formulae for electrodynamics & GR. It would be interesting to hear more about how the measurement postulate may relate to the future dependency of the Feynman path integral
Love your presentation style, sehr geehrte Frau Hossenfelder! Also the fresh updates you give to overused graphical elements like @1:07..
I finally got and intuition for this by following a baseball into Earth's gravity well (it took many, many tries).
I was trying to visualize the temporal gradient, when suddenly time and space unified and I could see the geodesic.
The curving path through spacetime of no effort.
And I was like "Of course, what else would a baseball do? It doesn't have rockets."
One of your best videos Sabine.
So anyway I have this Theory of Everything, should I email it to you?
Just post a summary & url at the Theories of Everything website.
Doesn't it fit in the margin of your post?
Well does your theory says you should email it or not?
I think you can only send it if you do it in a song
Plz cc me… thanks
amazing !!! Least action is always fascinating tool for complicated problems.
Thanks Sabine, vielen Dank! I would be very much interested if you did a follow-up of this video by explaining the relationship between (K - V) and (K + V), given that the first links to the PLA and the Lagrangian, and the second to the Hamiltonian. And by the same token, how the L and H differ and relate (or not) to each other, and what each one is most useful for.
A 2nd question relates to the definition of K and V: that is, how general can the definition of “kinetic” and “potential” be? Are spatial coordinates essential, or just a particular specification, even including the generalized coordinates q_i? What is the most general “space” that K and V can handle?
Thanks again for a very clear presentation, as is typically the case!
At first glance, the thing we call "Weltformel" looks disappointing. Just a short equation. However, there is so much more behind it. Fascinating stuff!
That's kind of the nature of math. You take a big complicated thing that's too hard to actually even fully understand (i.e., QM or GR), and you represent it with a single letter, and then be amazed that math can describe physics. ;-)
@@darrennew8211 Lustro upadku człowieka
To naprzykład dialog wewnętrzny człowieka z osobowości który napotyka dźwięki punktowe naprzykład gdy Człowiek jest w dialogu wewnętrznym i usłyszy trzask gałęzi drzewa pod swoim butem lub odskoczy mu kamyk na drodze po ruchu nogi człowieka który idzie i toczy dialog wewnętrzny. Człowiek winien być uważny na punkty dzwięku z otoczenia i punkty dialogu wewnętrznego w nim samym. Dźwięki oznaczają że Błąd dialogu osobowości człowieka jest Błędem człowieka. Błąd jest pozytywny co znaczy potwierdzony że wystąpił występuje .I człowiek winien odejść od ściężki tego dialogu wewnętrznego naprzykład ze ścieżki osądu lub rozwiązywania problemów w uczuciach złości gniewu obniżonego poczucia wartości. Lub stanów uczuciowych naprzykład po odrzuceniu odpowiedzialności za własny upadek co jest uczuciem pragnienia samouznania się po sytuacji gdy zrozumiał że kierował uczucia niskie złe w sobię samym wobec innych ludzi osobowości osobowości ludzie to tacy którzy kreują
Swój neurotyczny obraz własny do oceniania się Tłem środowiska w którym żyją i pragną wymagają od siebię lub innych ludzi .Powrócę teraz do lustra upadku od Boga które jest żeczywistością w której żyjemy każda osobowość + Lustro upadku =upadek gdy osobowość jest myśleniem o sobię samym i innych ludziach bez zatrzymania się w Zero Myśli i miłości jedności z Bogiem i ludźmi.
Nie ma człowiek osobowości niezmiennej w czasie A mimo to człowiek ocenia się w czasie jako osobowość swoją osobowścią używając z teraźniejszej osobowości zranionych uczuć myślami o sobę samym co pobłebia utrwala w czasie zranione uczucia i nie pozwala w stanie trwania zranionych uczuć rozwiązywać własnych problemów. Tak trzaski z lustra upadku naprzykład dzwiek wyłaczającego się nagle czajnika lub trzask okna grzejnika aluminiowego dźwięki jak stygnie lub nagrzewa się głównie chcę zwrócić uwagę na dźwięki w otoczeniu człowieka te które są dzwiękami punktowymi z dialogiem wewnętrznym aby sobię przyznawać że się jest w błędzie. Sytacja dodatkowa to zrozumienie wieloznaczności i kierunków czy dotyczy mnie to dla osób zewnętrznych czy mnie samego tak odpowiedź na te pytania można uzyskać tocząc dialog wewnętrzny sontanicznie z zaskoczenia. Konflikty są również wyraźnie widoczne w w strąceniach przedmiotów własnymi rękami lub układzie przedmiotów w taki sposób że Człowiek sam sobię przeszkadza coś zrobić nie należy planować stanowiska pracy prywatnie w domu lepiej się uczuć z błędów powstających z obecnej w sobię woli dla siebię samego lub z woli w sobię dla innych ludzi. Ludzie lubią szybkie decyzje w kilka sekund lub minut w ich życiach nie testują nowych decyzji takich nad którymi pracuje się w sobię przez tygodnie miesiące. Ludzie nie pracują w pielęgnowaniu obiektów wewnętrznych uczuć idealnych w swoich osobowościach uczucia idealne pięknie są używane jako zasób do zwrócenia się do myśli od których uczucia pięknie giną ranią ludzie uczucia pięknie myślami lub pracują w uczuciach trudnych do zniesienia nad swoimi relacjami z bliskimi rodziną w tych uczuciach nie rozwiązują problemów lecz przekonują się wrogo wobec innych ludzi.
Czasem doprowadzają się do cierpienia i nastepnego dnia ich organizmy mają zamiast uczuć odbicia od dna na którym byli czują się lepiej lecz pamiętają co mysleli i kontynuują proces myślowy na poziomie niedekwatnym niszcząc w sobię lepsze samopoczucie którego nie wypracowali w przekonaniach. Uzupełniają obraz negatywnymi informacjami dla wzmocnienia szkodliwych przekonań. Dotyczy to mniej lub bardziej ciągle lub czasami każdego.
at 5:14 it refers to the odd fact that the light "knows" the future to find the shortest path, I know the solution is explained after, but I want to give another view. starting from point A if you want to reach the point B you have to select the direction of the light to reach it according to the physics laws, so there is nothing odd, you are selecting the direction to reach B. if you select the direction randomly the light from A will reach the border between the 2 medium and will change angle such that the famous equations are satisfied, and such that any point it passes it in the second medium is also the shortest path. This seems less odd, you don't need to know the future and I don't get why even bringing this up. Am I missing something?
You are right-on. I wrote a similar comment.
@@sauerjoseph for quantum theory is different?
you already answered yourself: "such that any point it passes it in the second medium is also the shortest path" (well, it's fastest path, not shortest path). Also, you're saying "will change angle such that the famous equations are satisfied" well where do the famous equations come from? Why are they that way? They are that way so that light travels the fastest to any point it hits, and it needs to know how long other paths would take to make sure it is taking the fastest path.
I think that indeed the particle "experiments on" or "tests" taking multiple paths to its future position, and then *chooses* the path of least energy. Yes, you read correctly: the particle chooses according to the laws of physics governing it's environment. Why can I say this so confidently? 2 reasons: 1) the particle is indeed a *probability* distribution, each point in the distribution taking a possible energy path. Note that the distribution is not only spacial (i.e. the particle's position) but also *temporal* (i.e. the particle's time, or proper time is also a distribution in spacetime). Each path then becomes a possible solution to the equation of the "theory of everything" (which we have not derived yet). (2) in electrical engineering, we use simulators to calculate the transient voltage/current based on set of rules / equations in the same manner the particle chooses it's path: via convergence, similar to the perturbation theory. Without these, no integrated circuit designs would be possible.
Sabine, you are a treasure to physics and ALL education. How I wish I had such a lucid teacher five decades ago. Except for the brief time I knew Feynman, I can't imagine a more inspiring and clear explanation of this topic.
Agreed.
Reminds me of John Mayer teaching pentatonic scales.
Hello Sabine, I think there are typos in equations for the path lengths (after 4 min 30 s). I seems that h_1 and h_2 must be flipped
5:19 I don't think the light ray 'picks' the right place to change direction. It's just pointed at that point and changes the direction based on the angle of incidence and the speeds in the mediums. For it to pass through B, you chose the right place to point the light to.
What am I getting wrong here?
@Aayush Dutt: You’re not getting anything wrong. Mathematicians just run out of stuff to do and physicists like funding
The light ALWAYS takes the quickest path through the medium. If it were just being bumped along 'in real time' based on ONLY present information, then how could it take the quickest path every time, never making a slower 'trial' run?
@@Boogaboioringale this is conspiratorial thinking.
I think the light just changes the angle in a specific way the moment it hits the water. Right?
@@maxwelldillon4805 The direction in the medium is set by the interaction of the light's E field with the material's E field. There's a great fermilab video about it
Best video I have watched in a long period of time. Thank you❤
Such a clear presentation !!
It seems that we keep circling back to the ideas of "time" and "future" -- which are not supposed to be part of the quantum domain. Despite Lee Smolin's attempts to reinvent time as a fundamental force, it seems more like an emergent to me, and is subject, itself, to the principle of least action. Perhaps time "switched on" with the Higgs field, since our ideas of mass are based on inertia, which is dependent on time. Just sayin'.
Neutrino masses (AFAIK) do not depend on the Higgs. However, massless particles don't experience time, so your idea may have merit.
(Edit: I earlier wrote that quarks likewise did not get their masses from the Higgs. That was incorrect.)
Sabine's personal belief is that the world is superdeterministic, which is what she's insinuating again at the end of the video. If the future is already determined, then it's fine for physics to take the future into account. The future can "affect" the present because it really already "happened", we just haven't gotten to it yet.
Nice
@@tomkerruish2982 I thought that was the whole point of finding the Higgs. To explain why elementary particles have mass at all. Most of our mass if from the energy of all the particles being bound together. But alone?
@@SimonSozzi7258 I've since edited my comment, as quarks so indeed get their masses from the Higgs (according to the standard model). However, the very tiny masses of neutrinos are still of unknown origin.
I'm a bit confused at 3:45 -- what exactly is at A? Is it a point source radiating out in all directions, or a focused beam. If the former, wouldn't the light cover the entire surface between A and B. And if the latter, then the entry angle (alpha) is per-determined. hence no mystery.
If the former, the only ray that hits B will have done it by the fastest path to B. If the latter, the entry angle is predetermined (assuming we already know that it travels in a straight line while in the same medium), but not the inside angle, because point B isn't predetermined. The light bends such that for any point it hits, it will have traveled the fastest path to it (so it doesn't go in a straight line, because then the points it hits would have faster paths to them)
@@vibaj16 Yes, that's pretty much what I said. In the former, the surface is covered completely, thus the volume of water is saturated in light. Every "B" has a corresponding surface point -- so no mystery. In the latter, light gets to some non-fixed point B AFTER it hits the surface. The light from A could care less where B ends up being -- so again no mystery. I guess I am just missing what is so "mysterious" about what seems to be common sense.
@@ravenlord4 The point is, why does light bend such that it takes the fastest possible path to B? How does it know it's the fastest path?
@@vibaj16 My point is that it doesn't "need" to know. "B" is simply an incidental point along the line of refraction that light from "A" will always take. There is nothing privileged or special about B. Think of it this way. If the first license plate on a car you see today reads "DWH-4452" do you remark "Wow! What are the odds THAT plate appears?" Well to be sure, the odds are millions to one, but there are millions of cars, and you had to see SOME plate, and there is nothing privileged about that plate. It is only remarkable if for some reason you decide to look for that particular plate that day. Now that would be something to write home about. So to recap, Point B above is just some random point in the water that just happens to be in the path that the beam of light from point A took. There is nothing remarkable about it. There has to be SOMETHING where B is, and B happens to be it.
This was fascinating, thank you
excellent video, thank you Sabine.
It really is a theory of everything, I've even seen employees adopt the principle of least action :)
They go even further. A worker in place stays in place when untouched
And employers pay them the smallest possible wage with smallest possible workers rights
A counter-example proves it's not a theory of everything: The practice of least action during sex will lead to no action in the future.
@@brothermine2292 it seems to require an external source of will/energy otherwise it will be least action to the end point of equalising the differential. So i think its one of those cases of 'external forces'.
You never mentioned Ted Chiang's Stories of Your Life (and Others)! This story is the basis of Arrival, but the story goes into the theory of least action in some depth (spoiler: the dependence on the future is real in this fictional universe). Sabine, you must read this and deconstruct it. Ted is the living writer who is most likely to be possessed by genius - and this is far from the only evidence. You might be able to help him.
This story is the basis of "Arrival" the movie.
Interesting ... The idea reminds me of how Bellman Equation offers a super-structure that already encapsulates the Euler equation (and some other aspects of the calculus of variations).
The idea is elegant, profound yet simple, and altogether brilliant.
thanks for you persistence each detail
This video ended too soon.
Interesting, never thought about it that way before.
each point, in a way, is aware of what all other points would do were they in similar situations. the aether is functioning similarly at all points. it is of one mind. changes in local conditions change the relationships of constants to one another until the constants break, as up becomes left, and forward becomes down.
great stuff sabine
This is the best video i have ever followed with Sabine
Classical mechanics says that the physical world is intrinsically lazy: it always takes the path of least action.
Quantum mechanics adds to this that the physical world is also intrinsically stupid: it tries every other path first.
(not mine; wish it were)
Also, 11:28 you've got your bra and ket reversed.
I don’t get it why people are still looking for the answer to everything. It’s 42.
😊
Enlightening. Thank you.
1) This is a fascinating exposition of the material and 2) I'd love to read some of these source documents, and 3) I hope it's diff eq light reading.
Doesn't this imply that future is predetermined?
Or rather, considering probabilistic nature on small scales, the future is better defined the closer it gets?
Yes, it is.
But please don't observe it... 😉
The future is determined in as much as Newton’s second law or Maxwell’s equations etc predict it (see video at 10:05), at least for classical physics.
For being a show that tries to take the "gobbledygook" out of physics,
there's still a lot of 'time travel' mumbojumbo in this episode.
Because yes: *light "knows" about the future!* WE ALL DO! Spooky? Hardly!
It's called *_determinism:_* any future point B is *_encoded_* in the initial physical parameters. 🤔
This is what I learned and was fascinated by it when I read the Feynman lectures on Physics. Also recommend his QED book.
Thank you for this video. I am an almost retired mathematician, and I'm trying to interest my friends in physics and mathematics. Your explanations are beautiful.
ok, that was an amazing video, answering a lot of questions i had and posing even more but in the different, curious way. thank u :))
the way i've always understood action (or maybe it was the lagrangian? can't remember) was that it was a measure of 'activity' (used in a very non-rigorous manner)
L = T - V where T is the kinetic energy and V is the potential energy
when L is very positive, most of the energy is in kinetic energy and not potential energy, so the system is very 'active' in terms of movement
when L is very negative, most of the energy is stored as potential energy, so there's not a lot of movement and thus not a lot of 'activity'
You are so much fun to lessen to you make me think and at the same time laugh. Brilliant lady, thanks.
Your very own ‘Science Without The Gobbledegook’ follows this principle!!! Brava, Frau Sabine!!! We salute you!!!