It's a high bar, but this might be the best episode of SpaceTime yet. I understood action, the Lagrangian, and the Hamiltonian perfectly, where before I had only struggled. And what's more, it gave me a glimpse at the most fundamental questions and hints of answers. Absolute masterclass of communication.
@Fernando Franco Félix "this might be the best episode of SpaceTime yet" I was about to say the same thing. Explaining the principle of least action so clearly as it relates to GR and QM helps me understand those topics so much more intuitively than I had previously; in the exact same way that it elucidated mechanics when I was first saw it applied there. On the opposite side of that coin, explaining GR and QM in terms of the principle of least action helps me understand the principle of least action so much more clearly than I had previously when I encountered it for the first time in mechanics. Bravo and thank you.
Super ! I am fascinated how so complicated topics can be communicated so concisely and to the point of the objective of the video. No single podcast solves it all but this one is close to be called THE BEST EVER!
sometimes i like to wonder how much Matt actually understands of this stuff. and then i realize Matt knowing what he's talking about is the path that requires the least action.
@@valasfar1557 AND he has some amazingly solid resources to draw from. I have been watching all his content for many years but keep coming back to this specific episode because I think I have a use for it in another field. Just need to do the work
They probably have script database where they simply search for terms and then actually go for that part of video. Otherwise, this would be too much of work.
@@ruslankazimov622 Actually I just searched for "PBS Space Time" plus whatever topic I didn't want to explain in this video and checked to see if we had a video about it
@@falnica Great to hear this from the man himself. That also works I guess, since there are autogenerated subtitles and people in comments also mention the keywords.
14:00 "... each seeking a path through (spacetime) the configuration space of ideas (of spacetime) guided by mysterious principles (of spacetime) not the least of which is the action (of spacetime) pointing the shortest way to the fundamental nature OF SPACETIME" NAILED IT!
I never realized that proper time reduces to the Lagrangian for massive particles... I think I just reached god mode. Best physical intuition of the Lagrangian I've seen
Interestingly, in a novel "The story of your life" by Ted Chiang, which the movie "Arrival" is based on, the aliens' science is built around the concept of variational principle and Snell's Law is used as an example how one needs to know the starting and ending points to figure out what's going on in intermediate points. This fundamentally affected how they (non-linearly) think and experience time
@@ritemolawbks8012 the mathematics and problem solving challenges/complexity found in Classical/Newtonian Physics are much higher than those found in Quantum Mechanics.
@Noah Snell Being that I doubt even Einstein could solve his own field equations without help, I'm sure most of the world is satisfied with someone who looks like stereotypical physics professors confirming the math checks out.
@@PetraKann I don't think the field of Quantum Mechanics is ready for my math skills. I tend to let the equations use me as vessel to reveal the beauty and mystery of the natural word.
@@ritemolawbks8012 Mathematics can be like that - but when it is, it has nothing to do with a connecting with reality. That apparent connection is coincidental and based on illusion. Remember a circle, or a sphere, or a square etc, as defined by Mathematical formulae doesn't exist in nature. AS far as Quantum Mechanics is concerned there isnt even agreement on the interpretation of this Theoretical framework - irrespective of its predictive accuracy in the Laboratory. If you are waiting for an equation to pop up so that you can experience and understand the beauty and mystery found in the natural world. you may miss your organic connection with it. After all, we are a product and part of the natural world.
From the path integral perspective in qft you can see that it is irrelevant whether it is a maximum or minimum, it just needs to have vanishing derivative
This is one of the most profound episodes of Spacetime I’ve seen in my ~ 4 years of subscription. Veritasium was also on fire this week. Bravo Matt, bravo!
In the short story “Story of your Life“, the basis for the movie “Arrival”, the aliens with a Doctor-Manhattan-style perception of time regarded action as fundamental and defined concepts like velocity and acceleration in terms of action and other things. It hadn’t occurred to them to treat velocity and acceleration as fundamental.
My physics education thru a PhD completely confused me about the advantages of Lagrangian and Hamiltonian mechanics over Newtonian mechanics, and never explained action as well as this briefing did. Bravo!
For cases like yours, one professor always recommended to try to work out the equations of motion of the double pendulum using Newtonian mechanics. I agree with him, it's enlightening.
@@zray2937 You don't even have to go that far. Lagrangian mechanics completely trivializes a single pendulum, whereas it's still quite complicated in Newtonian mechanics.
@@zray2937 One time in an oral exam during my 1st year at uni studying physics (so before we were introduced to Lagrangian mechanics) the professor told me to derive the equations of motion for a double pendulum. I came to him 10 minutes later disappointed, not having got anywhere with it but he wasn't phased at all by my inability and just started asking his normal exam questions. After the exam I asked him why he asked me to derive the double pendulum and he said "well I saw you were done with your other tasks so I wanted to keep you entertained, I never expected you to solve it"
At 7:59 Matt O'Dowd says "All objects moving through spacetime move through paths that minimize the time measured on that path." In fact, freely falling objects follow paths that *maximize* the time measured on that path. If an object wiggled back and forth needlessly while going from one spacetime point to another, relativistic time dilation would make the time measured along that path *shorter*. This is actually visible in an earlier formula for the action S. It has a minus sign in it: the action is *minus* mc² times the proper time.
Maybe he should have said “for that path” instead of “on that path”. As he is referring to how the observed path is created from a given beginning to an end, rather than about the path itself. But for constrained paths such as energetic magnetic field lines, your observation may be useful.
To be fair, you probably wouldn’t understand a lot of this without the base you already had. Think about how much of this would make any sense after your first physics course.
Am I one of the few in here without a Physics Degree? Thank you Matt for making such complex and incredible academic achievements obtainable and understandable to the common person
Nope. I have no degree, I don't understand half of what he says, but I have a vague idea of the general gist of it. I sometimes think I should get into physics for real. Like.. I don't understand the equations, and I forget many of the comparisons he makes, I miss a few words here and there, but I get some concepts that I saw in other videos and other channels. So for example, one thing I've seen that I keep in my mind and I remembered again while watching the relativity bit is that there is a relationship between lightspeed and time, in which anything in the universe, as it gets closer to lightspeed, will perceive time going slower. So lightspeed is the speed limit because time would basically stop. They are two metrics of something that is the same.
The action principle was one of the most interesting concepts I learned in undergraduate classical mechanics. It really puts into perspective how important the calculus of variations is. Proving that the shortest distance between two points in flat Euclidean space is a straight line, is a perfect example of this.
So true. This and the Noether-Theorem (i think there is also a vid on that on this channel) were definitely light bulb moments in my classical mechanics class.
Powerful way to summarize GR (Einstein Hilbert action) and the rest of physics (Standard model path integral) into two simple equations. Tied for second and third place are Noether's symmetries and also the geometry view of nature, that is that GR and standard model including the interactions can be understood as geometry ('symmetry implies interaction' and curvature implies potential energy Einstein-Civita connection=GR, gauge symmetry/curvature/connection=EM).
When we learned Lagrangian mechanics in my analytical mechanics class, it was during the first week of online classes due to the covid shutdown, so I didn't really get good instruction on it. This has cleared up a lot of questions and also shown me how beautiful this principle of action is. Thanks for the great video.
This was a really good episode. I've been watching for a few years and am myself a junior physics undergraduate. I found the entire episode entertaining; my favorite bit though was reframing the Lagrangian under special relativity and discovering that it's simply the requirement that proper time is kept constant. The Hamiltonian always felt natural enough since it represents the total energy of the system, but the Lagrangian always felt artificial and arbitrary. Combining the common (for a physics major) knowledge of how kinetic and potential energy affect the proper time of an observer via relativity to explain the Lagrangian was really the exciting bit for me.
Great video! I have a master's in physics and still learned something from this video about one of the basic principles in physics. The different forms of action were never explained or connected this clearly in my university courses.
Did you notice that Matt goofed with the proper time? Compare the twin scenario: for the twin who remains in inertial motion the most amount of proper time elapses. For the twin who travels a longer spatial length than the stay-at-home sibling a smaller amount of proper time elapses. In GR: the path of inertial motion is the path of the _most_ proper time elapsing
its just another example of differential vs integral equations...minimizing functionals is a question of choosing the integrated funciton that minimizes the integral
The lead up to and delivery of the statement "All objects moving through spacetime move through paths that minimize the time measured on that path" just gave me chills. Such a concise and simple build-up to something fundamental to our universe that seems so complex and simple at the same time.
The Euler-Lagrange equation is a thing of true beauty, very useful in General Relativity for generating them damn critical Christoffel symbols. GR is built on the principle of least action.
In the case of gravitational lensing, isn't the light still traveling in a straight line? I thought it's only spacetime that bends, making the light appear curved from our perspective, even though it was moving straight all along.
Assuming Einstein Equivalence holds true: Light, like everything else in free-fall, obeys the geodesic equation and their paths are called "geodesic." These are the "straightest" paths. The difference between light and massive particles is that geodesics for massive particles are a maximum for the proper time, while proper time is not defined for light (the massless case).
Yes, light always moves at the fastest possible speed in a straight line. Mass bends spacetime, and you end up calculating a lot (of combinations) of curvature differentials in a 3x3 or 4x4 matrix, or even 16*4*4 matrices to describe a GEODESIC == straight line within curved space(time)
This is amazing. As a physics student, I've seen the Lagrange-Euler equations, principle of least action, and the stationary phase method (for optics) all in separate classes. Still, the way you guys manage to string together these concepts so clearly, also incorporating both relativity as well as quantum mechanics, has given me so much new insights as to what these concepts mean. It's scratching this "but why" itch I still so often don't get scratched in these classes; thank you.
Ah, this explains why my head didn't actually explode while my mind was blown. It's so logical and simple and I feel like I know less than before this video started.
This is such an eye-opener. Action and fields should be discussed more often at a more fundamental level. It is much more intuitive than standard particle stuff and wave-particle duality.
3:14 I remember using this method to solve problems in my graduate Mechanics class. It involved minimizing an integral for the path. It is true that Lagrangian Mechanics makes it possible to solve problems that are essentially impossible using simple Newtonian Mechanics.
I've been pondering how to teach what action principles are to intelligent non-physicists since I was in graduate school. This was very, very well done. Thank you for giving me an example of such good pedagogy.
This comment made me look up a word in the dictionary, thank you! I agree as well that this video is well made. P.s Ped-a-go-gy Noun : the art, science, or profession of teaching; esp : EDUCATION 2
Also of possible interest are Leonard Susskind's 3 semi-technical books on essential physics, his "theoretical minimum" series, starting with "The Theoretical Minimum: What You Need to Know to Start Doing Physics." Later volumes handle quantum mechanics and relativity. The "theoretical minimum" of the title is kind of a pun-he's trying to teach the minimum amount of physics one needs to get a grasp of the field as a whole, but least action is a core idea. Reviewer John Gribbon put it well in a review for the Wall St. Journal: "At the heart of this book, both physically and metaphorically, is the "principle of least action" ("action" being a technical term that refers, basically, to the overall energy in a system over time). The most important idea in physics, it can be summed up in the phrase 'the universe is lazy.'" -Tom
This is the best lecture on the principle of least action I have ever seen. You just helped me finish my paper on energies of the Planck era. Thank you!
A cappella science did a song parody of a song from Hamilton, making it about the physicist William Rowan Hamilton instead of about the politician. In addition to Hamilton’s life, it also addresses the Hamiltonian and Quaternions. It is good! “He tried extending the complex, found the next step fickle, his kids would ask him ‘dad, can you multiply triples?’ ‘Not yet, I can only subtract and add back’ “ etc.
It seems the whole Space Time team was in flow-state for this episode. Superbly efficient, taking the path of least action to effectively collapse the probability of information into reality.
Woah, this might be the first PBS Space Time I've completely understood without going through the referenced previous PBS Space Time videos! Tbf I have watched quite a lot of Space Time videos, but half the time I was stuck pretending I understood the video while guessing what it actually meant, whilst with the other half I had to do further readings on wikipedia to get a firmer grasp on what was actually discussed. In all of those times though I felt Matt and the Space Time team doing their best to simplify the discussion such that even non-physicist normies like me can still understand, so long as they've watched enough of the alluded videos Matt mentions.
It's like learning how to ride a bike of ideas, my handlebars may wobble without the training wheels, but I'm not constantly falling down anymore. In other words - it's getting intuitive.
@@ernestolombardo5811 I don't know how to ride a bike either so me finding most of this channel's videos hard makes even more sense with that analogy lol. I feel like I've understood more since then (that or the videos have just gotten simpler lately with the illustrations featuring that glasses black guy). Recent PBS Space Time videos doesn't feel as difficult as I remember the older videos being.
Indeed a particle maximizes it's proper time, not minimizes. Example: the twin paradox. The traveling, I. E. accelerated twin experiences less time. Spacetime isn't entirely intuitive, a path that seems longer (using the Euclidean metric) is actually shorter in the lorentzian metric, I. E using relativity
This is one of the best PBS Spacetime episodes, absolutely wonderful explanation and how everything was tied together. I feel I learned a lot of how things actually influence each other in the grand scheme of things.
It's when they do take action that the trouble starts. "No man's life, liberty or property are safe while the Legislature is in session." - Gideon John Tucker
Excellent video! Thanks for delving into this important subject and bringing clarity with masterfull didatic skils to get these beautifull and fundmental ideas across out to a wider audience!
Quoting Feynman: “When I was in high school, my physics teacher-whose name was Mr. Bader-called me down one day after physics class and said, ‘You look bored; I want to tell you something interesting.’ Then he told me something which I found absolutely fascinating, and have, since then, always found fascinating.... The subject is this-the principle of least action." Well, we were also bored, and Space Time provided! :)
Love this episode. Learning Lagrangian and Hamiltonian mechanics was the best thing ever to happen in my life when i studied Physics. That and learning to solve differential equations with a lot of methods. That´s when i realised that i prefered theoretical physics to working in an experimental lab. Sometimes when my friends talk about how their kids are their best accomplishment i jokingly say if they tried Classical Mechanics.
I just can't believe there are people in the world that those equations make sense to. I mean, I looked at them, shook my head and thought "what kind of abstract thinking does someone need to have to be able to see that and say I understand"!!!
Good point! Excellent video!! Reminds me of my days doing doctoral studies under David Ritz Finkelstein back in the day, at Ga. Tech, where he adopted a Least Action Principle variational approach even on the most fundamental level, in his quantum topology account, in varying a discretely dynamic topology fundamentally tiled by a hypercubical lattice of elementary and entangled units of quantum process (chronons). So it's action, all the way down. On the Plack scale, there's only action, and its derivatives--information and energy, whose nature and interconnection will continue to baffle and elude philosophers like myself trying to sort that all out, conceptually--and not to mention the physicists, plumbing the depths like plumbers with their mathematical bags of tools, field-theoretic wrenches, multilinear Clifford algebraic ball and socket ratchet joints, etc. Whole lotta messy shite down there!!
Props to Matt on being among the few English speakers to get my name basically right on the first try. Truly a master of the principle of least [linguistic] action!
This is a masterpiece of high level science communication! Hats off 🎩 to the PBS Space Time team. This is probably the best Space Time video ever and one of the best science videos on TH-cam 🎥! I am lost in awe for nature once again, after a lot of time.
Thank you, this was immeasurably helpful and reassuring. I have always intuited this principle, but never had it explained in a way that fully described its functions, moreover its breadth of application.
When I first started watching this channel (about 3 years ago) I knew very very little aside from a H.S. physics class. Now I have a much deeper understanding, especially with the graphics and visual almost tactile explanations. I still get lost by the math but the ideas, concepts and words they get through. These videos make me think for hours and hours after each day, contemplating the universe. Thank you so much for reinvigorating my love for physics and in a weird way philosophy as well.
I'm confused. How can light take the path of least proper time if it travels at the speed of light, and therefore doesn't experience time? Every path it could travel would take 0 time, so how does it choose a path?
It turns out that there is only ONE path a light particle can take that has zero proper time. This is how people calculate the path of a photon in GR, they set the proper time (spacetime interval) to zero and this tells you how the photon position in your frame (x,y,z) must change as a function of your frame time (t). Ie a path for the photon.
I thought light takes all possible paths at the same instant. In fact, I have been bothered by light not experiencing time and finally realized it is the only way to reconcile the bulk universe with our experience of time. The photon has experienced the universe in an instant. We, as confined energy, experience local time mediated by the force carriers known as gravitons that affect the spacetime field. It’s a weakly binding negative energy and somehow must mediate the process of decoherence with our environment. Anything traveling less than the speed of light experiences local time and is causally linked, since simultaneity does not exist. This action between events may define the geometry of space and is governed by the positive energy of dark energy which continually extends the action in one direction known as the arrow of time and also giving spacetime its thermodynamic properties. Thus both the concept of the bulk universe and the passage of time are real depending on the motion of the observer.
@@jackheinzel8803 So you are saying it’s in the math, not really intuitable? Thanks 🙏🏻 I am not really a mathematician but I am an epistemologist so the point itself is important to me apart from the physics involved.
I wonder: entropy increases/differences decrease (energy spreads out evenly), the said heat death in a very far future -> while it makes sense up to some point, I kind of strugle to imagine that at the very "last" moment, it is possible for the system to come to a 100% halt, which means that nothing moves. at some point there should remain some back and forth (not just because of uncertainty). If a system is perfectly balanced, which the universe was not at the beginning, it can not come to a full halt if my understanding of physics are correct, since there will always remain some bouncing of particles back and forth, even though it becomes less and the bouncing spreads out more and more. This actually - I realize now while writing - maybe relates to the fact that information should not be erazable, but if the system would come to a 100% halt at some point, you would lose all the information from the time before, since no state change ocure. Is this maybe also indirect the reason why we always have those fluctuations (QT), because for a system it is impossible to come to a 100% halt, not the other way around (two balls, removing friction, etc, would when they start moving keep moving, multiple balls would spread out their kinetic energy, but will never come to halt)
Great episode. Minor corrections: 3:52-4:30 Note that there can be stationary paths that are neither minimal nor maximal. 7:59-8:19 In the simplest situations, it's a principle of *maximal* proper time. 8:27-8:31 The time in Fermat's principle is laboratory time, not proper time. E.g. in vacuum, the proper time of light is zero/frozen.
Hi, I co-wrote this video and this was actually something I wanted to address, but we had to cut it off because it was too long. In simple terms, the universe at its very core seems to be a set of symmetries which are manifested in the Lagrangian. This means that if we knew all the symmetries the universe follows we could describe it perfectly, but we don't know all the symmetries it follows, and we are not sure how those symmetries fit with each other If you want to learn more look up Neother's Theorem and Electroweak unification, or wait until we make that episode
the general relativity Lagrangian (see: Einstein-Hilbert Action) is not renormalizable. The other 3 forces are (thanks to the Higgs, and Ward Identities).
No. quantum-mechanics has very small scale effects with much shorter ranges (much larger inverse exponents), that do not appear on larger scales, as they very quickly average out to something much more predictable, that is more easily modeled with smaller exponents, like inverse squares for gravity, with much larger accumulative ranges, to the size of Laniakea. Unless you explode a very young universe very quickly, so that tiny differences cause huge effects. A GuT has the issue of low precision: You could realistically model Blackbody-Radiation to colorize a scene of hot stuff, but you need more than 32 bit precision for this, because the numbers, that you multiply for a physically precise simulation, already differ enough in size or have a too high exponent, that has you often divide by (way too close to) 0, if you only use 32 bit IEEEfloat precision. To save battery life, most arithmetic in mobile devices only uses 16 bit precision. for a simplified blackbody-model, that still works with 32 bit precision, you estimate the same function, but with much lower exponents and values of more equal sizes (by minimizing for least squares, or Chebyshev , or doing fourierAnalysis). Shadertoy has some Blackbody shaders with the most common Chebyshev-like approximations.
@@MrMetra101 Gravity is just the computational lag incurred when the universe tries to process a bunch of different lagrangians. The individual computations can't happen simultaneously, because they're already infinitely parallel path integral computations, so the local universe "hangs" while it waits for the queue of computations to clear. In other words, clocks lag in gravity wells because they have more to do besides tick forward.
The concept of the evolution of "configuration space" really rubs me off as an optimization in a computer simulation. The deeper you go into physics and computer science, the more the two seems linked at a fundamental level.
Any sufficiently advanced computer is indistinguishable from nature, to mangle the oft quoted sci-fi/fantasy trope. This makes perfect sense in my weird mind which considers laws of nature to be magical spells with huge areas of effect in the entire observable universe, or indeed magical spells to be laws of nature with a well defined area of effect. The observable universe is ultimately all just a big expanding multidimensional array of numbers with a series of algorithms iterating over the entire array every plank-time, putting the result in a new array and increasing the count variable by 1 plank time. The universe is also the computer this array runs on, the laws of nature are just the algorithms determining how numbers in different parts of the array used as input to the algorithms affect the output array on each step and science is ultimately just an attempt to approximately define these algorithms from their output. Put all this together, and then the universe is both simultaneously sufficiently advanced technology and magic, indistinguishable from each other and unseperatably equal. This line of thought arose from thinking too deeply about magical systems in fanfiction in a universe which is also a computer simulation, and how the interactions exist and work.
Can’t believe I knew all the science behind what you were talking, but only now I finally understood the connection between all of these. The fact that they are all seemingly same! Best episode of space time! I had to watch it like twice to get the whole point - amazing!
Well this would explain why masses are attracted to objects that slow down time, but that just delays answering the question. How are those objects causing time to slow in the first place?
@@EpicProDudeOfAwesome Good point, but I don't fully agree. I think it simplifies the question rather than delaying it. Instead of the need to explain two things, why mass causes 1: gravity, and 2: time dilation, we end up with only one thing left to explain.
How is it that Newton’s laws keep changing? 2nd law used to be “for every action there is an opposite and equal reaction.” Third law used to be f=ma. And force is not equal to change in momentum. Force times time equals the change in momentum.
THE TOP DOWN AND BALANCED UNDERSTANDING OF TIME AND SPACE, AS E=MC2 IS CLEARLY PROVEN TO BE F=MA ON BALANCE: Time wasn't “created”. INSTANTANEITY is fundamental to what is the FULL and proper UNDERSTANDING of physics/physical experience, AS ELECTROMAGNETISM/energy is gravity. Time is necessarily possible/potential AND actual IN BALANCE. E=MC2 IS F=ma ON BALANCE. Accordingly, time DILATION ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. E=MC2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. Gravity is ELECTROMAGNETISM/energy. Consider the man who IS standing on what is THE EARTH/ground. Touch AND feeling BLEND, AS ELECTROMAGNETISM/energy is gravity; AS gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; AS E=MC2 IS F=ma; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE. (THE EYE is the body ON BALANCE. Consider what is balanced BODILY/VISUAL EXPERIENCE.) The sky is BLUE, AND what is THE EARTH is ALSO BLUE. SO, objects AND MEN fall at the SAME RATE (neglecting air resistance, of course); AS E=MC2 IS F=ma; AS “mass”/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY; AS gravity IS ELECTROMAGNETISM/energy. It all CLEARLY makes perfect sense. I have explained why the rotation of WHAT IS THE MOON matches it's revolution. BALANCE and completeness go hand in hand. Carefully consider what is THE SUN. (Very importantly, outer “space” involves full inertia; AND it is fully invisible AND black.) The stars AND PLANETS are POINTS in the night sky. Again, time dilation ULTIMATELY proves ON BALANCE that E=MC2 is F=ma; AS ELECTROMAGNETISM/energy is gravity. Therefore, BALANCED inertia/INERTIAL RESISTANCE is fundamental. Gravity IS ELECTROMAGNETISM/energy. E=MC2 is CLEARLY F=ma ON BALANCE !!! By Frank DiMeglio
@@frankdimeglio8216 what you have just said is one of the most insanely idiotic things I have ever heard. At no point in your incoherent, rambling on response were you even close to anything that can be considered a rational thought. Everyone in this room is now dumber for having listened to it. I award you no points, and may God have mercy on your soul.
I do love this channel. So smart. Your breakdowns on the theories and facts about the strange way the universe works always gives a spark to that sweet spot in my brain. However sweet id is. Thanks for all the thoughts shared, and for making me think. God bless.
As others have said, this may be your greatest episode yet!!! It’s not often I have my mind BLOWN, but this did it!!! Please continue to include more of the heavier math, even in large general examples. Wonderful!
"He found a very simple and beautiful pattern in nature, and this has been inspiring us ever since - through Fermat, and Lagrange, and Dirac, and Feynman, each seeking a path through the configuration space of ideas, guided by mysterious principles, not least of which is the action, pointing the surest way to the fundamental nature of ... Space-time." - Phew, what an epic sentence!!!
This reinforces the Cosmological Natural Selection and Quantum Decoherence episodes. The macroscopic observed states will be the ones that survive the quantum decoherence since they result of constructive interference of wave functions
Question: Is the principle of maximum proper time the same as the principle of minimum proper time ie., are they both principles of the same principle of stationary time(and are these the same as stationary action)? I've heard of maximum proper time via the Einstein Hilbert action - objects prefer this path(maximum proper time) under gravity.
8:20 This... this just blew my mind! Somehow after years of studying and working with these things, something just clicked sending shockwaves through my whole mind and body. Thank you!
Ah, this is like Charlie Munger's "Inversion Thinking": Figure out what will cause your to fail financially and avoid doing those things. Constructor Theory is sort of like that, it seems: Figure out what breaks your real-world observations and cut those out of the progression towards a theory of everything.
I think the confusion with Constructor Theory is calling it a Theory when it is a process and yes a Theory but not in the way Physics uses the term Theory.
@@RedRocket4000 A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. String Theory says everything's strings, and Constructor Theory says everything's constructors.
I find it humorous how the universe can be so mysterious and inexplicable to our Simian hatchling brains, but for nature... well it's just doing what is always has, even if it's consistency is not always known to us. Regardless, I'm happy to share this world with y'all, thanks for producing these great videos guys; always such a treat.
Fascinating.. your delivery is so easy to follow. Thank you. It's very soothing learning from brilliant minds.. always connects some dots.. You were talking about Consciousness.. 🌌
This seems really cool. Are there any good resources to study the action versions of GR or QM directly without having seen the traditional versions? I am familiar with classical Lagrangian mechanics and have a background in pure math.
@@mattstarbuck7484 took a cursory look at the wikipedia page, and this is exactly what I was looking for. Are there any good books/lecture notes etc on this topic that you'd happen to know of? And would you recommend learning this directly or learning these things through the traditional approach first?
Well, usually the lagrangians of the respective theory are reconstructed after the equations of motion already have been discovered. The usefulness of the lagrangian is to derive the equations of motions for a system. Look up for example the Einstein-Hilbert action. Playing around with the lagrangian and action can be used to derive new theories as well though.
@@lakshaymd I’m a physics student so I learnt about gr first and then about the action later. David tong’s notes on gr has a good section on the action that I’d recommend. Hope that helps :)
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So when I take the least action, I’m called lazy, but when a particle does it, it’s oh how amazing!
XD
That's because most people just don't know any physics!
you are a heap of amazing(ly lazy) particles.
It's called smart.
Ha ha! I was thinking the same thing the whole time! The moral of the story is, work smart not hard.
It's a high bar, but this might be the best episode of SpaceTime yet. I understood action, the Lagrangian, and the Hamiltonian perfectly, where before I had only struggled. And what's more, it gave me a glimpse at the most fundamental questions and hints of answers. Absolute masterclass of communication.
I wrote this episode and your comment made me really happy
@@falnica you did very good work,sir!
@@falnica Very well done.
@Fernando Franco Félix
"this might be the best episode of SpaceTime yet"
I was about to say the same thing.
Explaining the principle of least action so clearly as it relates to GR and QM helps me understand those topics so much more intuitively than I had previously; in the exact same way that it elucidated mechanics when I was first saw it applied there. On the opposite side of that coin, explaining GR and QM in terms of the principle of least action helps me understand the principle of least action so much more clearly than I had previously when I encountered it for the first time in mechanics.
Bravo and thank you.
Super ! I am fascinated how so complicated topics can be communicated so concisely and to the point of the objective of the video. No single podcast solves it all but this one is close to be called THE BEST EVER!
sometimes i like to wonder how much Matt actually understands of this stuff. and then i realize Matt knowing what he's talking about is the path that requires the least action.
Uhh he has a PhD in astrophysics
@@valasfar1557 AND he has some amazingly solid resources to draw from. I have been watching all his content for many years but keep coming back to this specific episode because I think I have a use for it in another field. Just need to do the work
I think the most mind boggling thing about PBS:ST is their ability to remember and reference all the videos they've previously made 😂
ikr hahaha.
It get's though
They probably have script database where they simply search for terms and then actually go for that part of video. Otherwise, this would be too much of work.
@@ruslankazimov622 Actually I just searched for "PBS Space Time" plus whatever topic I didn't want to explain in this video and checked to see if we had a video about it
@@falnica Great to hear this from the man himself. That also works I guess, since there are autogenerated subtitles and people in comments also mention the keywords.
I appreciate how the buildup to the ending "space time" keeps getting longer and longer
14:00
"... each seeking a path through (spacetime) the configuration space of ideas (of spacetime) guided by mysterious principles (of spacetime) not the least of which is the action (of spacetime) pointing the shortest way to the fundamental nature OF SPACETIME"
NAILED IT!
@@secularmonk5176
Exactly! I was seriously BRUH'ing on that transition/outro.
The last episode will just be 15 minutes of preamble for that ending
@@secularmonk5176 The tension while anticipating that finale of any Space Time episode is several orders of magnitude higher than any movie.
@@kindlin BRUH'ing 🤣 captured my reaction perfectly too
This is by far the best high-level summary of Lagrangian mechanics I've ever seen.. and I'm only five minutes into the video.
How many have you seen?
I never realized that proper time reduces to the Lagrangian for massive particles... I think I just reached god mode. Best physical intuition of the Lagrangian I've seen
Well, for a particle moving in curved spacetime that's true, but it's not so simple anymore when other forces are involved
For reference: 6:58 - 8:31
Interestingly, in a novel "The story of your life" by Ted Chiang, which the movie "Arrival" is based on, the aliens' science is built around the concept of variational principle and Snell's Law is used as an example how one needs to know the starting and ending points to figure out what's going on in intermediate points. This fundamentally affected how they (non-linearly) think and experience time
This is similar to everything. Yes 🙌 thanks 🙏🏻 🥰
As a non-physicist, I found the progression from Newtonian to Lagrangian to General Relativity really interesting. Thanks for that. 😎
There's plenty of messy mathematics behind General Relativity that's not suitable for the non-physics-major population.
@@ritemolawbks8012 the mathematics and problem solving challenges/complexity found in Classical/Newtonian Physics are much higher than those found in Quantum Mechanics.
@Noah Snell Being that I doubt even Einstein could solve his own field equations without help, I'm sure most of the world is satisfied with someone who looks like stereotypical physics professors confirming the math checks out.
@@PetraKann I don't think the field of Quantum Mechanics is ready for my math skills. I tend to let the equations use me as vessel to reveal the beauty and mystery of the natural word.
@@ritemolawbks8012 Mathematics can be like that - but when it is, it has nothing to do with a connecting with reality. That apparent connection is coincidental and based on illusion.
Remember a circle, or a sphere, or a square etc, as defined by Mathematical formulae doesn't exist in nature.
AS far as Quantum Mechanics is concerned there isnt even agreement on the interpretation of this Theoretical framework - irrespective of its predictive accuracy in the Laboratory.
If you are waiting for an equation to pop up so that you can experience and understand the beauty and mystery found in the natural world. you may miss your organic connection with it. After all, we are a product and part of the natural world.
can we have an example where action is maximized rather than minimized?
yes, they are called instantons, and are a signal of field instabilities (thermodynamically unfavored)
Michael Bay movies
when you don't crap out of saving a life at your own peril.
From the path integral perspective in qft you can see that it is irrelevant whether it is a maximum or minimum, it just needs to have vanishing derivative
@@samanthaqiu3416 so do they exist in the real world, of just as hypothetical/mathematical oddities?
This is one of the most profound episodes of Spacetime I’ve seen in my ~ 4 years of subscription. Veritasium was also on fire this week. Bravo Matt, bravo!
In the short story “Story of your Life“, the basis for the movie “Arrival”, the aliens with a Doctor-Manhattan-style perception of time regarded action as fundamental and defined concepts like velocity and acceleration in terms of action and other things. It hadn’t occurred to them to treat velocity and acceleration as fundamental.
This is so interesting, thanks for this!
Lagrange was so far ahead of his time that ZZ Top wrote a song about him.
🎶 ah how how how how!
@@isaach1447 isaac glad to see you back in the club
Epic!
Slip inside my sleeping bag.
Well I heard it's fine
My physics education thru a PhD completely confused me about the advantages of Lagrangian and Hamiltonian mechanics over Newtonian mechanics, and never explained action as well as this briefing did. Bravo!
For cases like yours, one professor always recommended to try to work out the equations of motion of the double pendulum using Newtonian mechanics. I agree with him, it's enlightening.
@@zray2937 You don't even have to go that far. Lagrangian mechanics completely trivializes a single pendulum, whereas it's still quite complicated in Newtonian mechanics.
@@zray2937 One time in an oral exam during my 1st year at uni studying physics (so before we were introduced to Lagrangian mechanics) the professor told me to derive the equations of motion for a double pendulum. I came to him 10 minutes later disappointed, not having got anywhere with it but he wasn't phased at all by my inability and just started asking his normal exam questions. After the exam I asked him why he asked me to derive the double pendulum and he said "well I saw you were done with your other tasks so I wanted to keep you entertained, I never expected you to solve it"
Wed c
At 7:59 Matt O'Dowd says "All objects moving through spacetime move through paths that minimize the time measured on that path." In fact, freely falling objects follow paths that *maximize* the time measured on that path. If an object wiggled back and forth needlessly while going from one spacetime point to another, relativistic time dilation would make the time measured along that path *shorter*.
This is actually visible in an earlier formula for the action S. It has a minus sign in it: the action is *minus* mc² times the proper time.
Do you happen to have a sister named Joan? Just curious...
Maybe he should have said “for that path” instead of “on that path”. As he is referring to how the observed path is created from a given beginning to an end, rather than about the path itself. But for constrained paths such as energetic magnetic field lines, your observation may be useful.
Your writers are honestly so good. Not even just with the science stuff.
Work smarter, not harder is a cornerstone of reality. Love it
Not gonna lie, the 14 minutes taught me more about action than the 10 hours of Hamiltonian mechanics lectures back when I was at uni...
can you elaborate more on what this video helped you understand that you couldn't before?
To be fair, you probably wouldn’t understand a lot of this without the base you already had. Think about how much of this would make any sense after your first physics course.
I dont think that is possible.
Am I one of the few in here without a Physics Degree? Thank you Matt for making such complex and incredible academic achievements obtainable and understandable to the common person
Nope. I have no degree, I don't understand half of what he says, but I have a vague idea of the general gist of it. I sometimes think I should get into physics for real. Like.. I don't understand the equations, and I forget many of the comparisons he makes, I miss a few words here and there, but I get some concepts that I saw in other videos and other channels. So for example, one thing I've seen that I keep in my mind and I remembered again while watching the relativity bit is that there is a relationship between lightspeed and time, in which anything in the universe, as it gets closer to lightspeed, will perceive time going slower. So lightspeed is the speed limit because time would basically stop. They are two metrics of something that is the same.
Usually I watch yt videos at 1.5x-2x speed. This is the only one I watched at 0.75x speed. It's breathtaking. Thank you!
The action principle was one of the most interesting concepts I learned in undergraduate classical mechanics. It really puts into perspective how important the calculus of variations is. Proving that the shortest distance between two points in flat Euclidean space is a straight line, is a perfect example of this.
So true. This and the Noether-Theorem (i think there is also a vid on that on this channel) were definitely light bulb moments in my classical mechanics class.
I agree and when I use principle of least action in action I give you a like 👍
Absolutely. It's a brilliant subject and the fact that its use can be extended to cover effectively all known physics is quite incredible.
Powerful way to summarize GR (Einstein Hilbert action) and the rest of physics (Standard model path integral) into two simple equations. Tied for second and third place are Noether's symmetries and also the geometry view of nature, that is that GR and standard model including the interactions can be understood as geometry ('symmetry implies interaction' and curvature implies potential energy Einstein-Civita connection=GR, gauge symmetry/curvature/connection=EM).
A straight line in Euclidean space is the shortest line by design.
During graduate studies, this was one of the most revealing topics! Awesome visualisations! :)
Share this channel.
Dont just 'Hope' for it to grow.
Agreed!
When we learned Lagrangian mechanics in my analytical mechanics class, it was during the first week of online classes due to the covid shutdown, so I didn't really get good instruction on it. This has cleared up a lot of questions and also shown me how beautiful this principle of action is. Thanks for the great video.
This was a really good episode. I've been watching for a few years and am myself a junior physics undergraduate. I found the entire episode entertaining; my favorite bit though was reframing the Lagrangian under special relativity and discovering that it's simply the requirement that proper time is kept constant. The Hamiltonian always felt natural enough since it represents the total energy of the system, but the Lagrangian always felt artificial and arbitrary. Combining the common (for a physics major) knowledge of how kinetic and potential energy affect the proper time of an observer via relativity to explain the Lagrangian was really the exciting bit for me.
My professor once wrote on the board: e^{iS} he then turned to us and said “ i just wrote down all of physics.”
I'm having trouble finding anything about this on google, could you write this out in a different way maybe?...
@@lydiamulfinger6781 e^(iS)
@@lydiamulfinger6781 it’s the path integral formulation
e^{iS/ħ}.
@@albertorasa6220 hbar is always 1
I love listening to this, even though I don't always understand everything.
Strengthen your own basis then. Build a groundwork.
This is exactly where I started, soon the patterns start revealing deeper truths.
it's ok to just listen tho
Me too
Same. I understand the words, the lingo, so I understand what he is saying, but not the equations.
Great video! I have a master's in physics and still learned something from this video about one of the basic principles in physics. The different forms of action were never explained or connected this clearly in my university courses.
Did you notice that Matt goofed with the proper time? Compare the twin scenario: for the twin who remains in inertial motion the most amount of proper time elapses. For the twin who travels a longer spatial length than the stay-at-home sibling a smaller amount of proper time elapses. In GR: the path of inertial motion is the path of the _most_ proper time elapsing
its just another example of differential vs integral equations...minimizing functionals is a question of choosing the integrated funciton that minimizes the integral
The lead up to and delivery of the statement "All objects moving through spacetime move through paths that minimize the time measured on that path" just gave me chills. Such a concise and simple build-up to something fundamental to our universe that seems so complex and simple at the same time.
The Euler-Lagrange equation is a thing of true beauty, very useful in General Relativity for generating them damn critical Christoffel symbols. GR is built on the principle of least action.
I've always called them Christ - awful symbols
In the case of gravitational lensing, isn't the light still traveling in a straight line? I thought it's only spacetime that bends, making the light appear curved from our perspective, even though it was moving straight all along.
You are correct. Light is moving in the straightest line possible, which locally does appear straight.
Depends on your definition of "straight."
Assuming Einstein Equivalence holds true: Light, like everything else in free-fall, obeys the geodesic equation and their paths are called "geodesic." These are the "straightest" paths. The difference between light and massive particles is that geodesics for massive particles are a maximum for the proper time, while proper time is not defined for light (the massless case).
Yes, light always moves at the fastest possible speed in a straight line.
Mass bends spacetime, and you end up calculating a lot (of combinations) of curvature differentials in a 3x3 or 4x4 matrix, or even 16*4*4 matrices to describe a GEODESIC == straight line within curved space(time)
oh wow, never thought of it that way
This is amazing. As a physics student, I've seen the Lagrange-Euler equations, principle of least action, and the stationary phase method (for optics) all in separate classes. Still, the way you guys manage to string together these concepts so clearly, also incorporating both relativity as well as quantum mechanics, has given me so much new insights as to what these concepts mean. It's scratching this "but why" itch I still so often don't get scratched in these classes; thank you.
Ah, this explains why my head didn't actually explode while my mind was blown. It's so logical and simple and I feel like I know less than before this video started.
This episode made me emotional. my face muscles just took the shortest path from :( to :) thank you PBS Space Time!
This is such an eye-opener. Action and fields should be discussed more often at a more fundamental level. It is much more intuitive than standard particle stuff and wave-particle duality.
3:14 I remember using this method to solve problems in my graduate Mechanics class. It involved minimizing an integral for the path. It is true that Lagrangian Mechanics makes it possible to solve problems that are essentially impossible using simple Newtonian Mechanics.
I've been pondering how to teach what action principles are to intelligent non-physicists since I was in graduate school. This was very, very well done. Thank you for giving me an example of such good pedagogy.
This comment made me look up a word in the dictionary, thank you! I agree as well that this video is well made.
P.s Ped-a-go-gy Noun : the art, science, or profession of teaching; esp : EDUCATION 2
Also of possible interest are Leonard Susskind's 3 semi-technical books on essential physics, his "theoretical minimum" series, starting with "The Theoretical Minimum: What You Need to Know to Start Doing Physics." Later volumes handle quantum mechanics and relativity. The "theoretical minimum" of the title is kind of a pun-he's trying to teach the minimum amount of physics one needs to get a grasp of the field as a whole, but least action is a core idea. Reviewer John Gribbon put it well in a review for the Wall St. Journal:
"At the heart of this book, both physically and metaphorically, is the "principle of least action" ("action" being a technical term that refers, basically, to the overall energy in a system over time). The most important idea in physics, it can be summed up in the phrase 'the universe is lazy.'" -Tom
@@TLMuse Thank you for the reccomendation
“The principle of least action” is also in the running for the title of my autobiography 🙃
You're never going to actually write it, are you? :P
Teacher: Why didn't you complete your homework ?
Me: I did. I was practicing the 'Principle of least Action'
This is the best lecture on the principle of least action I have ever seen. You just helped me finish my paper on energies of the Planck era. Thank you!
It had been a long time since I had to rewatch a whole episode to understand things
Great material, really insightful, congrats
It's so cool to see a video I wrote realized like this
SHARE
When will we get a musical called "Hamiltonian"?
A cappella science did a song parody of a song from Hamilton, making it about the physicist William Rowan Hamilton instead of about the politician. In addition to Hamilton’s life, it also addresses the Hamiltonian and Quaternions.
It is good!
“He tried extending the complex, found the next step fickle,
his kids would ask him ‘dad, can you multiply triples?’
‘Not yet, I can only subtract and add back’ “ etc.
I asked my physics department to do this and they said no. Whyyy
It seems the whole Space Time team was in flow-state for this episode.
Superbly efficient, taking the path of least action to effectively collapse the probability of information into reality.
Woah, this might be the first PBS Space Time I've completely understood without going through the referenced previous PBS Space Time videos! Tbf I have watched quite a lot of Space Time videos, but half the time I was stuck pretending I understood the video while guessing what it actually meant, whilst with the other half I had to do further readings on wikipedia to get a firmer grasp on what was actually discussed. In all of those times though I felt Matt and the Space Time team doing their best to simplify the discussion such that even non-physicist normies like me can still understand, so long as they've watched enough of the alluded videos Matt mentions.
It's like learning how to ride a bike of ideas, my handlebars may wobble without the training wheels, but I'm not constantly falling down anymore.
In other words - it's getting intuitive.
@@ernestolombardo5811 I don't know how to ride a bike either so me finding most of this channel's videos hard makes even more sense with that analogy lol. I feel like I've understood more since then (that or the videos have just gotten simpler lately with the illustrations featuring that glasses black guy). Recent PBS Space Time videos doesn't feel as difficult as I remember the older videos being.
"Time flies when you're having fun."
So literally the purpose of the Universe is to have fun.
To have the least fun
You have discovered the meaning of life🧐
Indeed a particle maximizes it's proper time, not minimizes. Example: the twin paradox. The traveling, I. E. accelerated twin experiences less time. Spacetime isn't entirely intuitive, a path that seems longer (using the Euclidean metric) is actually shorter in the lorentzian metric, I. E using relativity
Yes, I see. This sky looks like sky.
I was totally out of my depth, which means you've set a good guideline for what I should learn next. Thank you!
So well explained, keeping the pace and reminders of prior info well, nice work
This is one of the best PBS Spacetime episodes, absolutely wonderful explanation and how everything was tied together. I feel I learned a lot of how things actually influence each other in the grand scheme of things.
I'm not lazy, I'm practicing the principle of least action.
The minimal/maximal principle of action: sounds like something CATS would come up with.
@@Thomas.Wright now I see why the Egyptians saw cats as divine, they're the actual makers of our universe
There is a book about the principle called _The Lazy Universe._
@@TheTokkie May your road lead you to warm sands, traveler!
"The Principal of Least Action" might also be the title of a video about Congress.
lol
It's when they do take action that the trouble starts. "No man's life, liberty or property are safe while the Legislature is in session." - Gideon John Tucker
that's how it was designed.
Haha gottem
There's nothing principled about Congress.
Amazingly clear, elegant, comprehensible and helpful. You folks are pushing the envelope of science education AND making it fun!
Excellent video!
Thanks for delving into this important subject and bringing clarity with masterfull didatic skils to get these beautifull and fundmental ideas across out to a wider audience!
The only thing I understood was the Nord VPN sponsor segment lmao
Quoting Feynman: “When I was in high school, my physics teacher-whose name was Mr. Bader-called me down one day after physics class and said, ‘You look bored; I want to tell you something interesting.’ Then he told me something which I found absolutely fascinating, and have, since then, always found fascinating.... The subject is this-the principle of least action."
Well, we were also bored, and Space Time provided! :)
Ah yes, from Lectures on Physics. Wonderful set of books. Highly recommended.
Love this video! Everything was sooo clear
this is one of the best videos... the explanation was on point and easy to understand relatively but not dumbed down..cheers❤️
I remember being amazed by this concept when reading Story of Your Life by Ted Chiang. I am amazed again at this video, thank you!
Which was the basis of the movie "Arrival" ... although they never had Renner's character talk about the principle of least action
Love this episode. Learning Lagrangian and Hamiltonian mechanics was the best thing ever to happen in my life when i studied Physics. That and learning to solve differential equations with a lot of methods. That´s when i realised that i prefered theoretical physics to working in an experimental lab.
Sometimes when my friends talk about how their kids are their best accomplishment i jokingly say if they tried Classical Mechanics.
I just can't believe there are people in the world that those equations make sense to. I mean, I looked at them, shook my head and thought "what kind of abstract thinking does someone need to have to be able to see that and say I understand"!!!
I love pausing the video to think about past videos and what Ive learned, just to have you review what I'm thinking during the video. Awesome content.
When people ask why I'm lazy and take the shortest path to achieving my goals, I finally have a video to justify why it's normal.
Good point! Excellent video!! Reminds me of my days doing doctoral studies under David Ritz Finkelstein back in the day, at Ga. Tech, where he adopted a Least Action Principle variational approach even on the most fundamental level, in his quantum topology account, in varying a discretely dynamic topology fundamentally tiled by a hypercubical lattice of elementary and entangled units of quantum process (chronons). So it's action, all the way down. On the Plack scale, there's only action, and its derivatives--information and energy, whose nature and interconnection will continue to baffle and elude philosophers like myself trying to sort that all out, conceptually--and not to mention the physicists, plumbing the depths like plumbers with their mathematical bags of tools, field-theoretic wrenches, multilinear Clifford algebraic ball and socket ratchet joints, etc. Whole lotta messy shite down there!!
Best explanation to the Lagrangian I could ever have. Thanks PBS and Matt!
Props to Matt on being among the few English speakers to get my name basically right on the first try. Truly a master of the principle of least [linguistic] action!
This is a masterpiece of high level science communication! Hats off 🎩 to the PBS Space Time team. This is probably the best Space Time video ever and one of the best science videos on TH-cam 🎥! I am lost in awe for nature once again, after a lot of time.
wow, I wrote this episode and I'm amazed at how many comments are expressing similar feelings to yours
Thank you, this was immeasurably helpful and reassuring. I have always intuited this principle, but never had it explained in a way that fully described its functions, moreover its breadth of application.
When I first started watching this channel (about 3 years ago) I knew very very little aside from a H.S. physics class. Now I have a much deeper understanding, especially with the graphics and visual almost tactile explanations. I still get lost by the math but the ideas, concepts and words they get through. These videos make me think for hours and hours after each day, contemplating the universe. Thank you so much for reinvigorating my love for physics and in a weird way philosophy as well.
I'm confused. How can light take the path of least proper time if it travels at the speed of light, and therefore doesn't experience time? Every path it could travel would take 0 time, so how does it choose a path?
You can still parameterise the path a photon takes but you're right that you can't call it the proper time.
It turns out that there is only ONE path a light particle can take that has zero proper time. This is how people calculate the path of a photon in GR, they set the proper time (spacetime interval) to zero and this tells you how the photon position in your frame (x,y,z) must change as a function of your frame time (t). Ie a path for the photon.
I thought light takes all possible paths at the same instant. In fact, I have been bothered by light not experiencing time and finally realized it is the only way to reconcile the bulk universe with our experience of time. The photon has experienced the universe in an instant. We, as confined energy, experience local time mediated by the force carriers known as gravitons that affect the spacetime field. It’s a weakly binding negative energy and somehow must mediate the process of decoherence with our environment. Anything traveling less than the speed of light experiences local time and is causally linked, since simultaneity does not exist. This action between events may define the geometry of space and is governed by the positive energy of dark energy which continually extends the action in one direction known as the arrow of time and also giving spacetime its thermodynamic properties. Thus both the concept of the bulk universe and the passage of time are real depending on the motion of the observer.
@@marishkagrayson Very interesting discussion or perspective. Thank you 🙏🏻 ❤️🔥🙌
@@jackheinzel8803 So you are saying it’s in the math, not really intuitable? Thanks 🙏🏻 I am not really a mathematician but I am an epistemologist so the point itself is important to me apart from the physics involved.
Fundamental nature of space time: nature is lazy
I actually used that as a memory aid in school to remember nature always wants to reach the lowest energy state
Not “lazy” but “optimally efficient” ;)
@@logicplague2077 least difference
¨I'm not lazy mom!, I'm optimally efficient¨
I wonder: entropy increases/differences decrease (energy spreads out evenly), the said heat death in a very far future -> while it makes sense up to some point, I kind of strugle to imagine that at the very "last" moment, it is possible for the system to come to a 100% halt, which means that nothing moves. at some point there should remain some back and forth (not just because of uncertainty). If a system is perfectly balanced, which the universe was not at the beginning, it can not come to a full halt if my understanding of physics are correct, since there will always remain some bouncing of particles back and forth, even though it becomes less and the bouncing spreads out more and more. This actually - I realize now while writing - maybe relates to the fact that information should not be erazable, but if the system would come to a 100% halt at some point, you would lose all the information from the time before, since no state change ocure. Is this maybe also indirect the reason why we always have those fluctuations (QT), because for a system it is impossible to come to a 100% halt, not the other way around (two balls, removing friction, etc, would when they start moving keep moving, multiple balls would spread out their kinetic energy, but will never come to halt)
Great episode. Minor corrections: 3:52-4:30 Note that there can be stationary paths that are neither minimal nor maximal. 7:59-8:19 In the simplest situations, it's a principle of *maximal* proper time. 8:27-8:31 The time in Fermat's principle is laboratory time, not proper time. E.g. in vacuum, the proper time of light is zero/frozen.
thank you, PBS and its crew for such a great job on science promotion, loved this one
If the configuration space Lagrangian seems to bridge some parts of quantum and relativity, what's missing to make this a theory of everything?
Gravity
Hi, I co-wrote this video and this was actually something I wanted to address, but we had to cut it off because it was too long. In simple terms, the universe at its very core seems to be a set of symmetries which are manifested in the Lagrangian. This means that if we knew all the symmetries the universe follows we could describe it perfectly, but we don't know all the symmetries it follows, and we are not sure how those symmetries fit with each other
If you want to learn more look up Neother's Theorem and Electroweak unification, or wait until we make that episode
the general relativity Lagrangian (see: Einstein-Hilbert Action) is not renormalizable. The other 3 forces are (thanks to the Higgs, and Ward Identities).
No. quantum-mechanics has very small scale effects with much shorter ranges (much larger inverse exponents), that do not appear on larger scales, as they very quickly average out to something much more predictable, that is more easily modeled with smaller exponents, like inverse squares for gravity, with much larger accumulative ranges, to the size of Laniakea.
Unless you explode a very young universe very quickly, so that tiny differences cause huge effects.
A GuT has the issue of low precision:
You could realistically model Blackbody-Radiation to colorize a scene of hot stuff, but you need more than 32 bit precision for this, because the numbers, that you multiply for a physically precise simulation, already differ enough in size or have a too high exponent, that has you often divide by (way too close to) 0, if you only use 32 bit IEEEfloat precision. To save battery life, most arithmetic in mobile devices only uses 16 bit precision.
for a simplified blackbody-model, that still works with 32 bit precision, you estimate the same function, but with much lower exponents and values of more equal sizes (by minimizing for least squares, or Chebyshev , or doing fourierAnalysis). Shadertoy has some Blackbody shaders with the most common Chebyshev-like approximations.
@@MrMetra101 Gravity is just the computational lag incurred when the universe tries to process a bunch of different lagrangians. The individual computations can't happen simultaneously, because they're already infinitely parallel path integral computations, so the local universe "hangs" while it waits for the queue of computations to clear. In other words, clocks lag in gravity wells because they have more to do besides tick forward.
The concept of the evolution of "configuration space" really rubs me off as an optimization in a computer simulation.
The deeper you go into physics and computer science, the more the two seems linked at a fundamental level.
It's almost as if computer science is based off of the fundamentals of physics and the rules of our reality.
Any sufficiently advanced computer is indistinguishable from nature, to mangle the oft quoted sci-fi/fantasy trope. This makes perfect sense in my weird mind which considers laws of nature to be magical spells with huge areas of effect in the entire observable universe, or indeed magical spells to be laws of nature with a well defined area of effect.
The observable universe is ultimately all just a big expanding multidimensional array of numbers with a series of algorithms iterating over the entire array every plank-time, putting the result in a new array and increasing the count variable by 1 plank time. The universe is also the computer this array runs on, the laws of nature are just the algorithms determining how numbers in different parts of the array used as input to the algorithms affect the output array on each step and science is ultimately just an attempt to approximately define these algorithms from their output.
Put all this together, and then the universe is both simultaneously sufficiently advanced technology and magic, indistinguishable from each other and unseperatably equal.
This line of thought arose from thinking too deeply about magical systems in fanfiction in a universe which is also a computer simulation, and how the interactions exist and work.
@@ThatCrazyKid0007 or it’s almost as if nature is just advancing from state to state based on a few pre-defined processing rules.
Can’t believe I knew all the science behind what you were talking, but only now I finally understood the connection between all of these. The fact that they are all seemingly same! Best episode of space time! I had to watch it like twice to get the whole point - amazing!
Don't you just love it when things click?
I've thanked you a lot in previous videos.. and I'll keep on thanking you for such amazing insightful videos.. Thank you.
You didn’t mention another fundamental property of action: its connection to the symmetries that underly all of nature via Noether’s theorem
we had to cut that part for time, but if I convince Matt and Andrew that will be next episode I write for the channel
Could this explain gravity? Time moves slower near heavy objects, actions will be cheaper when closer to that object => Move towards the object
Well this would explain why masses are attracted to objects that slow down time, but that just delays answering the question. How are those objects causing time to slow in the first place?
@@EpicProDudeOfAwesome Good point, but I don't fully agree. I think it simplifies the question rather than delaying it. Instead of the need to explain two things, why mass causes 1: gravity, and 2: time dilation, we end up with only one thing left to explain.
You explain physics like an origami lesson so clear that you can grab the concept. Thanks !!!
Beautiful presentation, your elegant style amazes me. Fluid and almost flawless.
I remember Newton's 2nd law is: ++F = d/dt(m•v) sum force equal momentum change.
How is it that Newton’s laws keep changing? 2nd law used to be “for every action there is an opposite and equal reaction.” Third law used to be f=ma. And force is not equal to change in momentum. Force times time equals the change in momentum.
THE TOP DOWN AND BALANCED UNDERSTANDING OF TIME AND SPACE, AS E=MC2 IS CLEARLY PROVEN TO BE F=MA ON BALANCE:
Time wasn't “created”. INSTANTANEITY is fundamental to what is the FULL and proper UNDERSTANDING of physics/physical experience, AS ELECTROMAGNETISM/energy is gravity. Time is necessarily possible/potential AND actual IN BALANCE. E=MC2 IS F=ma ON BALANCE. Accordingly, time DILATION ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. E=MC2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. Gravity is ELECTROMAGNETISM/energy.
Consider the man who IS standing on what is THE EARTH/ground. Touch AND feeling BLEND, AS ELECTROMAGNETISM/energy is gravity; AS gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; AS E=MC2 IS F=ma; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE. (THE EYE is the body ON BALANCE. Consider what is balanced BODILY/VISUAL EXPERIENCE.) The sky is BLUE, AND what is THE EARTH is ALSO BLUE. SO, objects AND MEN fall at the SAME RATE (neglecting air resistance, of course); AS E=MC2 IS F=ma; AS “mass”/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY; AS gravity IS ELECTROMAGNETISM/energy. It all CLEARLY makes perfect sense. I have explained why the rotation of WHAT IS THE MOON matches it's revolution. BALANCE and completeness go hand in hand. Carefully consider what is THE SUN. (Very importantly, outer “space” involves full inertia; AND it is fully invisible AND black.) The stars AND PLANETS are POINTS in the night sky. Again, time dilation ULTIMATELY proves ON BALANCE that E=MC2 is F=ma; AS ELECTROMAGNETISM/energy is gravity. Therefore, BALANCED inertia/INERTIAL RESISTANCE is fundamental. Gravity IS ELECTROMAGNETISM/energy. E=MC2 is CLEARLY F=ma ON BALANCE !!!
By Frank DiMeglio
@@frankdimeglio8216 what you have just said is one of the most insanely idiotic things I have ever heard. At no point in your incoherent, rambling on response were you even close to anything that can be considered a rational thought. Everyone in this room is now dumber for having listened to it. I award you no points, and may God have mercy on your soul.
@@frankdimeglio8216 you are trying to explain everything there is, in terms of the very little that you know... This is a bad recipe
I do love this channel. So smart. Your breakdowns on the theories and facts about the strange way the universe works always gives a spark to that sweet spot in my brain. However sweet id is. Thanks for all the thoughts shared, and for making me think. God bless.
As others have said, this may be your greatest episode yet!!! It’s not often I have my mind BLOWN, but this did it!!! Please continue to include more of the heavier math, even in large general examples. Wonderful!
"He found a very simple and beautiful pattern in nature, and this has been inspiring us ever since - through Fermat, and Lagrange, and Dirac, and Feynman, each seeking a path through the configuration space of ideas, guided by mysterious principles, not least of which is the action, pointing the surest way to the fundamental nature of ... Space-time." - Phew, what an epic sentence!!!
This reinforces the Cosmological Natural Selection and Quantum Decoherence episodes. The macroscopic observed states will be the ones that survive the quantum decoherence since they result of constructive interference of wave functions
Question: Is the principle of maximum proper time the same as the principle of minimum proper time ie., are they both principles of the same principle of stationary time(and are these the same as stationary action)? I've heard of maximum proper time via the Einstein Hilbert action - objects prefer this path(maximum proper time) under gravity.
yes
PBS Space Time is the only science channel where I feel more confused about a topic after listening, yet feel satisfied.
8:20 This... this just blew my mind!
Somehow after years of studying and working with these things, something just clicked sending shockwaves through my whole mind and body.
Thank you!
Ah, this is like Charlie Munger's "Inversion Thinking": Figure out what will cause your to fail financially and avoid doing those things. Constructor Theory is sort of like that, it seems: Figure out what breaks your real-world observations and cut those out of the progression towards a theory of everything.
I think the confusion with Constructor Theory is calling it a Theory when it is a process and yes a Theory but not in the way Physics uses the term Theory.
@@RedRocket4000 A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. String Theory says everything's strings, and Constructor Theory says everything's constructors.
Hope you make the updated quantum eraser video, based on Sabine Hossenfelder's
lol
Yes this!
Yea!
He will react in the Comment Part of the Video
8 mins in and it seemed as if I've watched 20-25 mins worth of content. Densely packed, yet concisely and clearly explained
Very good video. tying together so many fundamental concepts in a a clear and didactic manner. thank you
Do Lagrange Points in orbital mechanics have anything to do with this?
Yes, more physics!
That intro: "Ready....Action". Very well played.
This is absolutely MAGICAL! Thank you PBS SpaceTime Guy (presenter, writers, etc)!
I find it humorous how the universe can be so mysterious and inexplicable to our Simian hatchling brains, but for nature... well it's just doing what is always has, even if it's consistency is not always known to us. Regardless, I'm happy to share this world with y'all, thanks for producing these great videos guys; always such a treat.
One is caught up playing the impassioned protagonist in one’s Subjective Narrative of Self🎈
Fascinating.. your delivery is so easy to follow. Thank you. It's very soothing learning from brilliant minds.. always connects some dots.. You were talking about Consciousness.. 🌌
Awesome near mindblowing episode! And beautiful poetry with the key words at the end, Matt
This seems really cool. Are there any good resources to study the action versions of GR or QM directly without having seen the traditional versions? I am familiar with classical Lagrangian mechanics and have a background in pure math.
Look up the Einstein hilbert action!
@@mattstarbuck7484 took a cursory look at the wikipedia page, and this is exactly what I was looking for. Are there any good books/lecture notes etc on this topic that you'd happen to know of? And would you recommend learning this directly or learning these things through the traditional approach first?
Well, usually the lagrangians of the respective theory are reconstructed after the equations of motion already have been discovered. The usefulness of the lagrangian is to derive the equations of motions for a system. Look up for example the Einstein-Hilbert action. Playing around with the lagrangian and action can be used to derive new theories as well though.
@@lakshaymd I’m a physics student so I learnt about gr first and then about the action later. David tong’s notes on gr has a good section on the action that I’d recommend. Hope that helps :)
@@mattstarbuck7484 @Daniel
Thanks a lot! This is very helpful 👍