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.
@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.
@@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).
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.
@@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.
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.
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.
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.
@@mayabartolabac Only a few of his lectures were recorded and posted on UA-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.
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.
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".
@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.
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
@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.
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.
I have been a Physics teacher for 38 years and I am 60 years old. This was the best explanation of the principle of least action I have seen in my entire life!
'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?
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.
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.
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.
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
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 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.
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!
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 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.
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
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.
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'
For the sake of rigor, it's worthwhile to point out that in the form presented here, the action principle is known as Hamilton's Principle and it constitutes the foundation of Lagrangian Mechanics. It is an integral principle, describing the evolution of a dynamical system by an optimal path in its parameter space between two fixed configurations (the end points of the action integral). Equivalently, the differential form of the principle is simply given by Lagrange's equations, which are the equations of motion for the parameters (also known as degrees of freedom) in question. The name of Euler-Lagrange equations is usually employed for more general or more abstract problems that need not necessarily regard mechanical systems directly. The Principle of Least Action is a somewhat different variational principle that arises in Hamiltonian Mechanics, but sometimes the name and notation (specifically, the S label for the integral) get carried over in the context outlined above. They are however different things among the many results and methods of variational calculus. As for why the rock knows to obey variational principles, there is no real mystery given that the trajectory itself is completely specified by the initial conditions.
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.
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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.
@ 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?
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
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.
@@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
Time dilation is force. Put a clock in a wheel it slows down, Hefele Keating Experiment. Einstein's Lorentz and this equation measure all forces, F=(t'-t)hC^2 e 34 put in velocity in the Lorentz Get The Time dilation difference as Force of quantum gravity. Go sit in a wheel with your clock we will slow down time, except you got crushed by going light speed. The time dilation on acceleration is gravity.
You're right ... Physics is the interface and Math the implementation ... There are equations "labeling" fundamental theories: E=hf, E=mc^2, S=kT ... Yet i think that Nature is "smarter" then we think it is: there is a transient stage and a steady-state (e.g. for 2-slit experiment) and getting to the steady-state regime when the least action process is attained, Nature uses an actual random, adaptive search corresponding to "all paths'' (like streamers of a lightning finding its way to the ground). Thank you for another beautiful presentation.
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.
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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 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.
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.
1:15 Nature doesn’t need Trial and Error, Mankind does. 1:56 Straight Line if no force acting upon it 3:20 Least Time Path 6:10 Kinetic Energy Path Action, S 8:09 Optimum 9:51 Euler Lagrange Equations 10:36 All Paths, All End Points, Collapse to 1 End Point 11:40 Math - a language used to decipher nature
I don't quite understand why you find it so interesting that the object might "know the future", because as you said, the object just knows the next step from the previous one(s). But it got me thinking. In QM the particle doesn't make this "decision" of where it will go beforehand, it only decides where it is at random (based on the probability density) when you "ask" it. So this optimal path might just be rather the result of observation than something inherent to the object. We keep our eyes on the rock in space, and therefore it contiuously chooses the shortest path at every moment. Our observation of the object creates this reality as much as the object itself.
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!
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.
@@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?
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.
The action can actually not only be the minimum(least), it can also be the maximum, the inflection. The lagrangian can not only be T-V , it can be all kinds of functions of generalized coordinates, which can also satisfy the Euler-Lagrange equation.
Hi, Sabine. The math is correct at 4:24, but the diagram is mislabeled in two spots. 1. X should extend from the vertical through the point of incidence to the vertical through point A, and D should extend from the vertical through point B to the vertical through point A--instead, they both extend to the left edge of the diagram. 2. The h1 and h2 in the diagram should be swapped in order for the math to be correct. Thanks for making another awesome video, Sabine!!
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.
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
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 reminds me of "The Texas Sharpshooter". The Texas Sharpshooter fires a bullet from his gun at a barn wall, then finds the bullet hole and paints a target around it. Later he will claim this is evidence that he has amazing shooting skills, as the bullet hit the exact centre of the target. Of course, in reality he did not know where the bullet would hit the barn, just as the rock did not spookily know that it would land at point B.
Regarding the intuition behind why it can be called action in the kinetic context: if you look at it the other way round, (T-V) is the derivative of S wrt time, i.e. the momentary change of action. That means the more you increase your action in a certain moment, the more kinetic energy (amount of actual motion) and/or less potential energy (amount of possible motion that is not happening) you get in that moment. If you don't change your action in any moment, the balance between actual and possible motion remains stable, they can both increase or decrease but by the same amount -- like some kind of energy inertia. If you decrease your action, your actual motion is disappearing compared to your possibility. So much if we are differentiating wrt time. The principle is stated as differentiation wrt distance, i.e. along all the points on the path, regardless of how fast and which direction you move in any specific point. It states that the position-wise amount of the action should not change, so perhaps a better name would be a principle of path-wise stable action, or a principle of even distribution of action over path. In other words, if you want the rock to fly higher or do something unexpected, you have to act upon it, the rock and the universe won't do it on its own, they're just doing their usual lazy thing. To get more general, we usually think of time as "moving" evenly and compare change of position wrt time and call that velocity. In these terms, change of position could be thought of as the effect of the action, regardless of how much time it takes. Then the principle can be restated as: the amount of action you need for a unit of effect of that action is stable, it does not change. Ever. You could also say, that the universe will not waste action for no effect.
“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.
@@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 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. 😆
@@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.
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 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.
"Equations are smarter than physicists" - anon. One of the most interesting topics in the history of science, is the resistance to accepting the consequences of some new equation, for instance the time it took to accept that the quantum equations were really implying probabilities. cf Newton: 'Hypotheses Non Fingo'
Liebe Frau Professor(in). You should not forget (I don't believe - even for a moment - You did.) that with each possible path a phase is associated. The classical path "usually" is the path where this phase is stationary. Yes, the particle goes through every possible path between A and B. But the phase associated whit all these paths varies so wildly that the waves that arrive at point B will cansel each other out, leaving only those paths where the phase is stationary to contribute significantly to the trajectory. The particle doesn't have to foresee the future to know it is going to point B. It all happens naturally. That is the beauty of Feynman's formalism. It completely solves the mystery of how the particle knows what is the path of least action so elegantly and simply.
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?
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?
@@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
The least action principle has recently been generalised/expanded in a fundamental way, such that it comes even closer to a 'theory of everything': in the in 2009 proposed theory of 'Lagrangian multiforms' the Lagrangians, which in that theory are components of a continuous (or discrete) p-form in a multi-time space of independent variables of arbitrary dimension, emerge themselves as solutions of an extended set of Euler-Lagrange equations. Thus, this theory changes the goal posts: the multiform principle not only selects the most optimal trajectory for a given Lagrangian, but it also selects the Lagrangian components itself. The drawback is that the resulting Lagrangians correspond to integrable systems which are deemed very special and rare, but they amount to some kind of critical points in what could be considered a 'space of theories', namely those where the equations of motion become, in a sense, insensitive to the dimensionality of the space of independent variables. An example of a solution of the set of EL equations is the Lagrangian for the Ernst equations of GR describing gravitational waves. Another example is the Lagrangian for the Einstein-Maxwell-Weyl equations. That this theory only provides special Lagrangians (corresponding to integrable systems) may be seen as a drawback for a general methodology, but as a founding principle it is perhaps precisely what is needed: the conventional equation \delta S=0 allows one, in principle, to plug in any Lagrangian one choses, and hence is not predictive on the form of the theory. The multiform principle, which has only very specific type of solutions (i.e. input Lagrangians), does predict the form of the Lagrangian, and this is what we would expect from a foundational principle - after all, one wouldn't expect 'Nature' to allow for arbitrary choices of Lagrangians put in by hand, or engineered on the basis of other secondary principles. Having said this, it remains to be proven how truly 'physical theories' fit into this new principle, e.g. the standard model. But the fact that certain important reductions of the Einstein equations fit in naturally, seems promising for actual physics to be contained in this - so far mostly mathematical theory. The pioneering paper in this direction was: "Lagrangian multiforms and multidimensional consistency, J. Phys A: Math Theor 42 (2009) 454013, (and there has been quite a bit of subsequent work by various groups on the mathematical aspects, but not yet so much on the physics).
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."
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.
@@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'.
Two minor corrections: in the figure in 4:21, h1 and h2 should be swapped. Also in the same figure, x and D should stop at the x coordinate of point A. Other than that, thank you for this great video, it is very interesting and insightful!
There was a good tv serie couple years ago called "DEVS" and focused on the theory that everything that happens and will happen, can be predicted / determined if you know every effect of everything on everything at one point in time.. Everything happens because something else happened before. "DEVS" is a must see for those who are curious about the theory that the universe is DETERMINISTIC.
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.
@@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?
@@Simonjose7258 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.
@@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.
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. 🤔
The apparent dependence on future comes across because the quantum particle follows all paths; and collapses in the future (or when any observation is made) where the Feynman Path Integral yields high probabilities - which turns out to be exactly where the classical action is stationary.
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.
What I am interested in is the critical angle. Below the critical angle the light is reflected, and above the critical angle the light is refracted. The question is, what happens at exactly the critical angle? Is there indeterminacy in the refraction/reflection switch? From a stick in water, light is reflected at all angles so some of the light rays must intersect the surface at the exact critical angle. Another question is, for a slow light ray coming from the water, how many air molecules are needed to reset the speed higher?
Shortest path is possible on the angle of motion. U change angle & path changes. Also path is medium depending. U change medium path change. Also it depends on nature of motion. If it is straight it will reach at perpendicular of destination. But if it is wave or spiral or projectile. It will travel depending on force & friction. Boomerang may not travel shortest path.
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.
The "squiggle" is the lowercase Greek "delta" and expresses variation or change, like in delta-v (change in velocity). Now I understand why the Lagrange equations are so important... Thank you!
The hypothesis of optimal intent: Given a series of boundaries and limits; produce the optimal path while under influence by antagonistic or/and protagonist intent.
Very good deconstruction Sabine:the futural moment a la Fermat und Dirac - "borrowing from the future" which yields immense power - is not* dealt with by either GUT or UFT - or even QM. But it's the key to why Measurement is totally integral to the make-up of our reality. Love the stuff, btw :) JM
I stopped beliving in theories a long time ago, I've got tons of my own... but if a certified experiment or a precise valid observation relives something new, no matter how radical it is, I belive it.
As I figured out (not being a physicist, just a regular consumer of pop-science videos on YT) nearly all greatest mysteries of physics boil down to the single truly *fundamental* question how the Universe came into being. But inside this very question there is another one, even more intriguing: how come things do not fall apart, how the Cosmos retains its integrity? It is not a trivial one and it's really worth some deliberation. Some physicists more aware of the epistemological nitty-gritty of their work tend to assert that the "laws of physics" as they call their discoveries concerning observable, repetitive patterns of transformations of different forms of matter and energy are merely imperfect approximations of some hidden, perhaps never fully knowable 'objective' reality and their role is just to provide us with some usable tools, models adequate enough to become the basis for experimental work and scientific predictions. As the data amount and new observations are made, sometimes not consistent with previous assumptions, these models are being refined, closing the gap between current mathematical descriptions and the pursued truth in this sort of asymptotic approach. However there still remains the master conundrum of why at all there are any such regularities that allow science to exist at all, why all electrons look and behave the same, why properties of particles don't fluctuate wildly every instant, why there is any order in the Universe rather than sheer chaos. One might evoke the "anthropological principle", but this does not tackle the ensuing question why among all possible universes there is even possible at least one uniform Universe comprising standardized matter. Doesn't it really point towards some preexisting template which had given matter and energy their apparently constant forms and properties? Hence there is my question: do you believe in Platonic ideas? As for me, the more I learn about intricacies of the micro world, the more I do.
Very good video with clear explanations. Minor quibble, in diagram of reflection, angles of incidence and reflection were shown measured from the mirror. Should be from the normal surely.
The danger of a theory of everything is, that you may end up with a theory of nothing. I did IT-security and set up an IT security policy for our company. It was long, detailed, not very marketable, but I must say, it was also good. When discussing it with a colleague, me wanting to make it considerably shorter, the colleague, fed up maybe, at a certain moment suggested a policy with only one statement: “There be security”.
Dr. Sabine, just read chapter7 in your book 'Existential Physics', and understand know, what made you so enthused about this principle. Without checking the math totally, it's enlightened!
Dieses Video war einfach toll! Es erinnere mich an einen Kurs, den ich in der Universität gemacht habe, der Angewandte-Differenzialgleichungen hießt, wobei ich den 2005 Artikel von Katalicky und Jicha, den ein Modell für den Verkehrsfluss, das die Euler-Lagrange-Gleichungen benutzt, studierte. Sehr cool! Bitte machen Sie mehr Videos mit Kalkül, das gefällt mir. Danke schön.
"...the particle goes to all points anyway. Except... it doesn't." Mr. Everett would like a word with you. MWI plus the principle of least action together make all laws of physics statistical in nature: things tend to do the kinds of things we observe them tending to do because it would be harder (less optimal, requiring greater action) and therefore is less likely for them to do otherwise. But they do do otherwise, in a much smaller number of possible worlds; because everything that possibly could happen does happen. We just tend to usually see the kinds of things that are most likely to happen happening... kinda by definition. The real interesting questions left in physics after that is "what kinds of things are possible to happen and how likely is it for them to happen?", which is a question of which of the infinitely many possible kinds of mathematical structures our concrete universe is.
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.
The problem with the mirror example is that the minimal path length rule only applies to perfect mirrors. If I replace the mirror with a grating, then the entire thing falls apart completely. Different wavelengths will now be reflected at different angles and those angles do not have to be symmetric to the normal of the grating. We make good use of that in high quality spectrometers by shaping the response function with the shape of the grating surface. And if I make a hologram, then I can reflect an incoming wave front any which way I like.
Mathematics is not only a code or a language. It has underlying principles, like, well, a language. It has a grammar as a way to select what is a valid sentence. Mathematics, as languages, are a product of "Reason" and they must follow Reason to be what they are. If Reason is just a human attribute, then every "intelligent" entity should have its own. But, then, those entities wouldn't be able to communicate among themselves. For me, it follows that Reason is not only an attribute of every intelligent entity (i.e. universal) but the substance of cognition. It is not a tool, it is us being intelligent beings. Then, It follows that human mathematics is just a language that expresses the same truths (or sentences) about the world. We should be able to compare mathematics from alpha centauri to ours and establish an equivalence or translation.
One of Sabine's best, exposing the future line integral of Feynman's leading to an exquisite explanation of QM. This future involves the entire path of Schrodinger's wave equation, resulting in the unitary evolution creating classical objects like planets, stars, black holes and singularities. Hawking predicted the future, while Maldacena revealed the infinite axiom algorithm of QC functions.
It's just too bad that the path integral doesn't do what you and Feynman think it does. Feynman made a conceptual mistake there when he postulated that. What we need to get to classical objects from quantum fields is constant weak measurement. That was already known in 1927/1929, two decades before Feynman even came up with the path integral formulation. I doubt he paid attention to those papers, though. His own lectures and writings give, to my best knowledge, no indication that he knew about Heisenberg's and Mott's work in that direction.
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.
Sabine, I gather your idea is to start with a Feynman diagram whose functionals have finite length and resolution since they start in some earlier past (e.g., a lab setup) and end at some later past (e.g., a lab measurement). You extend those functionals to the beginning and end of time, giving them effectively infinite resolution as with any wave train Fourier transform (comms 101). With the added resolving power of infinitely long functionals, the bundle of in-phase functionals shrinks to a diameter of zero in XYZ space, and the whole blurry mess of _probability_ functions disappears. The opportunity for a "pilot wave" also disappears since pilot waves are another way of expressing the fuzziness and uncertainty of Feynman's finite path integrals. Your infinitely tight in-phase functionals eliminate that too. You end up with precisely what Minkowski proposed for relativity, only at the quantum level via your infinite extension of the path integral. Retrocausality, or whatever folks want to call it, is inherent in this approach since those infinite-length functionals convey infinitely precise information in both directions. Your justification for treating the unknown future as known - and it's an excellent one - is that the principle of least action in the quantum domain _works_ by using Dirac's functionals, which are inherently time-embedded.[1] So here's the oddly simple problem: By eliminating all quantum uncertainty, specifically by compressing the in-phase bundle to an infinitesimal diameter in their XYZ slice, you also make each such point infinitely massive. Planck uncertainty doesn't suddenly give you a pass merely because you used path integrals, especially since path integrals and quantum uncertainty are two sides of the same Fourier-transform coin. Yes, I know, renormalization, or this trick, or that trick, whatever. Particle physics, in particular, stopped bothering with deep debugging and regression analysis decades ago, preferring to slap messy fixes on top of bad ideas. Been there, done that. You're still violating quantum uncertainty with all of this. The good news is that your idea is closer to correct than most if you can drop all the Minkowski (and Hilbert, oh my) nonsense about spacetime providing infinite resolution for precisely zero cost. Your model sounds essentially correct _in the non-existent limit of infinite energy_. But observationally - via labs, telescopes, and actual data - our universe doesn't have infinite energy. It would collapse if it did, and notably, it doesn't. The fix is to treat your model as a finite, quantum-limited _approximation_ of a block universe. Does it see into the future? Yes. Does it reach into the past, sometimes doing profoundly weird things? Check. Do simple events here entangle themselves with events in the indefinitely distant future, possibly even billions of years hence (think cosmic photons)? Sure. Is the future fully determined? _No._ It's not even close. For any finite complex system, you can only encode a level of certainty proportional to the total energy of your carrier wave. Our carrier wave is the total positive energy of our universe - the sum of its visible matter, radiation, and dark "matter." This sum is vast, but it's _not_ infinite. That's especially true after you divvy it up for the task of moving around all of those Higgs-mechanism rest-mass fermions that are the true marvels of our universe. Are some items transcendent across ages of time? Sure, though you mostly need to go to the photons and neutrinos for good examples. Are other items locked down so tightly that they see no further than a few millimeters into the past or future? Again, sure. Atoms in warm, dense matter are an excellent example of mundane, minimally transcendent items. Be honest: Were you seriously worried the atoms in your body would suddenly go quantum on you and drift off into the cosmos? [2] Chemistry only works because complex compounds in warm matter only engage in the more localized, less chaotic forms of functional transcendence. Most things having narrow, focused transcendence is a good thing, not a bad one. Finally, in searching for citations on the idea that the universe might simultaneously support an asymptotic version of Sabine's superdeterminism and an uncertain future in which people can still, to some degree, choose their fates, I only found one relevant quote. It's an apt one, though: "I don't know if we each have a destiny, or we're all just floating around, accidental like on a breeze. But I think, maybe, it's both." --F. Gump, 1994 ---------- [1] Dirac's remarkable insight was that such an odd approach would work for quantum mechanics. Oddly, he grew to despise his own idea. He doubled down on using only Hamiltonians and was generally annoyed at Feynman for having so much success with path integrals. I suspect that bothered Feynman since Dirac was one of the few early quantum figures he genuinely respected. [2] Observation is momentum pairs. Atoms do it, and even chemical bonds do it. It's part of how physics is going to become seriously fun again. ---------- Terry Bollinger CC BY 4.0 2022-05-21.23 :35 EDT Sat sarxiv.org/apa.2022-05-21.2335.pdf
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
From a purely logical point of view, space is infinitely large. From this it follows that matter can also become infinitely large and the speed infinitely slow. Conversely, there would also have to be infinitely small space with the associated matter, which is infinitely fast. That would mean: 1. Light is NOT the fastest thing there is. 2. There is no such thing as nothing at all. 3. Everything is (intelligent) matter. 4. Everything is connected or entangled with everything. Because of the laws of nature, it is also likely that basic structures, large and small, will repeat themselves indefinitely. This would result (quasi the “theory of everything”): (Radioactive/decaying)atom = star system/galaxy = universe Rein von der Logik her ist der Raum unendlich groß. Daraus ergibt sich, dass die Materie wohl auch unendlich groß werden kann und die Geschwindigkeit unendlich langsam. Im Umkehrschluss müsste es dann auch den unendlich kleinen Raum geben mit der dazugehörigen Materie, die unendlich schnell wird. Das würde bedeuten: 1. Licht ist NICHT das Schnellste was es gibt. 2. Es gibt überhauptnicht das Nichts. 3. Alles ist (intelligente) Materie. 4. Alles ist mit Allem verbunden bzw. verschränkt. Aufgrund der Naturgesetze ist auch wahrscheinlich, dass sich grundlegende Strukturen im Großen wie im Kleinen unendlich wiederholen. Daraus ergäbe sich (quasi die "Weltformel"): (Radioaktives/zerfallendes)Atom = Sternsystem/Galaxie = Universum
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!
People, the principle of Least Action unifies classical physics in a very elegant way. The PLA is also consistent with relativity and Maxwell's equations (which were discovered by Oliver Heaviside shortly after Maxwell's death. Ms. Hossenfelder has left out the only mathematically challening part of the narrative, namely all mention of the calculus of variations.
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.ua-cam.com/video/ZQNWVQc5sNI/v-deo.html
me too
Yes
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.
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...
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:
ua-cam.com/play/PL9s_vYCJclAYXFwhuMynZz8CNnoUAG5mr.html
@@mayabartolabac Only a few of his lectures were recorded and posted on UA-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_UA-cam thx dude
This video ended too soon.
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.
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.
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
@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.
I have been a Physics teacher for 38 years and I am 60 years old. This was the best explanation of the principle of least action I have seen in my entire life!
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.
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!
'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.
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.
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.
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
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 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.
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!
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.
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
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.
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'
For the sake of rigor, it's worthwhile to point out that in the form presented here, the action principle is known as Hamilton's Principle and it constitutes the foundation of Lagrangian Mechanics. It is an integral principle, describing the evolution of a dynamical system by an optimal path in its parameter space between two fixed configurations (the end points of the action integral). Equivalently, the differential form of the principle is simply given by Lagrange's equations, which are the equations of motion for the parameters (also known as degrees of freedom) in question. The name of Euler-Lagrange equations is usually employed for more general or more abstract problems that need not necessarily regard mechanical systems directly.
The Principle of Least Action is a somewhat different variational principle that arises in Hamiltonian Mechanics, but sometimes the name and notation (specifically, the S label for the integral) get carried over in the context outlined above. They are however different things among the many results and methods of variational calculus. As for why the rock knows to obey variational principles, there is no real mystery given that the trajectory itself is completely specified by the initial conditions.
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.
@ 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 ua-cam.com/video/MIBfKJHMWHU/v-deo.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.
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 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
Time dilation is force. Put a clock in a wheel it slows down, Hefele Keating Experiment. Einstein's Lorentz and this equation measure all forces, F=(t'-t)hC^2 e 34 put in velocity in the Lorentz Get The Time dilation difference as Force of quantum gravity. Go sit in a wheel with your clock we will slow down time, except you got crushed by going light speed. The time dilation on acceleration is gravity.
You're right ... Physics is the interface and Math the implementation ... There are equations "labeling" fundamental theories: E=hf, E=mc^2, S=kT ... Yet i think that Nature is "smarter" then we think it is: there is a transient stage and a steady-state (e.g. for 2-slit experiment) and getting to the steady-state regime when the least action process is attained, Nature uses an actual random, adaptive search corresponding to "all paths'' (like streamers of a lightning finding its way to the ground). Thank you for another beautiful presentation.
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 :)
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.
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.
1:15 Nature doesn’t need Trial and Error, Mankind does.
1:56 Straight Line if no force acting upon it
3:20 Least Time Path
6:10 Kinetic Energy Path Action, S
8:09 Optimum
9:51 Euler Lagrange Equations
10:36 All Paths, All End Points, Collapse to 1 End Point 11:40
Math - a language used to decipher nature
I don't quite understand why you find it so interesting that the object might "know the future", because as you said, the object just knows the next step from the previous one(s). But it got me thinking. In QM the particle doesn't make this "decision" of where it will go beforehand, it only decides where it is at random (based on the probability density) when you "ask" it. So this optimal path might just be rather the result of observation than something inherent to the object. We keep our eyes on the rock in space, and therefore it contiuously chooses the shortest path at every moment. Our observation of the object creates this reality as much as the object itself.
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!
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?
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.
The action can actually not only be the minimum(least), it can also be the maximum, the inflection. The lagrangian can not only be T-V , it can be all kinds of functions of generalized coordinates, which can also satisfy the Euler-Lagrange equation.
Hi, Sabine. The math is correct at 4:24, but the diagram is mislabeled in two spots. 1. X should extend from the vertical through the point of incidence to the vertical through point A, and D should extend from the vertical through point B to the vertical through point A--instead, they both extend to the left edge of the diagram. 2. The h1 and h2 in the diagram should be swapped in order for the math to be correct. Thanks for making another awesome video, Sabine!!
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.
6:46 Sabine, S is usually used to denote path or trajectory, it's the space that the object moves through.
Thanks Sabine. This time I have to watch several times with pauses to consider.
This reminds me of "The Texas Sharpshooter". The Texas Sharpshooter fires a bullet from his gun at a barn wall, then finds the bullet hole and paints a target around it. Later he will claim this is evidence that he has amazing shooting skills, as the bullet hit the exact centre of the target. Of course, in reality he did not know where the bullet would hit the barn, just as the rock did not spookily know that it would land at point B.
Regarding the intuition behind why it can be called action in the kinetic context: if you look at it the other way round, (T-V) is the derivative of S wrt time, i.e. the momentary change of action. That means the more you increase your action in a certain moment, the more kinetic energy (amount of actual motion) and/or less potential energy (amount of possible motion that is not happening) you get in that moment. If you don't change your action in any moment, the balance between actual and possible motion remains stable, they can both increase or decrease but by the same amount -- like some kind of energy inertia. If you decrease your action, your actual motion is disappearing compared to your possibility. So much if we are differentiating wrt time. The principle is stated as differentiation wrt distance, i.e. along all the points on the path, regardless of how fast and which direction you move in any specific point. It states that the position-wise amount of the action should not change, so perhaps a better name would be a principle of path-wise stable action, or a principle of even distribution of action over path. In other words, if you want the rock to fly higher or do something unexpected, you have to act upon it, the rock and the universe won't do it on its own, they're just doing their usual lazy thing.
To get more general, we usually think of time as "moving" evenly and compare change of position wrt time and call that velocity. In these terms, change of position could be thought of as the effect of the action, regardless of how much time it takes. Then the principle can be restated as: the amount of action you need for a unit of effect of that action is stable, it does not change. Ever. You could also say, that the universe will not waste action for no effect.
“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?
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.
"Equations are smarter than physicists" - anon. One of the most interesting topics in the history of science, is the resistance to accepting the consequences of some new equation, for instance the time it took to accept that the quantum equations were really implying probabilities. cf Newton: 'Hypotheses Non Fingo'
Liebe Frau Professor(in).
You should not forget (I don't believe - even for a moment - You did.) that with each possible path a phase is associated. The classical path "usually" is the path where this phase is stationary. Yes, the particle goes through every possible path between A and B. But the phase associated whit all these paths varies so wildly that the waves that arrive at point B will cansel each other out, leaving only those paths where the phase is stationary to contribute significantly to the trajectory. The particle doesn't have to foresee the future to know it is going to point B. It all happens naturally. That is the beauty of Feynman's formalism. It completely solves the mystery of how the particle knows what is the path of least action so elegantly and simply.
This is my favorite explanation of "principle of least action" yet
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
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
The least action principle has recently been generalised/expanded in a fundamental way, such that it comes even closer to a 'theory of everything': in the in 2009 proposed theory of 'Lagrangian multiforms' the Lagrangians, which in that theory are components of a continuous (or discrete) p-form in a multi-time space of independent variables of arbitrary dimension, emerge themselves as solutions of an extended set of Euler-Lagrange equations. Thus, this theory changes the goal posts: the multiform principle not only selects the most optimal trajectory for a given Lagrangian, but it also selects the Lagrangian components itself. The drawback is that the resulting Lagrangians correspond to integrable systems which are deemed very special and rare, but they amount to some kind of critical points in what could be considered a 'space of theories', namely those where the equations of motion become, in a sense, insensitive to the dimensionality of the space of independent variables. An example of a solution of the set of EL equations is the Lagrangian for the Ernst equations of GR describing gravitational waves. Another example is the Lagrangian for the Einstein-Maxwell-Weyl equations. That this theory only provides special Lagrangians (corresponding to integrable systems) may be seen as a drawback for a general methodology, but as a founding principle it is perhaps precisely what is needed: the conventional equation \delta S=0 allows one, in principle, to plug in any Lagrangian one choses, and hence is not predictive on the form of the theory. The multiform principle, which has only very specific type of solutions (i.e. input Lagrangians), does predict the form of the Lagrangian, and this is what we would expect from a foundational principle - after all, one wouldn't expect 'Nature' to allow for arbitrary choices of Lagrangians put in by hand, or engineered on the basis of other secondary principles. Having said this, it remains to be proven how truly 'physical theories' fit into this new principle, e.g. the standard model. But the fact that certain important reductions of the Einstein equations fit in naturally, seems promising for actual physics to be contained in this - so far mostly mathematical theory.
The pioneering paper in this direction was: "Lagrangian multiforms and multidimensional consistency, J. Phys A: Math Theor 42 (2009) 454013, (and there has been quite a bit of subsequent work by various groups on the mathematical aspects, but not yet so much on the physics).
This is the best video i have ever followed with Sabine
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."
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.
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'.
Two minor corrections: in the figure in 4:21, h1 and h2 should be swapped. Also in the same figure, x and D should stop at the x coordinate of point A. Other than that, thank you for this great video, it is very interesting and insightful!
There was a good tv serie couple years ago called "DEVS" and focused on the theory that everything that happens and will happen, can be predicted / determined if you know every effect of everything on everything at one point in time..
Everything happens because something else happened before.
"DEVS" is a must see for those who are curious about the theory that the universe is DETERMINISTIC.
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?
@@Simonjose7258 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.
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. 🤔
The apparent dependence on future comes across because the quantum particle follows all paths; and collapses in the future (or when any observation is made) where the Feynman Path Integral yields high probabilities - which turns out to be exactly where the classical action is stationary.
I use the Principle of Least Action when there's a chore I don't want to do. I find a couch, lie down, and optimize my comfort. Physics works!
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.
What I am interested in is the critical angle. Below the critical angle the light is reflected, and above the critical angle the light is refracted. The question is, what happens at exactly the critical angle? Is there indeterminacy in the refraction/reflection switch? From a stick in water, light is reflected at all angles so some of the light rays must intersect the surface at the exact critical angle.
Another question is, for a slow light ray coming from the water, how many air molecules are needed to reset the speed higher?
Shortest path is possible on the angle of motion. U change angle & path changes. Also path is medium depending. U change medium path change. Also it depends on nature of motion. If it is straight it will reach at perpendicular of destination. But if it is wave or spiral or projectile. It will travel depending on force & friction. Boomerang may not travel shortest path.
Your very own ‘Science Without The Gobbledegook’ follows this principle!!! Brava, Frau Sabine!!! We salute you!!!
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.
The "squiggle" is the lowercase Greek "delta" and expresses variation or change, like in delta-v (change in velocity). Now I understand why the Lagrange equations are so important... Thank you!
The hypothesis of optimal intent: Given a series of boundaries and limits; produce the optimal path while under influence by antagonistic or/and protagonist intent.
Very good deconstruction Sabine:the futural moment a la Fermat und Dirac - "borrowing from the future" which yields immense power - is not* dealt with by either GUT or UFT - or even QM. But it's the key to why Measurement is totally integral to the make-up of our reality. Love the stuff, btw :) JM
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!
I stopped beliving in theories a long time ago, I've got tons of my own... but if a certified experiment or a precise valid observation relives something new, no matter how radical it is, I belive it.
the best part is the story telling, truly multimedia with history science and maths.
i just love the way she starts to talk about something... " Thats what we'll talk about today". Its like YES TELL ME
Finally. I have been pushing you this direction for YEARS.
As I figured out (not being a physicist, just a regular consumer of pop-science videos on YT) nearly all greatest mysteries of physics boil down to the single truly *fundamental* question how the Universe came into being. But inside this very question there is another one, even more intriguing: how come things do not fall apart, how the Cosmos retains its integrity? It is not a trivial one and it's really worth some deliberation.
Some physicists more aware of the epistemological nitty-gritty of their work tend to assert that the "laws of physics" as they call their discoveries concerning observable, repetitive patterns of transformations of different forms of matter and energy are merely imperfect approximations of some hidden, perhaps never fully knowable 'objective' reality and their role is just to provide us with some usable tools, models adequate enough to become the basis for experimental work and scientific predictions. As the data amount and new observations are made, sometimes not consistent with previous assumptions, these models are being refined, closing the gap between current mathematical descriptions and the pursued truth in this sort of asymptotic approach.
However there still remains the master conundrum of why at all there are any such regularities that allow science to exist at all, why all electrons look and behave the same, why properties of particles don't fluctuate wildly every instant, why there is any order in the Universe rather than sheer chaos. One might evoke the "anthropological principle", but this does not tackle the ensuing question why among all possible universes there is even possible at least one uniform Universe comprising standardized matter. Doesn't it really point towards some preexisting template which had given matter and energy their apparently constant forms and properties?
Hence there is my question: do you believe in Platonic ideas? As for me, the more I learn about intricacies of the micro world, the more I do.
Very good video with clear explanations. Minor quibble, in diagram of reflection, angles of incidence and reflection were shown measured from the mirror. Should be from the normal surely.
The danger of a theory of everything is, that you may end up with a theory of nothing.
I did IT-security and set up an IT security policy for our company. It was long, detailed, not very marketable, but I must say, it was also good. When discussing it with a colleague, me wanting to make it considerably shorter, the colleague, fed up maybe, at a certain moment suggested a policy with only one statement: “There be security”.
Dr. Sabine, just read chapter7 in your book 'Existential Physics', and understand know, what made you so enthused about this principle. Without checking the math totally, it's enlightened!
Dieses Video war einfach toll! Es erinnere mich an einen Kurs, den ich in der Universität gemacht habe, der Angewandte-Differenzialgleichungen hießt, wobei ich den 2005 Artikel von Katalicky und Jicha, den ein Modell für den Verkehrsfluss, das die Euler-Lagrange-Gleichungen benutzt, studierte. Sehr cool! Bitte machen Sie mehr Videos mit Kalkül, das gefällt mir. Danke schön.
"...the particle goes to all points anyway. Except... it doesn't."
Mr. Everett would like a word with you.
MWI plus the principle of least action together make all laws of physics statistical in nature: things tend to do the kinds of things we observe them tending to do because it would be harder (less optimal, requiring greater action) and therefore is less likely for them to do otherwise. But they do do otherwise, in a much smaller number of possible worlds; because everything that possibly could happen does happen. We just tend to usually see the kinds of things that are most likely to happen happening... kinda by definition.
The real interesting questions left in physics after that is "what kinds of things are possible to happen and how likely is it for them to happen?", which is a question of which of the infinitely many possible kinds of mathematical structures our concrete universe is.
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.
The problem with the mirror example is that the minimal path length rule only applies to perfect mirrors. If I replace the mirror with a grating, then the entire thing falls apart completely. Different wavelengths will now be reflected at different angles and those angles do not have to be symmetric to the normal of the grating. We make good use of that in high quality spectrometers by shaping the response function with the shape of the grating surface. And if I make a hologram, then I can reflect an incoming wave front any which way I like.
Mathematics is not only a code or a language. It has underlying principles, like, well, a language. It has a grammar as a way to select what is a valid sentence. Mathematics, as languages, are a product of "Reason" and they must follow Reason to be what they are. If Reason is just a human attribute, then every "intelligent" entity should have its own. But, then, those entities wouldn't be able to communicate among themselves. For me, it follows that Reason is not only an attribute of every intelligent entity (i.e. universal) but the substance of cognition. It is not a tool, it is us being intelligent beings. Then, It follows that human mathematics is just a language that expresses the same truths (or sentences) about the world. We should be able to compare mathematics from alpha centauri to ours and establish an equivalence or translation.
One of Sabine's best, exposing the future line integral of Feynman's leading to an exquisite explanation of QM. This future involves the entire path of Schrodinger's wave equation, resulting in the unitary evolution creating classical objects like planets, stars, black holes and singularities. Hawking predicted the future, while Maldacena revealed the infinite axiom algorithm of QC functions.
It's just too bad that the path integral doesn't do what you and Feynman think it does. Feynman made a conceptual mistake there when he postulated that. What we need to get to classical objects from quantum fields is constant weak measurement. That was already known in 1927/1929, two decades before Feynman even came up with the path integral formulation. I doubt he paid attention to those papers, though. His own lectures and writings give, to my best knowledge, no indication that he knew about Heisenberg's and Mott's work in that direction.
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.
You are so much fun to lessen to you make me think and at the same time laugh. Brilliant lady, thanks.
Sabine, I gather your idea is to start with a Feynman diagram whose functionals have finite length and resolution since they start in some earlier past (e.g., a lab setup) and end at some later past (e.g., a lab measurement). You extend those functionals to the beginning and end of time, giving them effectively infinite resolution as with any wave train Fourier transform (comms 101).
With the added resolving power of infinitely long functionals, the bundle of in-phase functionals shrinks to a diameter of zero in XYZ space, and the whole blurry mess of _probability_ functions disappears. The opportunity for a "pilot wave" also disappears since pilot waves are another way of expressing the fuzziness and uncertainty of Feynman's finite path integrals. Your infinitely tight in-phase functionals eliminate that too. You end up with precisely what Minkowski proposed for relativity, only at the quantum level via your infinite extension of the path integral. Retrocausality, or whatever folks want to call it, is inherent in this approach since those infinite-length functionals convey infinitely precise information in both directions.
Your justification for treating the unknown future as known - and it's an excellent one - is that the principle of least action in the quantum domain _works_ by using Dirac's functionals, which are inherently time-embedded.[1]
So here's the oddly simple problem: By eliminating all quantum uncertainty, specifically by compressing the in-phase bundle to an infinitesimal diameter in their XYZ slice, you also make each such point infinitely massive. Planck uncertainty doesn't suddenly give you a pass merely because you used path integrals, especially since path integrals and quantum uncertainty are two sides of the same Fourier-transform coin.
Yes, I know, renormalization, or this trick, or that trick, whatever. Particle physics, in particular, stopped bothering with deep debugging and regression analysis decades ago, preferring to slap messy fixes on top of bad ideas. Been there, done that. You're still violating quantum uncertainty with all of this.
The good news is that your idea is closer to correct than most if you can drop all the Minkowski (and Hilbert, oh my) nonsense about spacetime providing infinite resolution for precisely zero cost. Your model sounds essentially correct _in the non-existent limit of infinite energy_. But observationally - via labs, telescopes, and actual data - our universe doesn't have infinite energy. It would collapse if it did, and notably, it doesn't.
The fix is to treat your model as a finite, quantum-limited _approximation_ of a block universe. Does it see into the future? Yes. Does it reach into the past, sometimes doing profoundly weird things? Check. Do simple events here entangle themselves with events in the indefinitely distant future, possibly even billions of years hence (think cosmic photons)? Sure. Is the future fully determined? _No._ It's not even close.
For any finite complex system, you can only encode a level of certainty proportional to the total energy of your carrier wave. Our carrier wave is the total positive energy of our universe - the sum of its visible matter, radiation, and dark "matter." This sum is vast, but it's _not_ infinite. That's especially true after you divvy it up for the task of moving around all of those Higgs-mechanism rest-mass fermions that are the true marvels of our universe.
Are some items transcendent across ages of time? Sure, though you mostly need to go to the photons and neutrinos for good examples. Are other items locked down so tightly that they see no further than a few millimeters into the past or future? Again, sure. Atoms in warm, dense matter are an excellent example of mundane, minimally transcendent items. Be honest: Were you seriously worried the atoms in your body would suddenly go quantum on you and drift off into the cosmos? [2] Chemistry only works because complex compounds in warm matter only engage in the more localized, less chaotic forms of functional transcendence. Most things having narrow, focused transcendence is a good thing, not a bad one.
Finally, in searching for citations on the idea that the universe might simultaneously support an asymptotic version of Sabine's superdeterminism and an uncertain future in which people can still, to some degree, choose their fates, I only found one relevant quote. It's an apt one, though:
"I don't know if we each have a destiny, or we're all just floating around, accidental like on a breeze. But I think, maybe, it's both." --F. Gump, 1994
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[1] Dirac's remarkable insight was that such an odd approach would work for quantum mechanics. Oddly, he grew to despise his own idea. He doubled down on using only Hamiltonians and was generally annoyed at Feynman for having so much success with path integrals. I suspect that bothered Feynman since Dirac was one of the few early quantum figures he genuinely respected.
[2] Observation is momentum pairs. Atoms do it, and even chemical bonds do it. It's part of how physics is going to become seriously fun again.
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Terry Bollinger CC BY 4.0
2022-05-21.23 :35 EDT Sat
sarxiv.org/apa.2022-05-21.2335.pdf
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
From a purely logical point of view, space is infinitely large.
From this it follows that matter can also become infinitely large and the speed infinitely slow.
Conversely, there would also have to be infinitely small space with the associated matter, which is infinitely fast.
That would mean:
1. Light is NOT the fastest thing there is.
2. There is no such thing as nothing at all.
3. Everything is (intelligent) matter.
4. Everything is connected or entangled with everything.
Because of the laws of nature, it is also likely that basic structures, large and small, will repeat themselves indefinitely.
This would result (quasi the “theory of everything”):
(Radioactive/decaying)atom = star system/galaxy = universe
Rein von der Logik her ist der Raum unendlich groß.
Daraus ergibt sich, dass die Materie wohl auch unendlich groß werden kann und die Geschwindigkeit unendlich langsam.
Im Umkehrschluss müsste es dann auch den unendlich kleinen Raum geben mit der dazugehörigen Materie, die unendlich schnell wird.
Das würde bedeuten:
1. Licht ist NICHT das Schnellste was es gibt.
2. Es gibt überhauptnicht das Nichts.
3. Alles ist (intelligente) Materie.
4. Alles ist mit Allem verbunden bzw. verschränkt.
Aufgrund der Naturgesetze ist auch wahrscheinlich, dass sich grundlegende Strukturen im Großen wie im Kleinen unendlich wiederholen.
Daraus ergäbe sich (quasi die "Weltformel"):
(Radioaktives/zerfallendes)Atom = Sternsystem/Galaxie = Universum
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!
People, the principle of Least Action unifies classical physics in a very elegant way. The PLA is also consistent with relativity and Maxwell's equations (which were discovered by Oliver Heaviside shortly after Maxwell's death.
Ms. Hossenfelder has left out the only mathematically challening part of the narrative, namely all mention of the calculus of variations.