The story started at 1:45 is in fact an apocryphal story. I found a copy of "QED: The Strange Theory of Light and Matter" by Richard Feynman in a bookshop and it has an introduction written by Anthony Zee. He claims in his introduction to have made up the story for one of his books and he decided to name the wise-guy student Feynman as an homage.
The book is Quantum Field Theory in a Nutshell! Though the argument the fictional student makes is actually how Feynman wrote in the intro to Quantum Mechanics and Path Integrals
I almost never comment videos on youtube, but I had to express my love for you guys. TH-cam really needs channels that go so deep into the theory but is still understandable by the "commoners" (well, most of the time). Patreon it is.
Feynman's infinite quantum paths are an illogical speculation because this infinite is too high to integrate. Feynman's infinite quantum paths are just too many. So, I should say too much, and no one can integrate ALL possible paths. FYI, math can only add or integrate countably many numbers or things, which is the lowest level of infinity, as many as all integers, and called Aleph zero. The infinity of Aleph zero or countable many is less than the infinity of all real numbers, which is called Aleph one. The infinity of all the possible paths would be at Aleph two, which is more than real numbers. So, integrating all the possible paths is illogical.
@@ztac_dex How does Sakurai compare to Gross' Relativistic Quantum Mechanics and Field Theory? Some don't like Gross' organization, but I can see why he presented it his way.
It's also often correct about things that everyone else gets wrong. I don't know HOW many times I've seen some dunce with a youtube science channel, claim if you fall into a black hole, you'll see the future of the universe play out in fast forward entirely. But this is the only one to my knowledge that got it right, that no, there's a certain time after which the photons from the rest of the universe will never reach you before you hit the singularity.
Feynman's infinite quantum paths are an illogical speculation because this infinite is too high to integrate. Feynman's infinite quantum paths are just too many. So, I should say too much, and no one can integrate ALL possible paths. FYI, math can only add or integrate countably many numbers or things, which is the lowest level of infinity, as many as all integers, and called Aleph zero. The infinity of Aleph zero or countable many is less than the infinity of all real numbers, which is called Aleph one. The infinity of all the possible paths would be at Aleph two, which is more than real numbers. So, integrating all the possible paths is illogical.
Now I finally understand that I was on the same level as Richard Feynmann because my teachers at school always told me that I was asking stupid, annoying questions. Feynmann did it also in the classroom.
I highly appreciate the way you explain all this, crystal clearly and very accurate which makes it easier to obtain a neat figurative picture. Thank you! I will certainly continue to enjoy your videos!
I recently saw a video of Feynman lecturing on this. I was blown away when he pointed out that under a carefully controlled experiment, you could remove parts of a mirror, the parts that contribute devonstructive interference, and the result is a brighter reflection than you would see with the whole mirror. You could also remove the center, allowing the photon to pass right through, but still get some photons to reflect, as there is some constructive interference near the center, so some positive probability they will reflect even without the center there.
Gareth Dean Leonard Susskind had a good definition of "particle" that definitely exists. If I try to repeat I'll totally screw it up, but I saw it in one of his continuing education lectures on string theory on youtube. The particle definitely exists, at least on his definition. It is the POINT particle that is a fantastically useful but probably nonsensical assumption of Quantum Mechanics that will probably have to disappear to combine it with relativity. String Theory is one way to do that, but a lot of its advocates, including Suskind, are not nearly as optemistic about it as they used to be. It is useful as a mathematical tool, but it might not actually be a description of the real universe, unfortunately.
+Sam String theory is a mathematical religion. If they want to be taken seriously, they finally need to deliver falsifiable predictions. If they don't it's no worth wasting precious lifetime on it.
By the way...the collapse of all possible paths down to the shortest possible path by the principle of least action represents a phase shift from one time field (the quantum "probabilistic" time field) to the next "causal" time field (mathematically defined as classical Newtonian physics) This phase shift is super important because our fundamental understanding of time (what we are able to measure as time progresses fundamentally changes. These changes are very real, and the boundary between time field is very real. another phase shift from one time field to the next comes in the form of the event horizon of a black hole the place where all possible causal time lines merge to the point where space and time literally become inverted. Everything that could happen in the universe (all future time) gets compacted down into a purely massive black hole. All possible timelines compressing down to an infant point defined by one instant (crossing the event horizon at the speed of light) is exactly the thing that Mr Feynman is describing with quantum mechanics. They are called time feilds because the time feilds themselves take up definite spatial boundaries, Lagrange points (which themselves are sort of a form of superposition) etc. I haven't seen this video but I love the way its explained because its a simple way to explain how time feilds give us entirely different sets of physics. You cannot combine General relativity with Classical mechanics or quantum mechanics because time itself has defined physical spatial boundaries throughout the universe. Time itself is the linchpin that holds all of this together, our misunderstanding of time is why no one has discovered a grand universal Theory of everything....The Universe doesn't need it in order to function like it does! The only thing that binds everything together is resonant frequency...Gravity itself is a form of resonant frequency and the laws of resonant frequency exist at all spatial universal scales. Time field theory is a Trip...the implications of it allow for all sorts of crazy crap to happen...things that are seemingly impossible, like the delayed choice quantum eraser...but just so happen to be very real phenomena. honestly I have been wrapping my head around this for over a decade and I cannot think of or find a better explanation. And by the way the principle of least action, least distance, least information, etc. are all as fundamental to the universe as the Universal fundamental constants...In this case they are universal Time Constants. Any "event" in the universe at some form represents a phase shift, every forceful interaction also induces some form time dilation...literal time-stamping of events even if hypothetically all possible paths leading up to said event could occur or even possibly have. its the Universes way of circling back against having to create an infinite amount of separate universe to account for every possible super position for every quantum event (many worlds interpretation) in the same way the infinite paths of Feynman diagrams always find a way to collapse down to one singular event.
That's because if your professor was skilled at what they were teaching, they wouldn't be a teacher. They'd be in the private sector raking in the Benjamin's. But hey, you still get a certificate in the end, so money well spent?
What he explained here is just the cream part of the much deeper concepts. The moment you get into the nitty-gritty part of QFT, you will see that things are not bed of roses. When Feynmann himself was asked to explain his theory in few words, he replied ,"...If you could explain in a few words what it was all about, it wouldn’t be worth no Nobel Prize!’” So give credit to profs who are making effort to make you understand QFT.
@@stapleman007 I was working in oil and pretty decent in programming. Part of why I teach physics is because what you're doing in the private sector only related to physics in that you're applying different mathematical models, statistical and processing techniques. It gets very monotonous and isn't particularly satisfying or fulfilling.
As a layperson who is fascinated by science, I try so hard to understand these videos, but after 4 or 5 im just wiped out. I will have to finish this video tomorrow, my brain is mush now.
I also love these videos and love how they are not “dumbed down” (well they are, but not as much...) For instance, they are not afraid to show and attempt to explain equations. However, while I can normally follow these episodes, this one lost me about halfway through. I guess it is above my pay grade as a simple engineer and not a PhD in Quantum physics...
Don't worry, you not stupid, Feynman himself said that his math is predictive, but he doesn't know himself what nature is actually doing underneath. Physicists tend to get very excited when they find a formula, but the truth is, they cant tell you how the universe is actually working. For example the Standard Model is an equation that gives them a pure orgasm, they call it "beautiful" because it is so predictive, but few can actually explain why, and none can show you what nature is actually doing. That "beautiful" equation actually tells us the universe should not exist at all... yeah, so much for math. In fact one of the problems I believe is they stuck in the damn math. Like ask these guys what antimatter is, they will tell you its because the square root of a number has 2 solutions. God must be laughing at them. If you want a good handle on this stuff, read this... you will have a model that you can get your head around. And it shows you why science can go wrong. _Archetypal Entanglement A Beautiful Mind Kindle Books_
Infinite slits making brain feel, I don't know, Abby Normal. Have sudden urge to dance and sing... Have you seen the well-to-do, up and down Park Avenue, On that famous thoroughfare, with their noses in the air...... Yeah, I'm gonna stick with math.
Actually, they're not, since our universe is finite, there is not an infinite number of paths available, nor is there an infinite number of variables within the path
We call that sign language and it's widely used in the animal kingdom. E.g. if a dog looks at you and wags it's tail, it tries to explain quantum gravity to you this way. And if a bee dances, it communicates how the Higgs boson exactly affected her last flight to the nearest wormhole.
Feynman is also famous for in under 20 seconds jumping up from bed, running around the coffee table, under the kitchen chairs, onto the living room couch, across the bathroom hallway, into the bedroom, through the bathroom, under the kitchen table, in and out of the kitchen, and then back to bed to chew on his antler. Feynman is my dog. I should have lead with that. I don't think he understands the Principle of Least Action yet.
Based on this video it seems more likely he runs through the window over the neighbor’s house onto a crosstown bus boards a flight to Portugal visits Mars returns via the Pacific Ocean dries off in the yard then slips under the bed. 😅
Reminds me of a detective trying to understand what happened to the two russians in a back alley on St-Patrick's Day... "Where're you going, nowhere" although his point of view might change the outcome of the investigation, he will proven wrong by a proper observation but then again, who is really right? The serial crusher theory or the toilet falling from the sky?
Quantum mechanics is really amazing, not just in that it explains so much about the micro world, but also how perfectly it makes use of areas of mathematics that had nothing to do with it in the beginning... though I can't help asking myself, "Why do we need to account for all the probabilities to explain the simplest of interactions?" Is there no better way???
Ah, the Cornu Spiral! I remember when my physics teacher at high school has introduced it to me, however, that was not in the context of quantum physics, but as a different view on optics. Now it all comes together nicely and makes sense.
One of my greatest difficulties in college learning advanced physics, was that when mathematical explanations were presented, there was little offered in terms of intuitive understanding. Mathematical solutions without intuitive or experiential grasp of what was going on made it difficult to understand the physics These videos offer exactly that intuitive and experiential understanding. At age 60, I now feel like I can go back to the math, complete the connection, and “get” the physics That should keep me busy in my retirement
Amazing video, I never thought I would see Feynman path integrals explained so brightly and so accurately at the same time! Are you gonna explain renormalization too? That would be crazy! In your last video, you had a very good presentation of QED but you didn't speak about internal symmetries and gauge theories, are you planning to address this subject too? I've always seen those as kind of a mathematical trick but can't really figure a physical meaning to them. I would love to see what you could say about them. Please keep up the good job!
We are getting to a point where physics is going to need much more computational power and big data analytics to simulate answers to the path integral questions Matt posits in this video (how do we simulate the outcome or paths that all quantum (electron for example) field particles can traverse in) . I think we are at the theoretical limit of what computation can answer and the answers will lead us to even more questions. what an exciting time to be alive! Also - love that reference to the Feynman van!
I remember being shown this in undergraduate physics. At the beginning our freshman year we had worked with the concept that, at the lowest level, classical physics had no preferred direction for the "arrow of time". Newton works forward and backward. Pool balls on a frictionless table. Obvious, right? A year later we started exploring antimatter from the quantum perspective and were shown the math for "antimatter forwards in time is normal matter backwards in time" thing, and we at first thought of it as merely a strange perspective within (or artifact of) the math, not a "real" thing. Nope. "Normal matter backward in time" is precisely as valid and accurate a description as "antimatter forward in time". At an over-simplified level, it's almost like saying "negative numbers are the anti-numbers of positive numbers" compared to "negative numbers are positive numbers going backwards on the axis". You can also split a number into is magnitude (always a positive value) and "direction" (positive or negative). It's weird because while we easily handle two "directions" on the number axis, we have trouble doing so for the time axis. If we think of antimatter as the "mirror" of normal matter, that mirror can have multiple *equally accurate* descriptions. We can "flip" parts of the particle definition, or we can "flip" the time axis. It's all the same. When we encounter the math for a specific situation, choosing one antimatter definition over another can greatly simplify the overall math.
The "antimatter is just regular matter travelling backwards in time" idea (which, for reference, is called the Feynman-Stueckelberg interpretation) can also be seen as a realisation of charge-parity-time symmetry. This page might be of interest to you: en.wikipedia.org/wiki/CPT_symmetry
+transylvanian This is a great point; there's nothing to distinguish the two interpretations from each other; both are characterised by the same mathematics, and there's no statement/result implied by one that isn't implied by the other. If there were, then we could focus on that defining property, and then confirm/deny it by experiment, thus verifying one of the possibilities over the other.
The antimatter as regular matter moving backwards in time interpretation also seems to offer a unique explanation to the question asked at 14:07 'Where did all the antimatter created in the Big Bang go?' If antimatter is regular matter moving backwards, then the antimatter created in the Big Bang may have formed a mirror/sister universe to our own moving backwards in time with it's future "advancing" into our past while our future "advances" into its past.
2:04 "That is the essence of science: ask an impertinent question, and you are on your way to a pertinent answer." Chapter 4 'The Hidden structure' From 'The Ascent of Man' ( 1973 ) by J. Bronowski ( 1908 - 1974 )
This is the best explanation of the basis of QFT I have seen. It is possible to explain this stuff without the heavy mathematics. This may inspire the viewer to further investigate the principle of least action, lagrangian and Hamiltonian mathematics which are such important principles of physics. Thank you.
Next time someone tells me not to cut corners I'm just replying "Don't you know the physics at all? Principle of least action clearly states that in our universe all objects will always take the path of least action". I knew I'd learn something from this video!
This is an amazingly excellent series of lectures -- this particular one, for example, does a fantastic job of explaining the Path Integral Formulation. So I hate to quibble about anything -- and my quibble is about language, not the physics or the math: "Infinite" is not the same as "infinitely many". So "infinite paths" would be "paths, each of which is infinite", i.e. "each of which is infinitely long." What is really meant is "infinitely many paths". In short, "infinite" is a *quality* and "infinitely many" is a *quantity*. If "infinite" were only and always being (mis)used this way, it would at least be understandable, despite being mistaken. But because "infinite" is occasionally used (in this same video) to mean "infinitely long", every time the word "infinite" is used the viewer has to stop and figure out "Does this mean infinitely many (a quantity) or does it mean infinitely long (a quality)?" BTW, this is an increasingly common, but always frustrating, usage.
This is a real nice & pedagogical lecture on the Feynman path integral. Comment to 4:24 "Feynman added one & only one piece of real physics...the principle of least action". It should be said that the path integral formulation (and the principle of least action) can be derived from the operator formalism without adding anything.
What Feynmans found was ::: That a particle doesn't leap from one part of space to another But that the particle communicates with other particles along it's path (or the path that it's taking) And each of those particles completes the function or errand of that original particle And so what Feynmans did when he separated the times (plural) In his scale Is just plot the particles taking the path And not the times Because the universe runs on effeciency Not on waistfullness
I think these paths are not taken at all, it is impossible to measure them because they are by definition only between interactions. It's just a mathematical model to calculate things, nothing else.
@@rfvtgbzhn Well I can't claim that I have measured them But I can plot them And control them And even tell them what to do If that's any consolation (on how this works) I do time travel , time displacement , and time distortion experiments 😉😉😉 Hey your pretty close Your the closest one yet Excellent !!!
I just love the comment section on this channel! So many good questions, answers, discussions... just pure heaven compared to most of the comments on TH-cam.
NItpick, but it should be Lagnrangian not Lagrangean. The former, relates to the function Kinetic - potential, while Lagrangean means something pertinent to Lagrange's work. Otherwise brilliant video, as always
Ever since that video you made when you had a cold, I think in response to another person that makes excellent videos it was going over the movement of our solar system and although we use the simplest point of view for their orbits it is still correct . Anyway so far these videos and dialects are some of the best channels out there.
I like this guy. He can describe something very complicated but understandably. Others Arvin ash for example does the opposite, he makes turning on a light incomprehensibly confusing. So…. Thanks and good job👍🏻
Also, since I'm early, I might as well ask something that's been bothering me. It is said that nothing can stop the gravitational collapse of a black hole into a point but what about the conservation of angular momentum? As a black hole shrinks, it must rotate faster. And there is a limit on how fast things can travel (c) meaning the black hole cannot shrink to a size where its particles are travelling at the speed of light. This creates a kind of "inertia" if you will, preventing the black hole from further collapse. And then there are centrifugal forces too, which get stronger with increasing rotation. I think that these forces will eventually lead to an equilibrium and prevent further collapse of the black hole. I guess I'm not the first person to have thought of this but could somebody please explain it to me?
Feynstein 100 I think it's as simple as the overwhelming gravitational force overtaking the centrifugal force. don't forget about the infinite ridiculousness of the singularity and the difference between it and the event horizon and what happens in between. I'm no expert just my best guess!
oh and I think that might have something to do with the relationship of the mass of the black hole and the size of the event horizon but I could be wrong because I believe not all black holes rotate?
You're taking general relativity too literal. GR does predict the breakdown of spacetime, but GR does not apply for spacetime that is broken. Sure, it's reasonable to assume GR works to some extend beyond the event horizon, but it's not granted. GR does not explain how singularities work and has conflicting predictions for any space moving faster than the speed of light (time travel paradoxes).
In 6:32 I wished Matt had pointed out one interesting feature of the "summing over histories" method: As it turns out, for paths that are close to what we recognize as the _classical path_ (a straight line from A to B) the phases of the corresponding amplitudes vary only slowly so the _amplitudes do not cancel each other but add up constructively_. However, for all those crazy paths remote from the classical path, the phases of neighboring paths vary so fast that there are always very close-by pairs of paths whose phase have an opposite sign and hence corresponding amplitudes _cancel each other_, meaning they contribute nothing to the overall amplitude.
Another interesting feature: The action _S_ (explained in 4:48) for a given path divided by Planck's constant ℏ essentially determines the phase of the amplitude of a path (the phase is _iS/ℏ_). Hence, in the classical world (typically for macroscopic scales) where _S_ is much larger than the tiny value of ℏ , i.e. _S/ℏ≫1_, phases of adjacent paths change so fast that only paths extremely close to what we recognize as the classical path don't cancel each other out and contribute to the overall amplitude. However, as you go to microscopic scales, _S_ becomes of order of ℏ, _S/ℏ≈1_, and the phases of adjacent paths change much slower so that more and more of the crazy paths that deviate from our classical expectation contribute to the final amplitude (allowing for interference patterns typical in the quantum but suppressed in the classical world). This continuous transition from classical to quantum is nicely captured by the ratio _S/ℏ_ in Feynman's path integrals.
I have a simple theory. Space is a fabric like structure made up of Electro Magnetism & Energy (and may be more).A photon can split this fabric into its individual components as it moves along (Energy moves along and it causes the split of Electro magnetism in other two dimensions). Similarly other quantum particles like Electron, Proton, Atoms can affect this fabric (the smaller the object, the more this effect is). These interactions with basic fabric of Space acts like a wave and that's what causes the interference patterns in double slit experiment
Entangled particles share a wavefunction. In essence you start of with one 'thing' at a point in space then split it into two 'blobs' of wavefunction that run off and do their own thing. BUT, because the two are linked they're still one object. (You can imagine them being 'linked' by a bridge of wavefunction with zero amplitude, like an invisible string. This is part of why entangled particles can't send information faster than light, they must be separated at less than light speed first.) When one is altered, it doesn't matter which, the entire wavefunction changes and splits into two separate parts. It's not that measuring one affects the other, rather there were never two separate things to start with.
Entanglement is a fundamental part of quantum mechanics. Whenever you can conceptually separate "pieces" of the description of your physical system, you may have to think about how to combine them again later. For systems that are separate, it is easy to combine: you just do what is called a "tensor product". However, if the systems interacted, there is no possible "split" of the description such that the combined system can be described by a tensor product of the separate descriptions. If this is confusing, it's like two jars with liquids that are identical apart from color. As long as you didn't mix them, you can easily separate them out again, but once they're mixed, they're mixed for good. Entanglement is nothing more than the fact that quantum mechanical descriptions "mix" in this inseparable way. It doesn't matter whether it's a quantum mechanical theory of particles or fields.
just a side note but have you ever wondered about the resemblance between decoherance and the second law of thermodynamics?They both seem to imply that time needs a direction.
+transylvanian I understand all that and I was very much aware of that line of thought also. It is the same line that goes from Newton all the way to Bolzmann to Schrödinger in which they keep using the same basic principle that the basic equations need to be time symmetrical. But why did Newton choose this? I think this is a far better question to ask then simply taking it for granted and trying to model all those phenomena that simply violate that idea and dismissing them by way of claiming that is is just to hard to calculate all those interactions (there are to many) and it is better at a certain point to model it in a statistical way while still clinging to the hope that fundamentally there is such a thing as time symmetry. The Copenhagen interpretation was perhaps one of the best attacks against this view but it has its downsides, I admit. I guess what I'm saying is that we need to go back to our first assumptions, remove the time symmetry and replace it with irreversability. Let's simply put that as the first basic assumption and go from there. I would like to refer here to the work of Ilya Prigogine (en.wikipedia.org/wiki/Ilya_Prigogine) and his school of thought in which he tried to do just that. Chaotic systems for example only seem that way if you look at them in a newtonian sense, meaning a single particle with a distinct place and speed, if you start from probability functions as being the basic discription for your system, the chaos dissolves away into a nice evolution of your functions.
+transylvanian yes, you are correct that time symmetry implies via Emmy Noether that energy is conserved. She made that mathematically clear in equisite detail. But you see again this is only so inside the model in which you try to represent nature. We have experimental verification that energy is conserved, yes but then again are we really sure? Every measurment must allow for a certain error, so everytime we claim that an experiment verified a certain theoretical point we actually say that we measured something in which the error was small enough for us to be confident enough about our claim. But there lies the rub of course, it is always in those very tiny errors that surprises lurq. A small example: Newtons laws calculate the orbits of the planets perfectly. This was verified again and again, of course as the measurments became better there was this strange error in the movement of Mercury. It wasn't thought of as a big deal at first but it took eventually a different discription of gravity to give a better model. I hear you when you say that all this sounds very filosophical and you rather prefer some solid mathematical theory in stead of some half baked truth. All I'm saying is that one should always realise that all these theories that we have always come down to some choice that was made because it made sense at the time but times are a changing...
Question that has always bugged me. Statement taken for granted: "Photon is an excitation of the electromagnetic field". How do you quantify excitation of a field? Is a single photon the smallest unit of excitation? If there are smaller units of excitation, then at what point does an excitation become a photon, and how can we tell?
no reply ... sadly. I'd say, it's about amplitude and frequency. or ... a photon is a term for an arbitrarily chosen frequency and amplitude range of excitations
The total probability of something occurring is proportional to the (square of) the length of the final arrow obtained from adding up all the arrows corresponding to the different ways it could happen. Most of these are, let's say, ridiculous ways; these generally have their arrows pointing every which way and so cancel each other out, adding very little to the final arrow. The, let's say, sensible ways have arrows pointing in very nearly the same direction and so reinforce one another, contributing to the bulk of the final arrow. I strongly recommend Feynman's book QED" The Strange Theory of Light and Matter for a fuller (and better) explanation.
And because of that and much more Richard Feynman is on of (if not the) the greatest mind ever existed. For those how are really interested: "Renormalization" solved the infinity problems. To understand this stuff truely a physics study is inevitable
I was actually going to get a pair at Walmart since the Solar eclipse will happen on a VERY SPECIAL day for me, My BIRTHDAY!! BUT, since I watch every episode here every week, I will just support you guys on Patreon, thank you for the amazing videos and please keep em coming!!!
Since the universe is expanding, does that also mean that the size of the Planke length is too? In other words, is the smallest possible measurement effected by the expansion of spacetime?
Well, the Planck length depends on the fundamental constants of the universe. So as far as I know, the expansion of the universe shouldn't really affect it.
No if the universe expands so fast that it reaches influence on the quantum level the universe will rip the atoms apart then the bosons.Till there is nothing left not even an universe.
It is not the path of least resistance, because nothing is resisting the movement of the particle. It is the path of least action because it is action in the part of the particle. An example of the path of least resistance is if you are walking through a crowd of people, you would look for openings in the crowd and move through those openings. That is what least resistance means. This is not equivalent to that, and therefore it needs a different name.
This reminds me of Ibn Battuta-Never going the Same Route Twice. He was a medieval Moroccan traveller and scholar, who is widely recognised as one of the greatest travellers of all time. He is known for his extensive travels, accounts of which were published in his Travels (Rihla). I had a roommate that said always go a different way to see a different perspective. Not a bad suggestion for the study of science.
Anne Frank is the attic sound proof? don't want the nazi's to hear you watching pbs spacetime. they might start watch it too and send some of their bastard people up in space!
Yeah but those places are always so chilly, terrible heating, that's the problem. You'd want a place you know had a nice furnace running, 24/7. I too am terrible.
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lohphat Yes, but the probabilities of those paths, I'd assume, will be so small and might have been considered just for continuity of the equation. Besides, the action quantity distances that need superluminal speed to traverse cancel out. 7:16
+z2Utube Even so, doesn't special relativity negate those paths? I mean, if the particle can't travel at that speed, then the probability of that path is automatically zero, even without the need for cancellation.
Yes and yes. The key is that paths of superluminal speeds are allowed within the confines of heisenbergs uncertainty principle. You'll never detect a particle moving fastest than the speed of light, but the underlying wave function can travel at superluminal speeds.
" Yes, but the probabilities of those paths, I'd assume, will be so small " Nope. Actually, the "normal" paths have "measure zero" in functional space, that is, if you plucked out a path at random, the probability that it would be what you would call a sensible path is exactly zero. The remaining paths are jagged, crazy, loop in on themselves, and so on. This jaggedness is intimately related to how the path integral is able to reproduce the features of quantum mechanics.
It's the Fields that do the talking. I wished when I took Quantum Mechanics it had been presented with Field Theory first. That's the conversation I find more interesting. It would also have made all concepts of quantum theory conceptually more understandable. Feynman was one in a Billion. How we need him today.
Brian Greene has said in a lecture that it should be called "String Hypothesis", since there is no data yet. I also seem to recall him saying that String Theory is a QFT.
![เปิดบ้าน โคตรสวย ป๋องกพล รู้จักตั้งนาน เพิ่งรู้ว่ารวย!!! l [Nickynachat]](http://i.ytimg.com/vi/tmgCF_2HfYI/mqdefault.jpg)
The story started at 1:45 is in fact an apocryphal story. I found a copy of "QED: The Strange Theory of Light and Matter" by Richard Feynman in a bookshop and it has an introduction written by Anthony Zee. He claims in his introduction to have made up the story for one of his books and he decided to name the wise-guy student Feynman as an homage.
Yes you are correct!
He did say it was probably apocryphal.
The book is Quantum Field Theory in a Nutshell! Though the argument the fictional student makes is actually how Feynman wrote in the intro to Quantum Mechanics and Path Integrals
@@raidermenand now that has been provided, yes. It’s additional info, not a counter point.
I almost never comment videos on youtube, but I had to express my love for you guys. TH-cam really needs channels that go so deep into the theory but is still understandable by the "commoners" (well, most of the time). Patreon it is.
Feynman's infinite quantum paths are an illogical speculation because this infinite is too high to integrate. Feynman's infinite quantum paths are just too many. So, I should say too much, and no one can integrate ALL possible paths.
FYI, math can only add or integrate countably many numbers or things, which is the lowest level of infinity, as many as all integers, and called Aleph zero.
The infinity of Aleph zero or countable many is less than the infinity of all real numbers, which is called Aleph one.
The infinity of all the possible paths would be at Aleph two, which is more than real numbers.
So, integrating all the possible paths is illogical.
This episode was pretty complicated. I love the level of this show, it's pretty high!
I had to rewatch today because last night I was too sleepy to understand anything. That doesn't usually happen with youtube videos lol
More channels like this??
Path integral is grad-level physics tbh. Further reading from Sakurai's Modern Quantum Mechanics
@@ztac_dex How does Sakurai compare to Gross' Relativistic Quantum Mechanics and Field Theory? Some don't like Gross' organization, but I can see why he presented it his way.
It's also often correct about things that everyone else gets wrong. I don't know HOW many times I've seen some dunce with a youtube science channel, claim if you fall into a black hole, you'll see the future of the universe play out in fast forward entirely. But this is the only one to my knowledge that got it right, that no, there's a certain time after which the photons from the rest of the universe will never reach you before you hit the singularity.
Not lazy. Efficient.
Reminds me of a computer game.
sinei david working smarter not harder
Isn't that same thing?
@@DA-cu5xo it's unlikely, considering how ridiculously accurate our models are, but it is possible!
conservation of energy makes the most sense.
This is fantastic work. I've never seen anything so in-depth that is also so accessible. Brilliant!
Feynman's infinite quantum paths are an illogical speculation because this infinite is too high to integrate. Feynman's infinite quantum paths are just too many. So, I should say too much, and no one can integrate ALL possible paths.
FYI, math can only add or integrate countably many numbers or things, which is the lowest level of infinity, as many as all integers, and called Aleph zero.
The infinity of Aleph zero or countable many is less than the infinity of all real numbers, which is called Aleph one.
The infinity of all the possible paths would be at Aleph two, which is more than real numbers.
So, integrating all the possible paths is illogical.
This has to be my favorite TH-cam channel. As an economics major, I still can't find another more entertaining, and educational channel on youtube.
The Principle of least action describes my life
No it doesn't, it never got around to it.
the time integral of your *L A G R A N G I A N not L A G R A N G E A N
No, your life describes the principle of least action
@@user-en5vj6vr2u could be either way. The mathematician was L A G R A N G E - so who’s to say how to correctly spell “of LaGrange”
In a Darwinian way, it describes all life.
10:36 accurately sums up the whole video and everything that you need to know about quantum mechanics.
So this Photon walks into a bar. But only sometimes.
MushroomManToad I did laugh at this hahahahahaha
Sometimes walks through a bar, which is all sorts of crazy!
ur wrong, a photon walks into a bar but only arrives at a place where many of him are likely to arrive if hes drunk (wave)
You seem like a funguy.
some times out of infinite times so mathamatically never (n/anfinity=0)
Now I finally understand that I was on the same level as Richard Feynmann because my teachers at school always told me that I was asking stupid, annoying questions. Feynmann did it also in the classroom.
Who needs notification when you are always on youtube
Couch King so true
I know right?
What an original comment, never seen this one before...
Couch King lol
Couch King true xD and your profile picture makes this even more legit
I highly appreciate the way you explain all this, crystal clearly and very accurate which makes it easier to obtain a neat figurative picture. Thank you! I will certainly continue to enjoy your videos!
I recently saw a video of Feynman lecturing on this. I was blown away when he pointed out that under a carefully controlled experiment, you could remove parts of a mirror, the parts that contribute devonstructive interference, and the result is a brighter reflection than you would see with the whole mirror. You could also remove the center, allowing the photon to pass right through, but still get some photons to reflect, as there is some constructive interference near the center, so some positive probability they will reflect even without the center there.
Is the video on TH-cam?
And THAT is why you should treat stuff as waves, particles are nice and all, but probably just a statistical aberration.
Gareth Dean Leonard Susskind had a good definition of "particle" that definitely exists. If I try to repeat I'll totally screw it up, but I saw it in one of his continuing education lectures on string theory on youtube. The particle definitely exists, at least on his definition. It is the POINT particle that is a fantastically useful but probably nonsensical assumption of Quantum Mechanics that will probably have to disappear to combine it with relativity.
String Theory is one way to do that, but a lot of its advocates, including Suskind, are not nearly as optemistic about it as they used to be. It is useful as a mathematical tool, but it might not actually be a description of the real universe, unfortunately.
Interesting. I heard he died a while ago, trying to fight of a group of wild creationists.
+Sam
String theory is a mathematical religion. If they want to be taken seriously, they finally need to deliver falsifiable predictions. If they don't it's no worth wasting precious lifetime on it.
By the way...the collapse of all possible paths down to the shortest possible path by the principle of least action represents a phase shift from one time field (the quantum "probabilistic" time field) to the next "causal" time field (mathematically defined as classical Newtonian physics) This phase shift is super important because our fundamental understanding of time (what we are able to measure as time progresses fundamentally changes. These changes are very real, and the boundary between time field is very real. another phase shift from one time field to the next comes in the form of the event horizon of a black hole the place where all possible causal time lines merge to the point where space and time literally become inverted. Everything that could happen in the universe (all future time) gets compacted down into a purely massive black hole. All possible timelines compressing down to an infant point defined by one instant (crossing the event horizon at the speed of light) is exactly the thing that Mr Feynman is describing with quantum mechanics.
They are called time feilds because the time feilds themselves take up definite spatial boundaries, Lagrange points (which themselves are sort of a form of superposition) etc. I haven't seen this video but I love the way its explained because its a simple way to explain how time feilds give us entirely different sets of physics. You cannot combine General relativity with Classical mechanics or quantum mechanics because time itself has defined physical spatial boundaries throughout the universe. Time itself is the linchpin that holds all of this together, our misunderstanding of time is why no one has discovered a grand universal Theory of everything....The Universe doesn't need it in order to function like it does! The only thing that binds everything together is resonant frequency...Gravity itself is a form of resonant frequency and the laws of resonant frequency exist at all spatial universal scales.
Time field theory is a Trip...the implications of it allow for all sorts of crazy crap to happen...things that are seemingly impossible, like the delayed choice quantum eraser...but just so happen to be very real phenomena. honestly I have been wrapping my head around this for over a decade and I cannot think of or find a better explanation.
And by the way the principle of least action, least distance, least information, etc. are all as fundamental to the universe as the Universal fundamental constants...In this case they are universal Time Constants. Any "event" in the universe at some form represents a phase shift, every forceful interaction also induces some form time dilation...literal time-stamping of events even if hypothetically all possible paths leading up to said event could occur or even possibly have. its the Universes way of circling back against having to create an infinite amount of separate universe to account for every possible super position for every quantum event (many worlds interpretation) in the same way the infinite paths of Feynman diagrams always find a way to collapse down to one singular event.
Say what now?
It's amazing how clearly some people can explain things as opposed to professors you're paying to learn from.
College sucks
That's because if your professor was skilled at what they were teaching, they wouldn't be a teacher. They'd be in the private sector raking in the Benjamin's. But hey, you still get a certificate in the end, so money well spent?
@@stapleman007 🤣
What he explained here is just the cream part of the much deeper concepts. The moment you get into the nitty-gritty part of QFT, you will see that things are not bed of roses. When Feynmann himself was asked to explain his theory in few words, he replied ,"...If you could explain in a few words what it was all about, it wouldn’t be worth no Nobel Prize!’”
So give credit to profs who are making effort to make you understand QFT.
@@stapleman007 I was working in oil and pretty decent in programming. Part of why I teach physics is because what you're doing in the private sector only related to physics in that you're applying different mathematical models, statistical and processing techniques. It gets very monotonous and isn't particularly satisfying or fulfilling.
As a layperson who is fascinated by science, I try so hard to understand these videos, but after 4 or 5 im just wiped out. I will have to finish this video tomorrow, my brain is mush now.
Equalized what u have to realize is that with quantum field theory, you must account for the fact the equations are fucking magic
I also love these videos and love how they are not “dumbed down” (well they are, but not as much...) For instance, they are not afraid to show and attempt to explain equations. However, while I can normally follow these episodes, this one lost me about halfway through. I guess it is above my pay grade as a simple engineer and not a PhD in Quantum physics...
Don't worry, you not stupid, Feynman himself said that his math is predictive, but he doesn't know himself what nature is actually doing underneath. Physicists tend to get very excited when they find a formula, but the truth is, they cant tell you how the universe is actually working.
For example the Standard Model is an equation that gives them a pure orgasm, they call it "beautiful" because it is so predictive, but few can actually explain why, and none can show you what nature is actually doing.
That "beautiful" equation actually tells us the universe should not exist at all... yeah, so much for math.
In fact one of the problems I believe is they stuck in the damn math.
Like ask these guys what antimatter is, they will tell you its because the square root of a number has 2 solutions.
God must be laughing at them.
If you want a good handle on this stuff, read this... you will have a model that you can get your head around.
And it shows you why science can go wrong.
_Archetypal Entanglement A Beautiful Mind Kindle Books_
Stick with it - there is no point in hearing stuff that you already know! This is real magic . . .
Infinite slits making brain feel, I don't know, Abby Normal. Have sudden urge to dance and sing...
Have you seen the well-to-do, up and down Park Avenue,
On that famous thoroughfare, with their noses in the air......
Yeah, I'm gonna stick with math.
Infinite paths are *fine, man*
Duuude. (taking another toke).
man.
We're made of vibrations and shit.
Bongo drum rim shot.
Actually, they're not, since our universe is finite, there is not an infinite number of paths available, nor is there an infinite number of variables within the path
Tripcore how do you know the universe is finite? Has it been proven or is this a theory?
"everything could have been anything else and have just as much meaning." - Nemo Nobody.
If you watch this video with the audio off, you still understand the concept due to handwaving.
We call that sign language and it's widely used in the animal kingdom. E.g. if a dog looks at you and wags it's tail, it tries to explain quantum gravity to you this way. And if a bee dances, it communicates how the Higgs boson exactly affected her last flight to the nearest wormhole.
Frank Schneider, you win the comments section.
I like his way of talking.
it's almost like Italian TV.
I just tried it
Feynman is also famous for in under 20 seconds jumping up from bed, running around the coffee table, under the kitchen chairs, onto the living room couch, across the bathroom hallway, into the bedroom, through the bathroom, under the kitchen table, in and out of the kitchen, and then back to bed to chew on his antler. Feynman is my dog. I should have lead with that. I don't think he understands the Principle of Least Action yet.
good boy
Based on this video it seems more likely he runs through the window over the neighbor’s house onto a crosstown bus boards a flight to Portugal visits Mars returns via the Pacific Ocean dries off in the yard then slips under the bed. 😅
The chance of you going everywhere is cancelled out by you going nowhere...and there you are.
Least action is the path I take most of the time! ;)
i think you are onto something,maybe they dont cancel out but do happen in parallel universes and you are just their average
Reminds me of a detective trying to understand what happened to the two russians in a back alley on St-Patrick's Day... "Where're you going, nowhere" although his point of view might change the outcome of the investigation, he will proven wrong by a proper observation but then again, who is really right? The serial crusher theory or the toilet falling from the sky?
I can't like this comment because it's at 69 likes 😂 noice 👍
I'm loving the direction these episodes are taking. Keep up the great work.
I can't watch now, because I'm working, but I had to stop by and say...
BEST TOPIC EVER!!!
Gustavo Valdiviesso back to work peon
Yeah, you are paid for a reason!
Aaron Smith jui
Gustavo Valdiviesso, this is really a non-trivial topic, not addressed on other popular phisics channels (at least I haven't seen it before)
dAvrilthebear And the wait was worth it. Great episode indeed!
The quality and breadth of this channel is so amazing. Thank you!
This video's got me feelin' Feynman!
Best - Comment - Ever!
Rob Spiess hahaha xD thats absolutely feynman
sir, you are a "feynman".
I walked into a bar one day and i asked, I want a Rie mann and a beer man!
Saul Goodman
This PBS QM playlist is the perfect companion to Sean Carroll's Biggest Ideas videos on QM and QFT
This whole series has been very good. I would definitely be interested in seeing more like it in the future.
Finally one video , that I stumble up on youtube, and find it worthwhile to explore it further
Quantum mechanics is really amazing, not just in that it explains so much about the micro world, but also how perfectly it makes use of areas of mathematics that had nothing to do with it in the beginning... though I can't help asking myself, "Why do we need to account for all the probabilities to explain the simplest of interactions?" Is there no better way???
Ah, the Cornu Spiral! I remember when my physics teacher at high school has introduced it to me, however, that was not in the context of quantum physics, but as a different view on optics. Now it all comes together nicely and makes sense.
Lost at 4:40. About a minute longer than the last two videos. I think I'm getting smarter.
Matt Folse bro I made it to 6:30 on one video. I'm a fucking genius
Matt Folse Old Dutch Saying “We grow too soon old and too late schmart!,)
I *really* want to like this comment but the counter is at the funny number.... Sorry bud, maybe next time
Pranav Limaye I respect that 🤣
@@Folse
Update: Just saw that someone else ruined it and brought it to 70.... So you may have the 71st thumbs up from me. Cheers bro 👍
''Basically, the Universe is Lazy'' - now I feel my deepest connection to the Universe.
0:36 - accurate picture of Heisenberg eh
One of my greatest difficulties in college learning advanced physics, was that when mathematical explanations were presented, there was little offered in terms of intuitive understanding. Mathematical solutions without intuitive or experiential grasp of what was going on made it difficult to understand the physics
These videos offer exactly that intuitive and experiential understanding. At age 60, I now feel like I can go back to the math, complete the connection, and “get” the physics
That should keep me busy in my retirement
Yeah, this doesn't give you the real physics, either. :-)
Donate $5 or burn your eyes out. Well played PBS Spacetime. Well played.
Lmao mate
*I'm cryimg*
Us poor 99%ers will all go blind.
because the sun is a deadly lazer
Love seeing Feynman's van in the video. I saw it in person, at FERMILAB!
Amazing video, I never thought I would see Feynman path integrals explained so brightly and so accurately at the same time! Are you gonna explain renormalization too? That would be crazy!
In your last video, you had a very good presentation of QED but you didn't speak about internal symmetries and gauge theories, are you planning to address this subject too? I've always seen those as kind of a mathematical trick but can't really figure a physical meaning to them. I would love to see what you could say about them.
Please keep up the good job!
You’re a smart guy
Feynman quantized the electromagnetic field into photons in his theory of quantum electrodynamics.
We are getting to a point where physics is going to need much more computational power and big data analytics to simulate answers to the path integral questions Matt posits in this video (how do we simulate the outcome or paths that all quantum (electron for example) field particles can traverse in) . I think we are at the theoretical limit of what computation can answer and the answers will lead us to even more questions. what an exciting time to be alive! Also - love that reference to the Feynman van!
when you make the video about antimatter, please explain that 'travelling backwards in time' thing. I'm very intrigued by that!
I remember being shown this in undergraduate physics.
At the beginning our freshman year we had worked with the concept that, at the lowest level, classical physics had no preferred direction for the "arrow of time". Newton works forward and backward. Pool balls on a frictionless table. Obvious, right?
A year later we started exploring antimatter from the quantum perspective and were shown the math for "antimatter forwards in time is normal matter backwards in time" thing, and we at first thought of it as merely a strange perspective within (or artifact of) the math, not a "real" thing.
Nope. "Normal matter backward in time" is precisely as valid and accurate a description as "antimatter forward in time". At an over-simplified level, it's almost like saying "negative numbers are the anti-numbers of positive numbers" compared to "negative numbers are positive numbers going backwards on the axis". You can also split a number into is magnitude (always a positive value) and "direction" (positive or negative).
It's weird because while we easily handle two "directions" on the number axis, we have trouble doing so for the time axis.
If we think of antimatter as the "mirror" of normal matter, that mirror can have multiple *equally accurate* descriptions. We can "flip" parts of the particle definition, or we can "flip" the time axis. It's all the same. When we encounter the math for a specific situation, choosing one antimatter definition over another can greatly simplify the overall math.
The "antimatter is just regular matter travelling backwards in time" idea (which, for reference, is called the Feynman-Stueckelberg interpretation) can also be seen as a realisation of charge-parity-time symmetry. This page might be of interest to you:
en.wikipedia.org/wiki/CPT_symmetry
jentleman It is travelling backwards because it annihilates normal matter.
Because everything was completely simmectric befor the big bang.
+transylvanian
This is a great point; there's nothing to distinguish the two interpretations from each other; both are characterised by the same mathematics, and there's no statement/result implied by one that isn't implied by the other. If there were, then we could focus on that defining property, and then confirm/deny it by experiment, thus verifying one of the possibilities over the other.
The antimatter as regular matter moving backwards in time interpretation also seems to offer a unique explanation to the question asked at 14:07 'Where did all the antimatter created in the Big Bang go?' If antimatter is regular matter moving backwards, then the antimatter created in the Big Bang may have formed a mirror/sister universe to our own moving backwards in time with it's future "advancing" into our past while our future "advances" into its past.
One of the most beautiful video narratives of a fluxing space time I have ever watched . Sublime.
I really like where this series is going
Everywhere at once?
2:04 "That is the essence of science: ask an impertinent question, and you are on your way to a pertinent answer."
Chapter 4 'The Hidden structure' From 'The Ascent of Man' ( 1973 ) by J. Bronowski ( 1908 - 1974 )
When he said "Space time" the first time, i thought the vid was over 🤣
Well your content on quantum theory gets even deeper , its hard to comprehend, but that's what we like!!!!
keep it up , thanks!
Great job ! Even for a theorethical Physicist, these videos are quite helpful
Keep it up
This is the best explanation of the basis of QFT I have seen. It is possible to explain this stuff without the heavy mathematics. This may inspire the viewer to further investigate the principle of least action, lagrangian and Hamiltonian mathematics which are such important principles of physics. Thank you.
I like how Walter White is now who we picture when anyone mentions Heisenberg.
I don't because I never liked this particular TV show.
I love PBS shows. It's one of the best educational video series out there.
Every time he says "spacetime" I think the episode's about to end xD
I came here just to point that, either by posting or commenting if already done 😅
After 3min I just knew I'd have to watch this at least 5 times to begin to get it. Love it.
I'd love to see that episode on the Matter/AntiMatter balance!
Next time someone tells me not to cut corners I'm just replying "Don't you know the physics at all? Principle of least action clearly states that in our universe all objects will always take the path of least action". I knew I'd learn something from this video!
This is an amazingly excellent series of lectures -- this particular one, for example, does a fantastic job of explaining the Path Integral Formulation. So I hate to quibble about anything -- and my quibble is about language, not the physics or the math: "Infinite" is not the same as "infinitely many". So "infinite paths" would be "paths, each of which is infinite", i.e. "each of which is infinitely long." What is really meant is "infinitely many paths". In short, "infinite" is a *quality* and "infinitely many" is a *quantity*.
If "infinite" were only and always being (mis)used this way, it would at least be understandable, despite being mistaken. But because "infinite" is occasionally used (in this same video) to mean "infinitely long", every time the word "infinite" is used the viewer has to stop and figure out "Does this mean infinitely many (a quantity) or does it mean infinitely long (a quality)?"
BTW, this is an increasingly common, but always frustrating, usage.
This is a real nice & pedagogical lecture on the Feynman path integral. Comment to 4:24 "Feynman added one & only one piece of real physics...the principle of least action". It should be said that the path integral formulation (and the principle of least action) can be derived from the operator formalism without adding anything.
Did anyone else yell, "Nnnnooooo!!!" around 11:35 or so?
Well, yes, but actually Nnnnooooo!!!
These last 3 episodes were amazing!!
Goal: Don't procrastinate all summer. Justification: This counts as study. Brain: OK, goal achieved, reward with whiskey.
I approve of your work-reward system. :) *clinks glass of bourbon*
cheers y'all! :)
clinks colorado bulldog
Very enlightening new information on photons and infinite paths of quantum physics.
What Feynmans found was ::: That a particle doesn't leap from one part of space to another But that the particle communicates with other particles along it's path (or the path that it's taking) And each of those particles completes the function or errand of that original particle And so what Feynmans did when he separated the times (plural) In his scale Is just plot the particles taking the path And not the times Because the universe runs on effeciency Not on waistfullness
Like a computer
I think these paths are not taken at all, it is impossible to measure them because they are by definition only between interactions. It's just a mathematical model to calculate things, nothing else.
@@MrOJ287 like an exponential computer
@@rfvtgbzhn Well I can't claim that I have measured them But I can plot them And control them And even tell them what to do If that's any consolation (on how this works) I do time travel , time displacement , and time distortion experiments 😉😉😉 Hey your pretty close Your the closest one yet Excellent !!!
@@fivforfivfor you claim you do time travel experiments? Have you published any paper about this? Otherwise I don't believe you.
I just love the comment section on this channel! So many good questions, answers, discussions... just pure heaven compared to most of the comments on TH-cam.
NItpick, but it should be Lagnrangian not Lagrangean. The former, relates to the function Kinetic - potential, while Lagrangean means something pertinent to Lagrange's work.
Otherwise brilliant video, as always
- You say potatoe. I say po~ta~to.
🎶 potatoe, , to~ma~to, , ? oops 🎶
Ever since that video you made when you had a cold, I think in response to another person that makes excellent videos it was going over the movement of our solar system and although we use the simplest point of view for their orbits it is still correct . Anyway so far these videos and dialects are some of the best channels out there.
Freaking love hate relationship with your cliffhangers. "Find out how, on the next episode of Space Time"
I like this guy. He can describe something very complicated but understandably. Others Arvin ash for example does the opposite, he makes turning on a light incomprehensibly confusing. So…. Thanks and good job👍🏻
Also, since I'm early, I might as well ask something that's been bothering me. It is said that nothing can stop the gravitational collapse of a black hole into a point but what about the conservation of angular momentum? As a black hole shrinks, it must rotate faster. And there is a limit on how fast things can travel (c) meaning the black hole cannot shrink to a size where its particles are travelling at the speed of light. This creates a kind of "inertia" if you will, preventing the black hole from further collapse. And then there are centrifugal forces too, which get stronger with increasing rotation. I think that these forces will eventually lead to an equilibrium and prevent further collapse of the black hole. I guess I'm not the first person to have thought of this but could somebody please explain it to me?
it's been bugging me too. somebody please explain.
Feynstein 100 I think it's as simple as the overwhelming gravitational force overtaking the centrifugal force. don't forget about the infinite ridiculousness of the singularity and the difference between it and the event horizon and what happens in between. I'm no expert just my best guess!
oh and I think that might have something to do with the relationship of the mass of the black hole and the size of the event horizon but I could be wrong because I believe not all black holes rotate?
As soon as the particles collapes enough, the even horizon will be formed whenever the particles actualy form the singularity or not IIRC.
You're taking general relativity too literal. GR does predict the breakdown of spacetime, but GR does not apply for spacetime that is broken. Sure, it's reasonable to assume GR works to some extend beyond the event horizon, but it's not granted. GR does not explain how singularities work and has conflicting predictions for any space moving faster than the speed of light (time travel paradoxes).
In 6:32 I wished Matt had pointed out one interesting feature of the "summing over histories" method: As it turns out, for paths that are close to what we recognize as the _classical path_ (a straight line from A to B) the phases of the corresponding amplitudes vary only slowly so the _amplitudes do not cancel each other but add up constructively_. However, for all those crazy paths remote from the classical path, the phases of neighboring paths vary so fast that there are always very close-by pairs of paths whose phase have an opposite sign and hence corresponding amplitudes _cancel each other_, meaning they contribute nothing to the overall amplitude.
Another interesting feature: The action _S_ (explained in 4:48) for a given path divided by Planck's constant ℏ essentially determines the phase of the amplitude of a path (the phase is _iS/ℏ_). Hence, in the classical world (typically for macroscopic scales) where _S_ is much larger than the tiny value of ℏ , i.e. _S/ℏ≫1_, phases of adjacent paths change so fast that only paths extremely close to what we recognize as the classical path don't cancel each other out and contribute to the overall amplitude. However, as you go to microscopic scales, _S_ becomes of order of ℏ, _S/ℏ≈1_, and the phases of adjacent paths change much slower so that more and more of the crazy paths that deviate from our classical expectation contribute to the final amplitude (allowing for interference patterns typical in the quantum but suppressed in the classical world). This continuous transition from classical to quantum is nicely captured by the ratio _S/ℏ_ in Feynman's path integrals.
Legend says mathematicians to this day are trying to figure out why it works :D
One more gift to humanity. Well done PBS space time!
2:45 Was Richard Feynman, who then went on to invent Outrun and Vaporwave.
I have a simple theory. Space is a fabric like structure made up of Electro Magnetism & Energy (and may be more).A photon can split this fabric into its individual components as it moves along (Energy moves along and it causes the split of Electro magnetism in other two dimensions). Similarly other quantum particles like Electron, Proton, Atoms can affect this fabric (the smaller the object, the more this effect is). These interactions with basic fabric of Space acts like a wave and that's what causes the interference patterns in double slit experiment
how does entanglement fit into QFT? Is it emergent from the properties of fields or more fundamental than that?
Entangled particles share a wavefunction. In essence you start of with one 'thing' at a point in space then split it into two 'blobs' of wavefunction that run off and do their own thing. BUT, because the two are linked they're still one object. (You can imagine them being 'linked' by a bridge of wavefunction with zero amplitude, like an invisible string. This is part of why entangled particles can't send information faster than light, they must be separated at less than light speed first.) When one is altered, it doesn't matter which, the entire wavefunction changes and splits into two separate parts. It's not that measuring one affects the other, rather there were never two separate things to start with.
Entanglement is a fundamental part of quantum mechanics. Whenever you can conceptually separate "pieces" of the description of your physical system, you may have to think about how to combine them again later. For systems that are separate, it is easy to combine: you just do what is called a "tensor product". However, if the systems interacted, there is no possible "split" of the description such that the combined system can be described by a tensor product of the separate descriptions. If this is confusing, it's like two jars with liquids that are identical apart from color. As long as you didn't mix them, you can easily separate them out again, but once they're mixed, they're mixed for good. Entanglement is nothing more than the fact that quantum mechanical descriptions "mix" in this inseparable way. It doesn't matter whether it's a quantum mechanical theory of particles or fields.
just a side note but have you ever wondered about the resemblance between decoherance and the second law of thermodynamics?They both seem to imply that time needs a direction.
+transylvanian I understand all that and I was very much aware of that line of thought also. It is the same line that goes from Newton all the way to Bolzmann to Schrödinger in which they keep using the same basic principle that the basic equations need to be time symmetrical. But why did Newton choose this? I think this is a far better question to ask then simply taking it for granted and trying to model all those phenomena that simply violate that idea and dismissing them by way of claiming that is is just to hard to calculate all those interactions (there are to many) and it is better at a certain point to model it in a statistical way while still clinging to the hope that fundamentally there is such a thing as time symmetry. The Copenhagen interpretation was perhaps one of the best attacks against this view but it has its downsides, I admit. I guess what I'm saying is that we need to go back to our first assumptions, remove the time symmetry and replace it with irreversability. Let's simply put that as the first basic assumption and go from there.
I would like to refer here to the work of Ilya Prigogine (en.wikipedia.org/wiki/Ilya_Prigogine) and his school of thought in which he tried to do just that. Chaotic systems for example only seem that way if you look at them in a newtonian sense, meaning a single particle with a distinct place and speed, if you start from probability functions as being the basic discription for your system, the chaos dissolves away into a nice evolution of your functions.
+transylvanian yes, you are correct that time symmetry implies via Emmy Noether that energy is conserved. She made that mathematically clear in equisite detail. But you see again this is only so inside the model in which you try to represent nature. We have experimental verification that energy is conserved, yes but then again are we really sure? Every measurment must allow for a certain error, so everytime we claim that an experiment verified a certain theoretical point we actually say that we measured something in which the error was small enough for us to be confident enough about our claim. But there lies the rub of course, it is always in those very tiny errors that surprises lurq. A small example: Newtons laws calculate the orbits of the planets perfectly. This was verified again and again, of course as the measurments became better there was this strange error in the movement of Mercury. It wasn't thought of as a big deal at first but it took eventually a different discription of gravity to give a better model.
I hear you when you say that all this sounds very filosophical and you rather prefer some solid mathematical theory in stead of some half baked truth. All I'm saying is that one should always realise that all these theories that we have always come down to some choice that was made because it made sense at the time but times are a changing...
Holy crap, this is such an elegant and powerful theory.
Question that has always bugged me.
Statement taken for granted: "Photon is an excitation of the electromagnetic field".
How do you quantify excitation of a field? Is a single photon the smallest unit of excitation?
If there are smaller units of excitation, then at what point does an excitation become a photon, and how can we tell?
no reply ... sadly. I'd say, it's about amplitude and frequency. or ... a photon is a term for an arbitrarily chosen frequency and amplitude range of excitations
Just turning something like this into real words is a bloody miracle. I hope somebody kept Feynman's brain. We may need it.
Feynman's own words are better, great book...Feynmans Q.E.D., the Strange Theory of Matter and Light.
Could someone explain me why the possible paths are represented as a spyral? Please 🙏
They represent the crazy paths particles could hypothetically go through
Miriam Ventura I think it’s the probability diagram in 2d space
The total probability of something occurring is proportional to the (square of) the length of the final arrow obtained from adding up all the arrows corresponding to the different ways it could happen. Most of these are, let's say, ridiculous ways; these generally have their arrows pointing every which way and so cancel each other out, adding very little to the final arrow. The, let's say, sensible ways have arrows pointing in very nearly the same direction and so reinforce one another, contributing to the bulk of the final arrow. I strongly recommend Feynman's book QED" The Strange Theory of Light and Matter for a fuller (and better) explanation.
And because of that and much more Richard Feynman is on of (if not the) the greatest mind ever existed.
For those how are really interested: "Renormalization" solved the infinity problems. To understand this stuff truely a physics study is inevitable
@transylvanian
And that is why I decided to do my PhD in experimental physics :D
8:13 I thought the video ended there.
Dave Null space time still holds a lot of surprises for humanity, like not ending where we think it should end! :)
11:28 I think a mosquito might have just entered my widely opened mouth after I heard that lovely sentence.
path of least resistance.
resistance is futile
All Your Base Are Belong To Us
Gary Palmer My uncle used to tell me that when he forced me down at his cellar
...
gay
I was actually going to get a pair at Walmart since the Solar eclipse will happen on a VERY SPECIAL day for me, My BIRTHDAY!! BUT, since I watch every episode here every week, I will just support you guys on Patreon, thank you for the amazing videos and please keep em coming!!!
Since the universe is expanding, does that also mean that the size of the Planke length is too? In other words, is the smallest possible measurement effected by the expansion of spacetime?
No ! The universe does not get expande like that . The "expanding "means that near a Planck length the universe add others pieces of planck lenghts.
Well, the Planck length depends on the fundamental constants of the universe. So as far as I know, the expansion of the universe shouldn't really affect it.
No if the universe expands so fast that it reaches influence on the quantum level the universe will rip the atoms apart then the bosons.Till there is nothing left not even an universe.
randar1969 You're funny.
No its more like lego, the universe grows not expands... Its getting bigger, not fatter...
Whoever makes these thumbnails is doing a great job
4:50: I feel like their beating around the bus for terminology, I've heard it best described as "the path of least resistance"
Exactly what it is.
They are just making the simple way more complex
It is not the path of least resistance, because nothing is resisting the movement of the particle. It is the path of least action because it is action in the part of the particle.
An example of the path of least resistance is if you are walking through a crowd of people, you would look for openings in the crowd and move through those openings. That is what least resistance means. This is not equivalent to that, and therefore it needs a different name.
This reminds me of Ibn Battuta-Never going the Same Route Twice. He was a medieval Moroccan traveller and scholar, who is widely recognised as one of the greatest travellers of all time. He is known for his extensive travels, accounts of which were published in his Travels (Rihla). I had a roommate that said always go a different way to see a different perspective. Not a bad suggestion for the study of science.
42!
69!
o c e a n m a n 420 gets you to 42.
It's about 1.405006118*10^51
四百二十燃やせ
I liked the inclusion of Feynman's van. For those who don't know, he really did have a van decorated with examples of his diagrams.
Too bad Leonard, Sheldon, Howard & Raj burned out that van!
Principle of least action → Principle nature is lazy
Lazy? Or smart?
Eco-nomical.
The best to learn for me... this episodes, thanks guys.
Can I just say that you look amazing? Just wow, Look at that hair.
Anne Frank you need to concentrate more on the content of the video
I am, a certain aspect of it...
Anne Frank is the attic sound proof? don't want the nazi's to hear you watching pbs spacetime. they might start watch it too and send some of their bastard people up in space!
Yeah but those places are always so chilly, terrible heating, that's the problem. You'd want a place you know had a nice furnace running, 24/7.
I too am terrible.
you could always take a nice warm shower
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Wouldn't a wildly divergent path require superluminal speed to traverse the longer distance and arrive in the same time as the straight-line distance?
lohphat Yes, but the probabilities of those paths, I'd assume, will be so small and might have been considered just for continuity of the equation. Besides, the action quantity distances that need superluminal speed to traverse cancel out. 7:16
+z2Utube Even so, doesn't special relativity negate those paths? I mean, if the particle can't travel at that speed, then the probability of that path is automatically zero, even without the need for cancellation.
Yes and yes. The key is that paths of superluminal speeds are allowed within the confines of heisenbergs uncertainty principle. You'll never detect a particle moving fastest than the speed of light, but the underlying wave function can travel at superluminal speeds.
" Yes, but the probabilities of those paths, I'd assume, will be so small "
Nope. Actually, the "normal" paths have "measure zero" in functional space, that is, if you plucked out a path at random, the probability that it would be what you would call a sensible path is exactly zero. The remaining paths are jagged, crazy, loop in on themselves, and so on. This jaggedness is intimately related to how the path integral is able to reproduce the features of quantum mechanics.
+Feynstien 100 One of the reasons QM and GR are still not on speaking terms I presume.
It's the Fields that do the talking. I wished when I took Quantum Mechanics it had been presented with Field Theory first. That's the conversation I find more interesting. It would also have made all concepts of quantum theory conceptually more understandable. Feynman was one in a Billion. How we need him today.
We should modify the Murphy's Law from "to happen" to "does happen" but only in quantum level
Murphy's law of physics: 'Variables won't, constants aren't.'
Murphy's law of QM: 'Positive outcomes interfere, negative outcomes collapse.'
I knew about the path integral approach but hadn't come across that analogy of infinite slits. So, that's cool.
'Lagrangean' should be spelled as 'Lagrangian'!
Lagrangean duality-optimization and Lagrangian duality theory are BOTH correct. 😉
Brian Greene has said in a lecture that it should be called "String Hypothesis", since there is no data yet. I also seem to recall him saying that String Theory is a QFT.
fun fact: i met one of Heisenbergs grand children in person. we had a few drinks. She is 22 and is a student of philosophy
sorry great-grandchildren
cool story bro
Is she hot, though?
kaczan3 I think that's better left uncertain. If you knew exactly how hot she was you wouldn't be able to determine anything else about her.
Hey baby...can I collapse your wave function?
This is both fascinating and very hard to comprehend at the same time.
ATTACK ON TITAN PREDICTED THE FUTURE
P A T H S
Elegant indeed. Makes me feel peaceful.