“Quantum Caustics” seems like a better description in my amateur opinion (because they resemble optical caustics, not caustic chemicals). They are areas of higher probability formed from paths converging in the same way that light paths converging creates areas of extra brightness Edit: So apparently the name has already been taken by “quantum catastrophe theory” or whatever. That’s too bad
This! I would have gone with resonance, as in audio or radio in cavities, but caustics is perhaps better. I think I must have missed something, because I can't see how "quantum scars" is anything new. We've seen interference patterns in cavities before in many fields, so I don't know how this proves anything besides particles-goes-bouncy-bouncy-a-lot.
We are truly entering a magical realm of engineering. In RF engineering people have started making physical waveguides or other physical features of the assembly to replace computing and these look like ancient runes of summoning that you'd see in a fantasy setting. Now we'll have the same arcane designs etched on nanoscale devices to similarly guide the wave but this time the wave of a single electron and then remove the uncertainty that would otherwise be found in such miniature devices. All of this by etching arcane runes into the material itself.
Wish I'd written this. So grateful to see someone else who is having a similar response to me!! The whole Baryonic resonances and shapes and 'runes' or 'sigils' that really are expressions of a much deeper truth. It's point of reference relativity and fractals and infinity all the way down.
@@Nat-oj2uc The wave is guided through complicated geometry to do things. The simplest form of this is splitting a wave into different frequency ranges, like passing a laser through a prism to put multiple colors through the same fibre but of course all of that works for radio frequency stuff as well as more.
@@MrRolnicek 🤯 Why does this remind me of some science fiction I read in the 80's? I'm trying to remember the author, Michael Moorcock? Like everyone without a tertiary education but an interest I've been fascinated with some aspects of science. This idea of light moving from one region to another is how I thought they were sure that space time was expanding. I clearly had the wrong end of it. (Of course 😂) I wonder if I will live long enough to watch them repudiate the non existence of free will? Because of course that feels very wrong to most of us I think.
There's nothing in the mathematical definition of chaos that says you must have density of periodic orbits over the entire space. Many chaotic systems exhibit this property only over a subset of the space, as in the case of strange attractors
This doesn’t make sense, if you let the experiment run for infinity, then retracing would happen infinitely often, won’t it? I think “chaotic” (unpredictable) and completely random is not the same thing. The predictability of a chaotic system drops in what can be described by a function, but it doesn’t mean that there won’t be repeating patterns, we just can’t predict when those repeating patterns will occur. That’s why we have the strange attractors in some systems that can even be described by simple trigonometry.
In classical mechanics it is recognized that chaotic systems often oscillate around points that are labeled "strange attractors" When the system is disturbed the new paths will follow and new pattern oscillating around a new point. The butterfly effect is a typical feature of chaotic systems. Weather is a chaotic system that is currently transitioning to a new pattern.
Another feature of chaotic systems is that the characteristics of the pertubation that will cause a it to transition to a new pattern are unpredictable, thus the "chaos." Basically, not every butterfly wing flap is equal.
@@Metalkatt you were supposed to make that comment 3.5 minutes AFTER the original one , you can't even get your late timing right, you are chaos personified !
0:09: A slight clarification, Quantum physics as a whole includes both linear frameworks (like Hilbert spaces and quantum mechanics) and non-linear dynamics (like those in QCD). But the argument holds true for the parts of quantum physics most people are familiar with.
Our informatics teacher descibed chaos as following: IN a recursive system, you cannot predict a state more than one iteration ahead, hence the outcome can not be predicted with a shortcut solution but instead has to be iterated through each recursive step. The conclusion: Recursive solver operation logic is by definition chaotic. Fractals would be a practical example. Or fluid simulations.
At 5:20 Sabine says that quantum chaos in physics doesn't exist, then1 second later she has a different haircut. Isn't this a kind of chaos in physics? 🙂
Well, my „quantum chaos“ lecture at university was exactly about what this paper addresses - lots of billiards and the question what happens in the mesoskopic realm where you have a mixture of classical/chaotic and quantum mechanical behavior. A fellow PhD student of mine measured the conductivity of a small superconducting billard to see if the DOS looks more qm or more chaotic. So to me this topic never seemed neglected. At my old university, there was always also a small group of theoreticians who used bohmian mechanics, which provides a more „natural“ approach to quantum chaos.
"Quantum" because it sometimes is there and sometimes isn't ?, because it is there and it isn't there at the same time ?, or because of the plasma ? while shaving, of course, when not shaving is in duality until measured or "spotted" by the Occam's razor😂😂😂😂
In transportation planning we have a term called "desire paths", which is when people tramp the same route across a grassy park or meadow so many times that they create a trail, and so you can see the route people naturally want to take, even if the park planners didn't provide a trail there. I think that would have been a much better term, though I suppose scientists would balk at the word "desire". But the term desire paths really isn't about "desires" so much as it is about natural movement patterns in a given space, so it really does seem to describe an analogous phenomenon.
@@Manuel_Bache "Quantum" just means that the discreteness of action can't be ignored in the effort to predict accurately the behavior of the system being measured. The Blurring (a.k.a. Bohr's "Uncertainty") Principle of Heisenberg applies.
Chaos theory doesnt mean things keep growing indefinitely. The weather is chaotic, but that doesnt mean the temperture will run away to infinity. It simply means its harder to predict as time goes on. It is sunny today, so it is likely sunny tomorrow, but next week's weather is likely unrelated to today's. Chaos is still probabilistic. Whether or not it rains next week is still going to be between 0 and 1. So "washed out by quantum uncertainky" sure matches with chaotic models to me, as predictions become more uncertain with time. Chaos models may be deterministic, but we can never measure with the precison needed for accurate longer term predixtions. So I dont see how its incompatible at all honestly.
"weather nest week unrelated to today's weather" sure. . .except for recurring, sustained parts of the universe involved, which are essentially identical! (given a 1 week time frame). - Language and the use of "terms of art", nomenclature, etc, when seeking successful communication and education of science, or any advanced field of study, must consider use of coherent, reasonable words, terminologies, analogies, metaphors. Otherwise, one person may "know" the facts, but any other person may not reasonably be expected to grasp, grok, comprehend, or learn the information intended to be communicated. Ya know what I mean?
You make sense. I've had a growing feeling the issue of chaos in nature--- quantum or macro level, is due to the relationship between uncertainty and probability. The first happens in your head. The second deals with limitations in measurement.
In my master thesis, I calculated propabilities of multi state in laser traps. The particles had a higher likelihood to go into certain combination of states just by the amount of combinatorics to achieve these states. It was never chaotic, dynamic yes, but not chaotic.
I think Sabine may be mistaken here. QM encompasses QED, which is linear, but also QCD is non-linear (gluon self-interaction) and therefore would possibly yield QM effects that exhibit chaos
I never bought the argument from linearity. The Liouville equation is also linear, as it operates on probability density, and yet it entails the complete classical Hamiltonian physics, including chaos. What's different in quantum mechanics are the discrete energy levels and the uncertainty relation.
The liouville equation is not linear. It is provably impossible to create non-linear system from linear operators. Into to group theory type stuff. There has to be some non-linearity somewhere in the law of physics and this experiment is interesting because it functionally proves that there isn't some overlooked, tiny non-linear term to the schrodinger equation. One less place that a non-linearity can be hiding.
In the notion of chaos it's important to understand the topology on the states - i.e. what it means for states to be close to each other. If a state B being "close to A" means that upon measurement it's revealed to be _exactly_ A with 99% probability then it's not a particularly useful notion for determining chaotic behavior - if they're the same with 99% probability, they're going to produce the same dynamics with 99% probability, forever. This applies to both quantum mechanics and the Liouville equation.
@@Amir_404 If the Liouville equation is nonlinear, you surely can point me to the term in which rho occurs in any way other than linear. Note that in the Liouville equation, location and momentum only appear as parameters of the function rho, the only object that evolves in that equation is rho.
QM is a linear theory because we choose it to be so, if only because non-linear theories, like GR, are too hard. But non-linear formulations of the Schrödinger equation do exist, both on classical and quantum levels, and have been found to be applicable to many situations, e.g., fibre optics, water waves, vortex filaments, etc.
@fzixkid-gh9rv Linearity is a weak field approximation to a more general non-linear description of nature. Also, we introduce constructs that help us mask nonlinearity behind new entities. It works, up to a point.
@@zdzislawmeglicki2262 Yes linear approximations are preferred for their "elegance" and calculability, but they are usually only accurate within certain ranges.
@@iAnasazi For the time being, yes, because we can't deal with non-linear math. Just have a look at Hirota's multi-soliton solutions of Sine-Gordon and KdV eqns. They're extremely complicated.
Why is Quantum Theory linear? Is it because H|Psi>=E|Psi> and superposition? But that's only part of the story. We often forget that when deriving this equations from first principles through Least Action f.i. we neglect higher order terms assuming they vanish...until they don't. Nothing is truely linear or you'd get infinity in the limit and Nature doesn't like infinite.
It always struck me when i'd go to conferences and see people talk about quantum chaos only to say that there isnt any chaos, just funny looking energy level diagrams. Though the measurement problem feels like it would definitelly be part of the solution since a measurement doesnt change the wavefunction in a linear fashion. Anyway, cool to see this being talked about
really, when i go to conferences, than people just tell me random things about the level spacing statistics and why it is chaotic, if it is not the poisson distribution and im like ,,i do not buy it.,, xD I think the biggest problem in closed quantum system is, that the eigenvalues do not change over time, whereas in a chaotic system they do change. If you however measure only a subsystem, then you can have chaniging eigenvalues or use a coupling to a bath (which is measuring a subsystem)...
2:09 when you use the example of washing out chaos, tbh I instantly thought of rain landing on a large puddle. Partially cover the large puddle and allow for rain run off (larger droplets) to land, creating large amplified waves next to small rain droplets hitting the surface and the larger droplets negate the smaller more frequent ones. Honestly I'll need to film it next time it happens and I'll post it, so this makes more sense. My point is that there has to be fixed outcome ranges in the quantum level universe, otherwise there wouldn't be any similarities in the macro world (gold wouldn't be gold) and everything could not coaless into what it is today.
Isn't the whole point of chaos theory that chaos can arise out of simple, deterministic and predictable systems? The motivating question at 0:20 implies that that shouldn't be possible, but I don't see what's puzzling about it.
@@triton62674 Like @elliottmcollins, I don't really see what's puzzling about this either. But if you want some sort of explanation for what happens when you transition between scales, maybe this will give an idea: Look into Mean Field Dynamics. From Wikipedia: "Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics." So, between a QM system, and one that deals with micro/macroscopic phenomena. The relevant thing here, is that while QM is linear, describing the effective evolution of one particle in a huge number of particles is non-linear. Anyway, yeah, feel like she should've explained why exactly this we should expect macroscopic systems to be linear. There's really no reason that should be the case, emergent phenomena are a thing. There's really no reason that should be the case, emergent phenomena are a thing.
I love it when Sabine explains deep scientific concepts. She is a great scientific educator, even when sometimes she goes out of scope trying to explain human behavior and sociopolitical issues, which most of his followers, like me, don't care about for being transient and trendy. Thanks, Sabine, for teaching us the wonders of science!
I actually read it as "Roles". Well they do say the brain is a prediction machine. Or maybe I was just getting crosstalk from a version of me in a parallel reality where the mistake wasn't made. 🙂
how about the unparting particle, then we can make sure that it will not be disproven or we let elon musk name it.. if he names it like his children, nobody will want to talk about it.
Interesting and thanks. I'm mainly familiar with Classical Mechanics as I studied Chemistry back in the day. But I can follow along. And I also had a couple of courses relating to inorganic solid states, doping, and bandwidth, humdrum cook things up in your basement sorts of things. Liked that electronics has advanced considerably since those days of yore. Also think that graphene technology is just a bit away. One of the main problems seems to be that of passivation as there can be oxidation problems that can seriously degrade your transistor, I've heard. Staying tuned.
Even in 'Chaos' there are Patterns - Because even in chaos there are boundries/limits - Once those boundries/limits are identified, Patterns can then be identified and/or predicted..
@@nosuchthing8 Just because results are chaotic within a range doesn't mean they have no patterns. Chaotic and ordered phenomena coexist within the same systems. The patterns need not be deterministic and stable, they may be probabilistic and quasi-stable.
@crawkn In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972.[1][2] He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.[3] The idea that small causes may have large effects in weather was earlier acknowledged by the French mathematician and physicist Henri Poincaré. The American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.[4 The above is what Wikipedia says about the subject. Its just the way the math works out. If there is a better way to model certain systems like weather, we don't know about it. Its the mathematical version of the following: For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the message was lost. For want of a message the battle was lost. For want of a battle the kingdom was lost. And all for the want of a horseshoe nail. Go pick up any book on differential equations. They have a special section on 'problem' equations. Those that are very dependent on initial conditions. If you model weather and run the sim assuming the temp is 70 degrees and not 70.1, the sim slowly then quickly diverged feom reality. This is why weather predictions can never be accurate that far out. Because the measured temperatures are always off from the actual temps. And the differences explode.
@@nosuchthing8 Apparently you are using the term "pattern" in a very precise way. If describing the Lorentz Attractor as exhibiting a pattern by your strict definition is disallowed, then you may have your observation. To my eyes, it appears to be a pattern, albeit not a strictly predictable one.
The fact that the system is constrained (e.g., probabilities can't go beyond [0,1]) is not an indication that a system is not chaotic. The Lorenz attractor is bound but is still chaotic.
true, it might even be that chaotic systems are bounded by definition? because you need to exclude trivially exponentially unstable systems like dx/dt=x
@@wadehodson9666 Pretty much: the system doesn't have to be bounded, but for a system to be called chaotic it should have an attractor (specifically a strange attractor, so with a positive Lyapunov exponent) and that attractor will be bounded.
I'm skeptical about this finding, the example demonstration suggests that there is a limit to the "washed outness" of their quantum particle. As in they decided there is a reasonable limit where the probability is sufficiently small to be disregarded. Practically I would expect there is a non-zero probability that it would escape the enclosure.
It makes a sort of sense. Fractals are self-similar (in fact, that is phenotypically their defining trait), and if a quantum field creates scars, I could easily see that the scars would be self-similar.
Learning about non-linear oscillators, chaos and all that in Junior-level Classial Mechanics course put the "WOW!" back into Physics for me. Thanks, Professor Peter Scott, UC Santa Cruz! There *is* more to life than boundary value problems!
Ironically, there is a subset of wave chaos that is only about boundary conditions. The stadium billiard is a good example of that. Even with purely linear dynamics, the fact that the boundary is irregular brings out all kinds of weird and wild phenomena.
@@jameshart2622 True; that's a interesting example. It's fascinating that macroscopic, non-linear Classical systems exhibit chaotic behavior. I thought of BVPs in the context of PDEs: (1) Solve the "Whoever" Equation subject to the following boundry conditions ... (2) Separate variables. (3) Write a solution as a series of suitable orthogonal functions. (4) Do complicated integrals to compute the expansion coefficients. (5) Repeat for the next problem.
First, that pattern would look cool on some merch along with a pithy quantum statement about scars, chaos, and butterflies. I would definitely buy it. Second, I don't understand how the confined electron stays "quantum" if its position is constantly being observed or "watched" as it moves around the confined space. It seems like such measurement should constantly collapse the wave function. Third, kudos to experimenters who can realize this with real materials in the lab, along with the programmers who came up with the simulation. I cannot even imagine how to observe or detect an electron confined to a bounded 2d plane. Fourth, thanks for interpreting the super-human language of the abstract into some semblance of normal human language that is informative and fun. Poor Albert. Good thing he had a helmet.
Thanks again Dr. Hossenfelder. I'm sorry, but your educational videos only motivate my high school level physics trained brain to cry out with likely obvious questions, hypothetical challenges and questions. 😀 Quantum Scars compared to Standing Wave patterns observed in classic photon-thru slits experiments: 1. are the symmetrical interference patterns from photons through slits, constitute same phenomenon as Quantum Scars? 2. are there any distinctly different phenomenon being documented/recorded in the Graphene related Scars, than wavefront interference? 3 are both results of photons through slits and Quantum Scars both using the science framework for structure of apparatus and type of measurement systems? 4 Do the findings of Quantum Scars have any bearing on the definition of "information" used in calculations and predictions used for theories of Information retention/loss related to interaction of external matter near Black Holes/singularities? 5. Could both (or either) the Quantum Scar measurements or the Photons through Slits experiments explain the Entanglement or Spooky Action At Distance? (seeming impossible simultaneously identical motion of distant sub-atomic particles) I'd rather never waste time with an automated Symantic Mimicry system. Are there expert physics-knowledge systems?
Scars emerge when the eigen-frequencies of the shape get very high. There are some eigenmodes that reveal scars and other (nearby) ones that do not. See the mushroom and the stadium for examples where there is an interesting division between ergodic and nonergodic modes. I computed 160,000 eigenvalues (total of lowest Dirichlet and Neumann modes) of the regular pentagon, which is incidentally the most non-analytic eigenvalues for any shape that anyone that I am aware of ever computed. To get "scars", you need a non-analytic solutions, something you didn't mention: You can't get them in the rectangle, for example. One thing I would like to examine is: How to relate quantum behavior to classical chaos, which should be straighforward with the quantity of eigenmodes I computed. The regular pentagon is interesting because it is the smallest regular polygon beyond the equilateral triangle and square (which both have known closed-form modes) that has zero close-form modes (except the lowest Neumann mode). I thought there were extremely few people in the world who ever heard of these scars and how they relate to chaos. Does the regular pentagon exhibit scars? Probably, but I don't know. Linearity is interesting, but a scar should show up with only one eigenmode, not a linear combination of them: Linearity is sort of irrelevant. Thank you for making this video!
@@gregrice1354 There's latent energy in every bit of space. This energy spontaneously results in random particle-antiparticle pairs popping into existence.
The use of graphene to showcase quantum scars is a fascinating demonstration of theory meeting reality. This connection to potential electronics applications is especially intriguing.
What is this chatgpt ass comment lmao?! The "topic of video" is a fascinating demonstration of "generic thing", this connection to "thing mentioned" is especially intriguing. "Theory meeting reality" being used to describe physics experiments, which are definitionally obviously that.... You can't be a human person.
ill check your courses on brilliant, you sre the first one that got me. great quality materials, very interesting topics, i like your humour too you are not bland ^^
You cannot have a "pendulum" without quantum mechanics because that underpins all of reality, so you might say chaos is an emergent phenomenon at larger than quantum scales. I'd go so far as to say that chaos is really just a property of non linear systems/algorithms, more closely related to pure mathematics than physics.
The quantum scars idea reminds me of tuning the intake and exaust manifold on an engine, and tuning wire traces on a circuit board to optimise flow in the direction desired at the speed desired.
So despite the details of the initial starting conditions, the quantum scar that forms over time arrives at the same shape? For some reason, that's a calming thought. Predictability may be boring, but when you're trying to make safe and reliable systems, it's quite helpful.
The scar depends on the initial state. What happens is loosely speaking that classically these scars are paths for particles, but they are unstable. The particle will not stay on them. In the quantum case, the wavefunction can settle on these particular patterns which are not a path themselves, but have an enhanced probability. You see in the earlier simulation that generically the scars you get are quite complicated.
Perhaps this is something like the Central Limit Theorem? @SabineHossenfelder So, what you're saying is that what we're looking at is the visual representation of the probability density function of the quantum field?
Dynamics of the parts of the system are determined by factors. If you have one factor, it's a completely determined system. The more factors (comparable in their influence on the parts of the system), the more chaotic the system. But it's always close system, because these factors are limited (localized), and movement of the entire system are determined by the main factor (in the larger system). In other words, you have an "attractor" (that can be moved) and a "local minimal energy region" around it with locked "chaotic" subsystem inside. In proper design, such "regions" are minimized (unless you need an anti drone rifle or a quiet room for sensitive talks)
"Quantum scars do not demonstrate the absence of chaos at the quantum level. Instead, they highlight the subtle way classical properties of a chaotic system can influence the structures of quantum states, despite the fundamental differences between classical and quantum dynamics. Why don’t quantum scars disprove quantum chaos? The equations of quantum mechanics are linear: The Schrödinger equation is linear, meaning it does not produce the kind of exponentially sensitive behavior to initial conditions that we associate with classical chaos. However, this does not imply an absence of complex phenomena. Quantum chaos manifests differently, often through statistical and spectral properties (e.g., the energy level distributions align with the predictions of random matrix theory). Quantum scars are semiclassical manifestations: Quantum scars reveal that certain periodic orbits of a classically chaotic system leave a visible imprint on quantum wavefunctions, even in the regime where classical chaos dominates. This does not mean chaos vanishes at the quantum level. Instead, these scars show how specific aspects of classical dynamics influence quantum solutions. Scars are exceptions, not the rule: Berry's conjecture states that in chaotic quantum systems, wavefunctions are globally "ergodic" and statistically distributed in a random manner. Scars represent local deviations from this average behavior, not a contradiction. So, does chaos exist at the quantum level? Quantum chaos is a well-established discipline that explores how classically chaotic dynamics translate into the quantum regime. Even though: Classical trajectories are no longer defined in quantum mechanics (due to Heisenberg's uncertainty principle), Quantum equations are linear, quantum chaos manifests through: Energy spectra: Energy levels in chaotic systems obey universal statistical distributions, such as those of random matrix theory. These distributions differ from those in integrable systems, where levels are regularly spaced. Wavefunction structures: Scars, ergodic patterns, and local singularities in wavefunctions demonstrate dynamic aspects connected to classical chaos. Quantum fluctuations: In a classically chaotic system, trajectories diverge exponentially over time. This dynamic translates into quantum fluctuations in observables or probability densities, though framed within the theory of probability fields. Conclusion: Quantum scars do not refute chaos at the quantum level; they enhance our understanding of the connections between classical and quantum chaos. While quantum equations are linear and classical chaotic behavior does not directly translate to the quantum regime, quantum chaos manifests through statistical and spectral properties that respect the fundamental principles of quantum mechanics." - chatGPT
I read an article this morning on ancient knots in ropes and how the could have possibly gave rise to mathematical reasoning and geomagnetic patterns... very cool. And read the article about this a few days ago. We live in a cool age of discovery. Great video.
2:23 Why would we expect the probability to smear evenly? Why isn't it sufficient to assume that the probability smears everywhere for it to be chaotic? In the classical example, does the point particle visit all areas of the table uniformly? Could it not be the case that even in the classical example, there are hot spots of higher and lower probability while still having the property that the particle eventually passes arbitrarily close to any point? What actually makes the quantum example non-chaotic?
Well in this case it’s not the trail of the particle that’s necessarily chaotic. It’s not like the example with the stars in the sky where some areas will be better filled than others because of the randomness. Here it’s the angle of the bounce of the particle, and the particle keeps moving between four walls. If there were any hotspots or blank spots, that would actually point to a pattern because the particle would repeatedly show preference for moving towards or avoiding moving towards a certain spot.
Just expressing my opinion: the biggest problem right now is still quantum perturbative gravity. The infinite degrees of freedom in quantum perturbative gravity precisely correspond to the degrees of freedom of the energy-momentum stress tensor of various fields. Attempting to eliminate these degrees of freedom is fundamentally incorrect because vacuum fluctuations inherently include the vacuum corrections of all fields. These vacuum corrections naturally carry the combinations of all possible degrees of freedom, which are formed by all fields and their combinations. Furthermore, all these degrees of freedom automatically correspond to the increased degrees of freedom at each loop of quantum perturbative gravity. Attempting to eliminate degrees of freedom is equivalent to claiming that the vacuum field lacks the corresponding fields and their associated gravitons. However, the vacuum inherently cannot consist of corrections from only a single field; it must involve corrections from all fields and their combinations. When the vacuum fields and their combinations interact through coupling, they precisely correspond to the existence of the infinite degrees of freedom of gravitons. Gravitons correcting themselves may introduce corresponding ghost fields. However, this can be addressed through interactions with curvature fields. For example, the scalar curvature field R^2 can be constrained via the energy-momentum stress tensor T^munu to derive a scalar field. The degrees of freedom of this scalar field can then absorb divergences. Additionally, the energy-momentum stress tensor T^munu inherently contains the degrees of freedom of all energy fields and their combinations. From this perspective, one can deduce that the corrections of all quantum fields in the vacuum precisely correspond to the infinite degree of freedom corrections of gravitons, further substantiating the validity of quantum perturbative gravity. In other words, we should first identify all vacuum corrections of energy fields and their combinations. Once these are identified, all possible degrees of freedom will naturally be included. These degrees of freedom will be absorbed into the corresponding physical quantities and will align with the infinite degree of freedom combinations of gravitons.
Good video explaining a tough concept! My thesis was defended in 2001, in... Quantum Chaos. I got tired of being told that it "did not exist", so I renamed it to "Quantum manifestations of chaos" an it worked like a charm. Yes, there is no exponential sensitivity to initial conditions in a quantum system, but, in systems with dynamical boundaries, for some time you can observe a mimic of chaotic behavior. Furthermore, the linear quantum theory only applies to closed sytems. As you increase size and go towards classical systems, a closed system becomes open and non-linear. Its a nice conceptual story from XX century physics... 😊
Applications of the Born Rule are NOT LINEAR: the probability density for finding a particle at a given position is proportional to the SQUARE of the amplitude of the system's wave function at that position. Once you take the square, you are no longer dealing with a linear equation. And lest anyone argue that squaring a variable won't introduce chaos, consider the sequence of equations for the Mandelbrot set: f c ( z ) = z^2 + c
@@Elisabeth-id6lc Agreed but the chaotic actions of double pendulums and such are in the real world where any predictions about the behaviour of matter from quantum mechanics require those probability calculations. The essence of the argument is whether quantum mechanics can predict the behavour of chaotic systems in the real world -- weather being given as an example in the video....
Is anyone else weirded out that this quantum scarring generates an argument for why amulets and glyphs and other special "occult" 2d geometric constructs/symbols might actually have a real effect on reality and matter? Like how in fictional summoning rituals you have to draw some elaborate exact shape on the floor that's made of a certain material or whatever or else the spell doesn't work? for a couple years I've been toying with the alignment between what speed running character behavior looks like in-game from an in-game perspective and what magic casting and sorcery look like from our perspective. This is more of that.
I'm not. If true, it would mean that such work was empirical (because while I think the classical and earlier periods do not at all get the credit they're due for what they knew, there was no quantum theory as such back then). However, why would you expect a quantum approach to provide information on classical systems? Whether or not quantum chaos exists, classical chaos certainly does. I'd like to hear more about the speedrunning behavior you've done. :)
You better get on this fantasy/scifi screenplay before someone else does! Bonus points if you find a way to work cellular automata oscillators into it somehow. (That's the first thing that came to my mind when I saw these quantum scars.)
Sabine, If one can’t predict the exact location of a particle in space thats exactly the definition of Chaos . With Chaos there is the “attractor” and hence you get its approximate location.
Only if she's able to catch him... Cats are ambush predators and the flightpattern of even a normal butterfly is nearly unpredictable per se... I guess the butterfly of chaos is even then unpredictable when he sits still... If I had to place a bet... my champion would be him. @RFC3514
Sabine is it possible that gravity emerges from symptoms of electromagnetism , when you move in the universe, the universe will have to "adjust" to your movement, to regain lowest energy state - im thinking that this force is maybe the exact friction of gravity. So maybe the gravity constant can be derived from just looking at all the matter in your vicinity able to have an immediate impact on your movement. Maybe you are to include the entire universe because the impact of the delayed signal , is worse the less of a signal, so it maybe becomes negligible by itself. And you will feel the gravity of the edges of the visible universe in the same sense than you can see the sun even though it does not travel instantly. So Im thinking that this part of the equation where you have a noticeable time delay may anyways be so small that it does not matter for the bulk of the result. But one could imagine that the integral over the entire space is actually the correct answer.
The term chaos seems paradoxical since, by definition, chaos should exist without pattern, yet the pattern-less tendency is what makes it a recognizable pattern. Really, chaos is unlikely to actually exist except in the world of imagination.
Using logic, since quantum particles are considered to be the smallest building blocks, chaos, per definition, should not exist in any system that is created from these blocks. Isn't it all just semantics? What physicists describe as "chaos" is just complex systems, which given a million years or so are fully resolvable, but just with not practically visible solution because of the large scale?
That's like saying nothing must be something because you can recognize it as such. Not saying you're wrong about chaos not actually occurring in nature, but by definition being patternless is not a pattern just because you can recognize it.
Tentative answer (@ 0:30): it's a series of iterative events with trigger points that result in cascades. Like a tower of wine glasses with single drops falling into the top glass at a regular rate. Once overfull, that glass will overflow until surface tension exceeds the flow. And some other glasses will also overflow as a result. (Yeah, it's incomplete, but fits having both chaos and and iterated universe. The cumulative effect is what we see, not the individual additions.) @ 3:34: Huh. Cool.
He is probably referring to the many worlds theory, in which one removes the collapse of the wavefunction. This makes the theory deterministic indeed, unfortunately it then no longer describes what we observe. People who use the many worlds theory then add other assumptions that bring back the indeterminism that we observe. I think these people are very confused...
Chaos theory is actually talking about deterministic systems. There is no randomness in a regular classical double pendulum, which is completely deterministic.
@@SabineHossenfelder They use it what for?* And which assumption does bring you to the conclusion that you're able to judge about their state of mind by watching them trying to solve a problem?* Do you have by any chance a PhD in theoretical Psychology which I know nothing about yet?*
With all due respect, chaos happens in systems where a small amount of positive feedback is regulated at scale. The system can then assume dual states called bifurcation which can happen again and again as the system progresses through time. If the amount of feedback is too low or too high The system will either be damped or undergo exponential growth. Chaos is achieved when the initial state and the recursion constants fall within set values.
This recent paper didn't really "uncover" anything. It was interesting because it was a more direct measurement than what has been done before. These scars have been observed in experiments since the 90s, but those were E&M experiments that were designed to be analogous to quantum billiards (i.e., the math is the same, but it isn't a direct measurement of a quantum system). This is a measurement done directly on a quantum system. The scars form along unstable periodic orbits, an effect that is of fundamental importance in the study of the quantum mechanics of classically chaotic systems. On a related note, "Quantum Chaos" is a short-hand for "the study of the quantum mechanics of classically chaotic systems". So, it isn't quite accurate to say "quantum chaos doesn't exist" simply because qm is a linear theory. There are definitely differences in the qm properties of classically chaotic systems when compared to classically integrable systems (e.g., the distribution of the spacing of energy eigenvalues). These differences make it a field that both exists and is worth understanding.
@@nosuchthing8 The paper is not irrelevant. It's an interesting result. I just don't think that Sabine put it in the correct context or represented the field of Quantum Chaos entirely correctly.
Why the condition for chaos changes from 0:55 small differences in initial state result in vastly different outcomes to 2:25 particles smear out evenly ? Funnily, the second condition, as one could understand it, is met for both quantum and classical, as in the quantum case, wave function "smears out evenly" too in the sense that regardless of the initial state for the given confined space, the resulting pattern is the same.
4:41 okay, the funniest part about the quanta is it is spiritual. The whole thing is spiritual. I've seen many of your videos and you singing and I know you are spiritual. I didn't realize that the Germans were extremely spiritual in the past and I would assume still. I got to show this stuff. It's really amazing and you could explain it to my wife Maria. Thank you very much Sabine for helping me❤
Sabine, I must immediately disagree with your statement that "Linear theories cannot be chaotic". Indeed, it was a long held belief that only non-linear operators can be chaotic. But that turned out to be so wrong that mathematics currently has an entire field called "Continuous linear chaotic operators". The easiest example is the right shift operator on l^2. That operator is continuous, linear and not only chaotic but hypercyclic (a stronger property)
Curious, with no degree or training in higher math, making questioning comment: Perhaps its only a matte of nomenclature in the specified field of math study, but anything labelled "hypercyclic" would be reasonably expected to be high-frequency patterns, or patterns repeating extremely often, and not in congruence with non-regular, irregular, chaos. No? (language issue or terms of art nomenclature issue?)
@gregrice1354 Well, not quite. Indeed, nomenclature in mathematics is often misleading. A point of a vector space is called hypercyclic with respect to an operator if applying that operator arbitrarily many times onto that point will eventually bring it arbitrarily close to any other point in the vector space. Which means that by simply starting at one point and following its path under the operator, you will eventually traverse the entire vector space in the sense that you will have gotten arbitrarily close to each and every point somewhere along your path. And an operator is called hypercyclic if it has a hypercyclic vector
When we talk about chaos in quantum systems governed by unitary evolution, we should consider it from the multiworld point of view: the wave function exists in a space of very large dimensionality; its value at each point is very small like 10^(-1000); thus, these two-dimensional examples are not relevant at all. Yes, maybe if we consider a closed system in the infinite timeframe, the chaos does not exist, but in real life this small timeframe of our life is totally suppressed by a huge dimensionality, and we can say (effectively) that the chaos exists.
This reminds me of the classical Buffon's needle experiment, where you randomly throw needles on a striped paper. The ratio of the needles that touch the line to the needles that do not is approximate Pi. The more needles you through the closer you get to Pi. Theoretically, if you throw infinite needles the ratio will be exactly Pi. There is no room for randomness in our universe, it is just patterns that we are not yet smart enough to recognize. The fact that reality is ordered and described by elegant mathematical laws is extraordinary. There is a mental source for it indeed.
How do you go from a simple abstract probability exercise to conclude that randomness does not exist? And how do you define "randomness"? You are describing an effect of statistical aggregation (LLN) in a clean symmetric completely abstract case. Try to think if instead of parallel strips (note that the concept itself of parallelism requires a postulate) you had a more complex shape. A Sierpiński triangle or whatever. Would you still get pi ? 🙂
@@W-HealthPianoExercises Randomness is the absolute absence of any predictable pattern. Order is the existence of these patterns, simple or complex. The absence of randomness is a belief of mine, but it is based on current knowledge. Many phenomenal were thought to be random until there is a theory that describes it comes along. Often this theory makes extra predictions about more patterns of nature. Mathematical laws describe everything we know about physics so far, from statistical patterns in QM to deterministic patterns in CM and GR
@@AiethingI think you are using your own current personal definitions of reandomness. The statement 'randomness is the absolute absence of any predictable pattern' oversimplifies the concept and does not accurately describe the nature of randomness. It is not defined by a lack of predictability. In fact, randomness can manifest in highly varying degrees depending on distributional properties. For instance, if I presented you with any chart of stock prices, you would likely be able to identify trends or patterns within what may appear to be random fluctuations. This illustrates that randomness is not a binary concept; it operates on a spectrum that includes both deterministic and stochastic behaviors. Moreover, you can even define randomness as a layer on top of fuzziness or deterministic chaos. Mathematical models are just our attempt to frame reality, but reality has no obligation to comply to our imagination nor has an obligation to be of mathematical nature at all. As in fact so far there is a greater evidence that math alone is not capable to capture reality. Think of consciousness. Think of life. Where is the math ? 🙂
“Quantum Caustics” seems like a better description in my amateur opinion (because they resemble optical caustics, not caustic chemicals). They are areas of higher probability formed from paths converging in the same way that light paths converging creates areas of extra brightness
Edit: So apparently the name has already been taken by “quantum catastrophe theory” or whatever. That’s too bad
You are so right. Your comment is very intriguing. 🎉
I thought they looked like caustics too, like in water.
Very insightful!
This!
I would have gone with resonance, as in audio or radio in cavities, but caustics is perhaps better.
I think I must have missed something, because I can't see how "quantum scars" is anything new. We've seen interference patterns in cavities before in many fields, so I don't know how this proves anything besides particles-goes-bouncy-bouncy-a-lot.
Statistics are not perfect like Maths.. real chaotic nature is not truth of experiences…. ❤
We are truly entering a magical realm of engineering.
In RF engineering people have started making physical waveguides or other physical features of the assembly to replace computing and these look like ancient runes of summoning that you'd see in a fantasy setting.
Now we'll have the same arcane designs etched on nanoscale devices to similarly guide the wave but this time the wave of a single electron and then remove the uncertainty that would otherwise be found in such miniature devices.
All of this by etching arcane runes into the material itself.
Wish I'd written this. So grateful to see someone else who is having a similar response to me!! The whole Baryonic resonances and shapes and 'runes' or 'sigils' that really are expressions of a much deeper truth. It's point of reference relativity and fractals and infinity all the way down.
Any science that is distinguishable from magic is insufficiently advanced.
Asimov's response to Clarke's third law.
What? Waveguides to replace computing..It makes no sense. Where is the wave guided and what you gonna do with it without computing
@@Nat-oj2uc The wave is guided through complicated geometry to do things. The simplest form of this is splitting a wave into different frequency ranges, like passing a laser through a prism to put multiple colors through the same fibre but of course all of that works for radio frequency stuff as well as more.
@@MrRolnicek
🤯
Why does this remind me of some science fiction I read in the 80's?
I'm trying to remember the author, Michael Moorcock?
Like everyone without a tertiary education but an interest I've been fascinated with some aspects of science.
This idea of light moving from one region to another is how I thought they were sure that space time was expanding.
I clearly had the wrong end of it.
(Of course 😂)
I wonder if I will live long enough to watch them repudiate the non existence of free will?
Because of course that feels very wrong to most of us I think.
There's nothing in the mathematical definition of chaos that says you must have density of periodic orbits over the entire space. Many chaotic systems exhibit this property only over a subset of the space, as in the case of strange attractors
Yes, I didn't understand how the "stadium" example was chaotic.
@@evanescentwave181 I think it's because no path ever is retraced, and so the pattern is sensitive to the starting point and angle of the ray.
This doesn’t make sense, if you let the experiment run for infinity, then retracing would happen infinitely often, won’t it? I think “chaotic” (unpredictable) and completely random is not the same thing. The predictability of a chaotic system drops in what can be described by a function, but it doesn’t mean that there won’t be repeating patterns, we just can’t predict when those repeating patterns will occur. That’s why we have the strange attractors in some systems that can even be described by simple trigonometry.
@@karlgustav9960us unable to predict doesn't mean it's chaotic
@@karlgustav9960 chaotic systems are deterministic but give rise to unpredictability, not randomness
In classical mechanics it is recognized that chaotic systems often oscillate around points that are labeled "strange attractors" When the system is disturbed the new paths will follow and new pattern oscillating around a new point. The butterfly effect is a typical feature of chaotic systems. Weather is a chaotic system that is currently transitioning to a new pattern.
Another feature of chaotic systems is that the characteristics of the pertubation that will cause a it to transition to a new pattern are unpredictable, thus the "chaos." Basically, not every butterfly wing flap is equal.
@@TheSonicfrog This is a misconception, chaos theory is completely predictable if you had the computing power.
@@MagruderSpoots AND the infinite precision of both compute and initial conditions
@@MagruderSpootsbut infinite computing power is hard to come by. Also, we don't have a complete theory of butterfly behaviour yet.
@@MagruderSpoots Having to iterate everything is the practical definition of unpredictability. Prediction means to guess in advance, not post hoc.
We all have that one friend with a P=3.5 of being late...
Hey, I resemble that remark.
@@Metalkatt you were supposed to make that comment 3.5 minutes AFTER the original one , you can't even get your late timing right, you are chaos personified !
Which means he's late even when there is no appointment.
@@iAnasazi I was late for my own birth. I was supposed to pop out on Halloween, but I overslept to Election Day.
@@Metalkatt Which one is scariest? 😅
0:09: A slight clarification, Quantum physics as a whole includes both linear frameworks (like Hilbert spaces and quantum mechanics) and non-linear dynamics (like those in QCD). But the argument holds true for the parts of quantum physics most people are familiar with.
Our informatics teacher descibed chaos as following: IN a recursive system, you cannot predict a state more than one iteration ahead, hence the outcome can not be predicted with a shortcut solution but instead has to be iterated through each recursive step. The conclusion: Recursive solver operation logic is by definition chaotic.
Fractals would be a practical example. Or fluid simulations.
That's just a half of a problem, because you need infinitely precise starting conditions to iterate on and it is obviously impossible
@@artghushelw and you would be most confidently incorrect
Chaos is equivalent to randomness made by (recursive) algorithms? That’s plausible but it needs a proof by finite automata or something.
I think the most important part : Chaos is deterministic.
How fractals are chaotic?
At 5:20 Sabine says that quantum chaos in physics doesn't exist, then1 second later she has a different haircut. Isn't this a kind of chaos in physics? 🙂
Well, my „quantum chaos“ lecture at university was exactly about what this paper addresses - lots of billiards and the question what happens in the mesoskopic realm where you have a mixture of classical/chaotic and quantum mechanical behavior. A fellow PhD student of mine measured the conductivity of a small superconducting billard to see if the DOS looks more qm or more chaotic. So to me this topic never seemed neglected. At my old university, there was always also a small group of theoreticians who used bohmian mechanics, which provides a more „natural“ approach to quantum chaos.
I really wish they’d gone with a different term than ‘scar’. It just reminds me of when I’m shaving and happen to notice a quantum pimple on my chin
"Quantum" because it sometimes is there and sometimes isn't ?, because it is there and it isn't there at the same time ?, or because of the plasma ?
while shaving, of course, when
not shaving is in duality until
measured or "spotted" by the
Occam's razor😂😂😂😂
In transportation planning we have a term called "desire paths", which is when people tramp the same route across a grassy park or meadow so many times that they create a trail, and so you can see the route people naturally want to take, even if the park planners didn't provide a trail there. I think that would have been a much better term, though I suppose scientists would balk at the word "desire". But the term desire paths really isn't about "desires" so much as it is about natural movement patterns in a given space, so it really does seem to describe an analogous phenomenon.
A Rut.
Well, that's what you get for observing it...
@@Manuel_Bache
"Quantum" just means that the discreteness of action can't be ignored in the effort to predict accurately the behavior of the system being measured.
The Blurring (a.k.a. Bohr's "Uncertainty") Principle of Heisenberg applies.
Chaos theory doesnt mean things keep growing indefinitely. The weather is chaotic, but that doesnt mean the temperture will run away to infinity. It simply means its harder to predict as time goes on. It is sunny today, so it is likely sunny tomorrow, but next week's weather is likely unrelated to today's.
Chaos is still probabilistic. Whether or not it rains next week is still going to be between 0 and 1. So "washed out by quantum uncertainky" sure matches with chaotic models to me, as predictions become more uncertain with time.
Chaos models may be deterministic, but we can never measure with the precison needed for accurate longer term predixtions. So I dont see how its incompatible at all honestly.
"weather nest week unrelated to today's weather" sure. . .except for recurring, sustained parts of the universe involved, which are essentially identical!
(given a 1 week time frame).
- Language and the use of "terms of art", nomenclature, etc, when seeking successful communication and education of science, or any advanced field of study, must consider use of coherent, reasonable words, terminologies, analogies, metaphors. Otherwise, one person may "know" the facts, but any other person may not reasonably be expected to grasp, grok, comprehend, or learn the information intended to be communicated. Ya know what I mean?
We've also got used to a probabilistic approach to the weather e.g. a 40% chance of rain next Friday.
You make sense. I've had a growing feeling the issue of chaos in nature--- quantum or macro level, is due to the relationship between uncertainty and probability.
The first happens in your head. The second deals with limitations in measurement.
"climate denier!" 😝
In my master thesis, I calculated propabilities of multi state in laser traps. The particles had a higher likelihood to go into certain combination of states just by the amount of combinatorics to achieve these states. It was never chaotic, dynamic yes, but not chaotic.
I think Sabine may be mistaken here. QM encompasses QED, which is linear, but also QCD is non-linear (gluon self-interaction) and therefore would possibly yield QM effects that exhibit chaos
I never bought the argument from linearity. The Liouville equation is also linear, as it operates on probability density, and yet it entails the complete classical Hamiltonian physics, including chaos. What's different in quantum mechanics are the discrete energy levels and the uncertainty relation.
The liouville equation is not linear.
It is provably impossible to create non-linear system from linear operators. Into to group theory type stuff. There has to be some non-linearity somewhere in the law of physics and this experiment is interesting because it functionally proves that there isn't some overlooked, tiny non-linear term to the schrodinger equation. One less place that a non-linearity can be hiding.
In the notion of chaos it's important to understand the topology on the states - i.e. what it means for states to be close to each other. If a state B being "close to A" means that upon measurement it's revealed to be _exactly_ A with 99% probability then it's not a particularly useful notion for determining chaotic behavior - if they're the same with 99% probability, they're going to produce the same dynamics with 99% probability, forever. This applies to both quantum mechanics and the Liouville equation.
@@Amir_404 If the Liouville equation is nonlinear, you surely can point me to the term in which rho occurs in any way other than linear. Note that in the Liouville equation, location and momentum only appear as parameters of the function rho, the only object that evolves in that equation is rho.
@@__christopher__ I think we might be talking about different equations because no part of this is linear: L{log(f)}=-Kf^2
@@Amir_404 yeah see the liouville equation on the wikipedia page for “liouville’s theorem (hamiltonian)”
QM is a linear theory because we choose it to be so, if only because non-linear theories, like GR, are too hard. But non-linear formulations of the Schrödinger equation do exist, both on classical and quantum levels, and have been found to be applicable to many situations, e.g., fibre optics, water waves, vortex filaments, etc.
Yes, but how nonlinear can QM be ? It's not strictly a choice to define it as linear
@fzixkid-gh9rv Linearity is a weak field approximation to a more general non-linear description of nature. Also, we introduce constructs that help us mask nonlinearity behind new entities. It works, up to a point.
@@zdzislawmeglicki2262 Yes linear approximations are preferred for their "elegance" and calculability, but they are usually only accurate within certain ranges.
Are they neccessary though?
@@iAnasazi For the time being, yes, because we can't deal with non-linear math. Just have a look at Hirota's multi-soliton solutions of Sine-Gordon and KdV eqns. They're extremely complicated.
Why is Quantum Theory linear? Is it because H|Psi>=E|Psi> and superposition? But that's only part of the story. We often forget that when deriving this equations from first principles through Least Action f.i. we neglect higher order terms assuming they vanish...until they don't. Nothing is truely linear or you'd get infinity in the limit and Nature doesn't like infinite.
It always struck me when i'd go to conferences and see people talk about quantum chaos only to say that there isnt any chaos, just funny looking energy level diagrams. Though the measurement problem feels like it would definitelly be part of the solution since a measurement doesnt change the wavefunction in a linear fashion. Anyway, cool to see this being talked about
really, when i go to conferences, than people just tell me random things about the level spacing statistics and why it is chaotic, if it is not the poisson distribution and im like ,,i do not buy it.,, xD
I think the biggest problem in closed quantum system is, that the eigenvalues do not change over time, whereas in a chaotic system they do change.
If you however measure only a subsystem, then you can have chaniging eigenvalues or use a coupling to a bath (which is measuring a subsystem)...
2:09 when you use the example of washing out chaos, tbh I instantly thought of rain landing on a large puddle. Partially cover the large puddle and allow for rain run off (larger droplets) to land, creating large amplified waves next to small rain droplets hitting the surface and the larger droplets negate the smaller more frequent ones. Honestly I'll need to film it next time it happens and I'll post it, so this makes more sense. My point is that there has to be fixed outcome ranges in the quantum level universe, otherwise there wouldn't be any similarities in the macro world (gold wouldn't be gold) and everything could not coaless into what it is today.
Sorry all I didn't watch the video until the end 😋
5:13 I like to think quantum chaos influences DNA to make people different but still alike.
Isn't the whole point of chaos theory that chaos can arise out of simple, deterministic and predictable systems? The motivating question at 0:20 implies that that shouldn't be possible, but I don't see what's puzzling about it.
If its fundamentals are linear any higher level behaviour should also be linear
@@triton62674 Like @elliottmcollins, I don't really see what's puzzling about this either. But if you want some sort of explanation for what happens when you transition between scales, maybe this will give an idea:
Look into Mean Field Dynamics. From Wikipedia: "Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics." So, between a QM system, and one that deals with micro/macroscopic phenomena. The relevant thing here, is that while QM is linear, describing the effective evolution of one particle in a huge number of particles is non-linear.
Anyway, yeah, feel like she should've explained why exactly this we should expect macroscopic systems to be linear. There's really no reason that should be the case, emergent phenomena are a thing. There's really no reason that should be the case, emergent phenomena are a thing.
@triton62674 What do we mean by linear here? Are there no nonlinear dynamics in physics?
I love it when Sabine explains deep scientific concepts. She is a great scientific educator, even when sometimes she goes out of scope trying to explain human behavior and sociopolitical issues, which most of his followers, like me, don't care about for being transient and trendy. Thanks, Sabine, for teaching us the wonders of science!
The research is really interesting but the (real) typo in the Julia Roberts headline made my day. Obviously, the intended word was "Roles" 😀
thank you! I couldn't figure it out and it was killing me
@@TheKnightGoesBrrrrrr Yes, so many options. Moles would have made sense too. Or soles. Perhaps even voles.
@Nonononono_Ohno Well, it could be hoses, homes, hopes and much more if they misplaced two letters.
I actually read it as "Roles". Well they do say the brain is a prediction machine. Or maybe I was just getting crosstalk from a version of me in a parallel reality where the mistake wasn't made. 🙂
Obviously, they meant to write hoes.
The real chaos in quantum physics is the argument between the scientists about what's the next hypothetical particle going to be.
how about the unparting particle, then we can make sure that it will not be disproven or we let elon musk name it.. if he names it like his children, nobody will want to talk about it.
One of the authors was my Electricity and Magnetism professor at UC Santa Cruz. He's a brilliant guy and explains physics topics very well!
Wow - the engaging, entertaining and informative graphics in this video really feel like a step up! Well done!
Interesting and thanks. I'm mainly familiar with Classical Mechanics as I studied Chemistry back in the day. But I can follow along. And I also had a couple of courses relating to inorganic solid states, doping, and bandwidth, humdrum cook things up in your basement sorts of things. Liked that electronics has advanced considerably since those days of yore. Also think that graphene technology is just a bit away. One of the main problems seems to be that of passivation as there can be oxidation problems that can seriously degrade your transistor, I've heard. Staying tuned.
Even in 'Chaos' there are Patterns - Because even in chaos there are boundries/limits - Once those boundries/limits are identified, Patterns can then be identified and/or predicted..
Not really. Just because a butterfly won't lead to someone flying to the moon doesn't mean the results aren't chaotic within a range
@@nosuchthing8 Just because results are chaotic within a range doesn't mean they have no patterns. Chaotic and ordered phenomena coexist within the same systems. The patterns need not be deterministic and stable, they may be probabilistic and quasi-stable.
@crawkn yes. They have no pattern. Go study the weather equation.
@crawkn
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972.[1][2] He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.[3]
The idea that small causes may have large effects in weather was earlier acknowledged by the French mathematician and physicist Henri Poincaré. The American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.[4
The above is what Wikipedia says about the subject.
Its just the way the math works out. If there is a better way to model certain systems like weather, we don't know about it.
Its the mathematical version of the following:
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
Go pick up any book on differential equations. They have a special section on 'problem' equations. Those that are very dependent on initial conditions. If you model weather and run the sim assuming the temp is 70 degrees and not 70.1, the sim slowly then quickly diverged feom reality.
This is why weather predictions can never be accurate that far out. Because the measured temperatures are always off from the actual temps. And the differences explode.
@@nosuchthing8 Apparently you are using the term "pattern" in a very precise way. If describing the Lorentz Attractor as exhibiting a pattern by your strict definition is disallowed, then you may have your observation. To my eyes, it appears to be a pattern, albeit not a strictly predictable one.
The fact that the system is constrained (e.g., probabilities can't go beyond [0,1]) is not an indication that a system is not chaotic. The Lorenz attractor is bound but is still chaotic.
true, it might even be that chaotic systems are bounded by definition? because you need to exclude trivially exponentially unstable systems like dx/dt=x
@@wadehodson9666 Pretty much: the system doesn't have to be bounded, but for a system to be called chaotic it should have an attractor (specifically a strange attractor, so with a positive Lyapunov exponent) and that attractor will be bounded.
Now this is a great episode! Lots of good physics and very interesting
Super interesting, all the best.
Fantastic! Among the best of this channel.
Hi Sabine, is there any relation between chaos attractors and quantum scars?
Thank you for your fascinating insights into quantum chaos and scars; I appreciate your engaging explanations.
thanks for linking papers👍
Thanks
this is Extremely useful, and important to know
mostly because it means developments can happen!
Thank you for this discussion.
I'm skeptical about this finding, the example demonstration suggests that there is a limit to the "washed outness" of their quantum particle. As in they decided there is a reasonable limit where the probability is sufficiently small to be disregarded. Practically I would expect there is a non-zero probability that it would escape the enclosure.
Intriguing, at the Q/C interface. More please, whenever you have new info. Thanks, Sabine and Happy this Time of Year
As also, Sabine is best, when talking about physics.
Thank you for this
Fascinating! I had missed this important result.
Why am I seeing fractals? 4:02
LSD?
It makes a sort of sense. Fractals are self-similar (in fact, that is phenotypically their defining trait), and if a quantum field creates scars, I could easily see that the scars would be self-similar.
Many fractals are produced by chaotic systems. They go hand in hand
drugs..?
Fractals are a bit disgusting.
Thanks for your contribution to science. Have a nice new year 😊
Learning about non-linear oscillators, chaos and all that in Junior-level Classial Mechanics course put the "WOW!" back into Physics for me. Thanks, Professor Peter Scott, UC Santa Cruz!
There *is* more to life than boundary value problems!
Ironically, there is a subset of wave chaos that is only about boundary conditions. The stadium billiard is a good example of that.
Even with purely linear dynamics, the fact that the boundary is irregular brings out all kinds of weird and wild phenomena.
@@jameshart2622 True; that's a interesting example. It's fascinating that macroscopic, non-linear Classical systems exhibit chaotic behavior.
I thought of BVPs in the context of PDEs: (1) Solve the "Whoever" Equation subject to the following boundry conditions ... (2) Separate variables. (3) Write a solution as a series of suitable orthogonal functions. (4) Do complicated integrals to compute the expansion coefficients. (5) Repeat for the next problem.
Good video, would've preferred a longer format for a little more explanation of what chaos is defined and how it relates.
First, that pattern would look cool on some merch along with a pithy quantum statement about scars, chaos, and butterflies. I would definitely buy it.
Second, I don't understand how the confined electron stays "quantum" if its position is constantly being observed or "watched" as it moves around the confined space. It seems like such measurement should constantly collapse the wave function.
Third, kudos to experimenters who can realize this with real materials in the lab, along with the programmers who came up with the simulation. I cannot even imagine how to observe or detect an electron confined to a bounded 2d plane.
Fourth, thanks for interpreting the super-human language of the abstract into some semblance of normal human language that is informative and fun. Poor Albert. Good thing he had a helmet.
Regarding your second question: It's a statistical pattern.
@@iAnasazi Thanks. I had the same question. Those wavefunctions should have been constantly collapsing.
Merry Christmas!
Thanks again Dr. Hossenfelder.
I'm sorry, but your educational videos only motivate my high school level physics trained brain to cry out with likely obvious questions, hypothetical challenges and questions. 😀
Quantum Scars compared to Standing Wave patterns observed in classic photon-thru slits experiments:
1. are the symmetrical interference patterns from photons through slits, constitute same phenomenon as Quantum Scars?
2. are there any distinctly different phenomenon being documented/recorded in the Graphene related Scars, than wavefront interference?
3 are both results of photons through slits and Quantum Scars both using the science framework for structure of apparatus and type of measurement systems?
4 Do the findings of Quantum Scars have any bearing on the definition of "information" used in calculations and predictions used for theories of Information retention/loss related to interaction of external matter near Black Holes/singularities?
5. Could both (or either) the Quantum Scar measurements or the Photons through Slits experiments explain the Entanglement or Spooky Action At Distance? (seeming impossible simultaneously identical motion of distant sub-atomic particles)
I'd rather never waste time with an automated Symantic Mimicry system. Are there expert physics-knowledge systems?
This is a very nice report on this paper.
happy xmas!!
brilliant presentation. Merry Christmas.
Quick haircut Sabine 5:28 and no chaos 😂
Scars emerge when the eigen-frequencies of the shape get very high. There are some eigenmodes that reveal scars and other (nearby) ones that do not. See the mushroom and the stadium for examples where there is an interesting division between ergodic and nonergodic modes. I computed 160,000 eigenvalues (total of lowest Dirichlet and Neumann modes) of the regular pentagon, which is incidentally the most non-analytic eigenvalues for any shape that anyone that I am aware of ever computed. To get "scars", you need a non-analytic solutions, something you didn't mention: You can't get them in the rectangle, for example. One thing I would like to examine is: How to relate quantum behavior to classical chaos, which should be straighforward with the quantity of eigenmodes I computed. The regular pentagon is interesting because it is the smallest regular polygon beyond the equilateral triangle and square (which both have known closed-form modes) that has zero close-form modes (except the lowest Neumann mode). I thought there were extremely few people in the world who ever heard of these scars and how they relate to chaos. Does the regular pentagon exhibit scars? Probably, but I don't know. Linearity is interesting, but a scar should show up with only one eigenmode, not a linear combination of them: Linearity is sort of irrelevant. Thank you for making this video!
Scientists: "Quantum mechanics are linear"
Elementary Particles constantly popping in and out of existence: "What am I, a joke to you???"
Umm. . .did you really mean "constantly"?
@@gregrice1354 Umm, have Virtual Particles stopped doing doing that, Elementary Particles = Virtual Particles in this case.
@@gregrice1354 There's latent energy in every bit of space. This energy spontaneously results in random particle-antiparticle pairs popping into existence.
The Schrodinger equation is linear, the measurement process isn't. Obviously the chaos is enabled by the latter.
Wonderful, very interesting!
The use of graphene to showcase quantum scars is a fascinating demonstration of theory meeting reality. This connection to potential electronics applications is especially intriguing.
What is this chatgpt ass comment lmao?!
The "topic of video" is a fascinating demonstration of "generic thing", this connection to "thing mentioned" is especially intriguing.
"Theory meeting reality" being used to describe physics experiments, which are definitionally obviously that.... You can't be a human person.
Thank you, Sabine.
It’s bounded chaos. No chaos - no change or movement. All chaos - no forms.
ill check your courses on brilliant, you sre the first one that got me.
great quality materials, very interesting topics, i like your humour too
you are not bland ^^
You cannot have a "pendulum" without quantum mechanics because that underpins all of reality, so you might say chaos is an emergent phenomenon at larger than quantum scales. I'd go so far as to say that chaos is really just a property of non linear systems/algorithms, more closely related to pure mathematics than physics.
Sabina, can you do a talk on indivisible quantum processes? Jacob Barandes sounds like he has solved the Measurement Problem.
I meant Indivisible Stochastic Processes.
0:58 good for her.
The quantum scars idea reminds me of tuning the intake and exaust manifold on an engine, and tuning wire traces on a circuit board to optimise flow in the direction desired at the speed desired.
So despite the details of the initial starting conditions, the quantum scar that forms over time arrives at the same shape? For some reason, that's a calming thought. Predictability may be boring, but when you're trying to make safe and reliable systems, it's quite helpful.
I don´t think that predictability is boring, it makes possible that we can do science in the first place.
The scar depends on the initial state. What happens is loosely speaking that classically these scars are paths for particles, but they are unstable. The particle will not stay on them. In the quantum case, the wavefunction can settle on these particular patterns which are not a path themselves, but have an enhanced probability. You see in the earlier simulation that generically the scars you get are quite complicated.
Perhaps this is something like the Central Limit Theorem?
@SabineHossenfelder So, what you're saying is that what we're looking at is the visual representation of the probability density function of the quantum field?
Dynamics of the parts of the system are determined by factors. If you have one factor, it's a completely determined system. The more factors (comparable in their influence on the parts of the system), the more chaotic the system. But it's always close system, because these factors are limited (localized), and movement of the entire system are determined by the main factor (in the larger system). In other words, you have an "attractor" (that can be moved) and a "local minimal energy region" around it with locked "chaotic" subsystem inside. In proper design, such "regions" are minimized (unless you need an anti drone rifle or a quiet room for sensitive talks)
"Quantum scars do not demonstrate the absence of chaos at the quantum level. Instead, they highlight the subtle way classical properties of a chaotic system can influence the structures of quantum states, despite the fundamental differences between classical and quantum dynamics.
Why don’t quantum scars disprove quantum chaos?
The equations of quantum mechanics are linear:
The Schrödinger equation is linear, meaning it does not produce the kind of exponentially sensitive behavior to initial conditions that we associate with classical chaos.
However, this does not imply an absence of complex phenomena. Quantum chaos manifests differently, often through statistical and spectral properties (e.g., the energy level distributions align with the predictions of random matrix theory).
Quantum scars are semiclassical manifestations:
Quantum scars reveal that certain periodic orbits of a classically chaotic system leave a visible imprint on quantum wavefunctions, even in the regime where classical chaos dominates.
This does not mean chaos vanishes at the quantum level. Instead, these scars show how specific aspects of classical dynamics influence quantum solutions.
Scars are exceptions, not the rule:
Berry's conjecture states that in chaotic quantum systems, wavefunctions are globally "ergodic" and statistically distributed in a random manner. Scars represent local deviations from this average behavior, not a contradiction.
So, does chaos exist at the quantum level?
Quantum chaos is a well-established discipline that explores how classically chaotic dynamics translate into the quantum regime. Even though:
Classical trajectories are no longer defined in quantum mechanics (due to Heisenberg's uncertainty principle),
Quantum equations are linear,
quantum chaos manifests through:
Energy spectra:
Energy levels in chaotic systems obey universal statistical distributions, such as those of random matrix theory. These distributions differ from those in integrable systems, where levels are regularly spaced.
Wavefunction structures:
Scars, ergodic patterns, and local singularities in wavefunctions demonstrate dynamic aspects connected to classical chaos.
Quantum fluctuations:
In a classically chaotic system, trajectories diverge exponentially over time. This dynamic translates into quantum fluctuations in observables or probability densities, though framed within the theory of probability fields.
Conclusion:
Quantum scars do not refute chaos at the quantum level; they enhance our understanding of the connections between classical and quantum chaos. While quantum equations are linear and classical chaotic behavior does not directly translate to the quantum regime, quantum chaos manifests through statistical and spectral properties that respect the fundamental principles of quantum mechanics." - chatGPT
I read an article this morning on ancient knots in ropes and how the could have possibly gave rise to mathematical reasoning and geomagnetic patterns... very cool. And read the article about this a few days ago. We live in a cool age of discovery. Great video.
2:23 Why would we expect the probability to smear evenly? Why isn't it sufficient to assume that the probability smears everywhere for it to be chaotic?
In the classical example, does the point particle visit all areas of the table uniformly? Could it not be the case that even in the classical example, there are hot spots of higher and lower probability while still having the property that the particle eventually passes arbitrarily close to any point?
What actually makes the quantum example non-chaotic?
You won't see scars in a macro example. Or the weather example
Well in this case it’s not the trail of the particle that’s necessarily chaotic. It’s not like the example with the stars in the sky where some areas will be better filled than others because of the randomness. Here it’s the angle of the bounce of the particle, and the particle keeps moving between four walls. If there were any hotspots or blank spots, that would actually point to a pattern because the particle would repeatedly show preference for moving towards or avoiding moving towards a certain spot.
Does this have any implications for fusion reactors?
Just expressing my opinion: the biggest problem right now is still quantum perturbative gravity.
The infinite degrees of freedom in quantum perturbative gravity precisely correspond to the degrees of freedom of the energy-momentum stress tensor of various fields. Attempting to eliminate these degrees of freedom is fundamentally incorrect because vacuum fluctuations inherently include the vacuum corrections of all fields. These vacuum corrections naturally carry the combinations of all possible degrees of freedom, which are formed by all fields and their combinations. Furthermore, all these degrees of freedom automatically correspond to the increased degrees of freedom at each loop of quantum perturbative gravity.
Attempting to eliminate degrees of freedom is equivalent to claiming that the vacuum field lacks the corresponding fields and their associated gravitons. However, the vacuum inherently cannot consist of corrections from only a single field; it must involve corrections from all fields and their combinations. When the vacuum fields and their combinations interact through coupling, they precisely correspond to the existence of the infinite degrees of freedom of gravitons.
Gravitons correcting themselves may introduce corresponding ghost fields. However, this can be addressed through interactions with curvature fields. For example, the scalar curvature field R^2 can be constrained via the energy-momentum stress tensor T^munu to derive a scalar field. The degrees of freedom of this scalar field can then absorb divergences. Additionally, the energy-momentum stress tensor T^munu inherently contains the degrees of freedom of all energy fields and their combinations.
From this perspective, one can deduce that the corrections of all quantum fields in the vacuum precisely correspond to the infinite degree of freedom corrections of gravitons, further substantiating the validity of quantum perturbative gravity.
In other words, we should first identify all vacuum corrections of energy fields and their combinations. Once these are identified, all possible degrees of freedom will naturally be included. These degrees of freedom will be absorbed into the corresponding physical quantities and will align with the infinite degree of freedom combinations of gravitons.
Good video explaining a tough concept! My thesis was defended in 2001, in... Quantum Chaos. I got tired of being told that it "did not exist", so I renamed it to "Quantum manifestations of chaos" an it worked like a charm. Yes, there is no exponential sensitivity to initial conditions in a quantum system, but, in systems with dynamical boundaries, for some time you can observe a mimic of chaotic behavior. Furthermore, the linear quantum theory only applies to closed sytems. As you increase size and go towards classical systems, a closed system becomes open and non-linear. Its a nice conceptual story from XX century physics... 😊
Thanks a lot. It was interesting and very helpful.
Great video and hope the butterfly will come back again in the future ❤️
I missed her funny flapping the arms like in previous videos, she was talking about the butterfly effect😉
Really interesting indeed! Thanks, Sabine! 😊
Merry Christmas!
Stay safe there with your family! 🖖😊
Applications of the Born Rule are NOT LINEAR: the probability density for finding a particle at a given position is proportional to the SQUARE of the amplitude of the system's wave function at that position. Once you take the square, you are no longer dealing with a linear equation. And lest anyone argue that squaring a variable won't introduce chaos, consider the sequence of equations for the Mandelbrot set: f c ( z ) = z^2 + c
But we take the square only to have a real value (the probability) instead of dealing with the complex values of the function.
@@Elisabeth-id6lc Agreed but the chaotic actions of double pendulums and such are in the real world where any predictions about the behaviour of matter from quantum mechanics require those probability calculations. The essence of the argument is whether quantum mechanics can predict the behavour of chaotic systems in the real world -- weather being given as an example in the video....
@@rossfraser2003 I think some kind of correspondence principle for chaotic behavior has yet to be found.
Is anyone else weirded out that this quantum scarring generates an argument for why amulets and glyphs and other special "occult" 2d geometric constructs/symbols might actually have a real effect on reality and matter? Like how in fictional summoning rituals you have to draw some elaborate exact shape on the floor that's made of a certain material or whatever or else the spell doesn't work? for a couple years I've been toying with the alignment between what speed running character behavior looks like in-game from an in-game perspective and what magic casting and sorcery look like from our perspective. This is more of that.
No it doesn't generate that argument anywhere but in your mind. This doesn't relate to that in anyway even slightly
I'm not. If true, it would mean that such work was empirical (because while I think the classical and earlier periods do not at all get the credit they're due for what they knew, there was no quantum theory as such back then). However, why would you expect a quantum approach to provide information on classical systems? Whether or not quantum chaos exists, classical chaos certainly does.
I'd like to hear more about the speedrunning behavior you've done. :)
You better get on this fantasy/scifi screenplay before someone else does! Bonus points if you find a way to work cellular automata oscillators into it somehow. (That's the first thing that came to my mind when I saw these quantum scars.)
The flower of life sacred geometry shape contains a visual representation of every equation math has discovered.
mmm...no. Sorry to deflate your meta bubble , but , I think you are looking for a smile on a dog...
Quantum scars, that looks absolutely fascinating! 😮
Sabine, If one can’t predict the exact location of a particle in space thats exactly the definition of Chaos . With Chaos there is the “attractor” and hence you get its approximate location.
Beautiful animation of the butterfly on the bobblehead.
Wow, exciting interesting, "Einstein´s butterfly problem" could free Schrödinger´s cat after hundred years in the box.
Yes, finally freedom
The living dead cat would then eat the chaos butterfly, and there would be no more tornados. I think that's how it works.
Only if she's able to catch him...
Cats are ambush predators and the flightpattern of even a normal butterfly is nearly unpredictable per se...
I guess the butterfly of chaos is even then unpredictable when he sits still...
If I had to place a bet...
my champion would be him.
@RFC3514
Sabine is it possible that gravity emerges from symptoms of electromagnetism , when you move in the universe, the universe will have to "adjust" to your movement, to regain lowest energy state - im thinking that this force is maybe the exact friction of gravity. So maybe the gravity constant can be derived from just looking at all the matter in your vicinity able to have an immediate impact on your movement. Maybe you are to include the entire universe because the impact of the delayed signal , is worse the less of a signal, so it maybe becomes negligible by itself. And you will feel the gravity of the edges of the visible universe in the same sense than you can see the sun even though it does not travel instantly. So Im thinking that this part of the equation where you have a noticeable time delay may anyways be so small that it does not matter for the bulk of the result. But one could imagine that the integral over the entire space is actually the correct answer.
The term chaos seems paradoxical since, by definition, chaos should exist without pattern, yet the pattern-less tendency is what makes it a recognizable pattern.
Really, chaos is unlikely to actually exist except in the world of imagination.
Using logic, since quantum particles are considered to be the smallest building blocks, chaos, per definition, should not exist in any system that is created from these blocks. Isn't it all just semantics? What physicists describe as "chaos" is just complex systems, which given a million years or so are fully resolvable, but just with not practically visible solution because of the large scale?
@jacka9612 true
@@aaronjennings8385 Chaos has pattern : strange attractors.
That's like saying nothing must be something because you can recognize it as such. Not saying you're wrong about chaos not actually occurring in nature, but by definition being patternless is not a pattern just because you can recognize it.
...and they willy wonka song? I'm waiting....
Tentative answer (@ 0:30): it's a series of iterative events with trigger points that result in cascades. Like a tower of wine glasses with single drops falling into the top glass at a regular rate. Once overfull, that glass will overflow until surface tension exceeds the flow. And some other glasses will also overflow as a result. (Yeah, it's incomplete, but fits having both chaos and and iterated universe. The cumulative effect is what we see, not the individual additions.)
@ 3:34: Huh. Cool.
Dr. Lawrence M. Krauss has said many times that quantum mechanics is 100% deterministic: what does he mean by that?
He is probably referring to the many worlds theory, in which one removes the collapse of the wavefunction. This makes the theory deterministic indeed, unfortunately it then no longer describes what we observe. People who use the many worlds theory then add other assumptions that bring back the indeterminism that we observe. I think these people are very confused...
Chaos theory is actually talking about deterministic systems. There is no randomness in a regular classical double pendulum, which is completely deterministic.
@@SabineHossenfelder They use it what for?*
And which assumption does bring you to the conclusion that you're able to judge about their state of mind by watching them trying to solve a problem?* Do you have by any chance a PhD in theoretical Psychology which I know nothing about yet?*
@@SabineHossenfelder ; Thank you.
Thanks Sabine.
Thank you for the video.
Thank you 🙏
With all due respect, chaos happens in systems where a small amount of positive feedback is regulated at scale. The system can then assume dual states called bifurcation which can happen again and again as the system progresses through time.
If the amount of feedback is too low or too high The system will either be damped or undergo exponential growth.
Chaos is achieved when the initial state and the recursion constants fall within set values.
how did u get a haircut by the end of episode... lol, looks lovely!
This recent paper didn't really "uncover" anything. It was interesting because it was a more direct measurement than what has been done before. These scars have been observed in experiments since the 90s, but those were E&M experiments that were designed to be analogous to quantum billiards (i.e., the math is the same, but it isn't a direct measurement of a quantum system). This is a measurement done directly on a quantum system. The scars form along unstable periodic orbits, an effect that is of fundamental importance in the study of the quantum mechanics of classically chaotic systems.
On a related note, "Quantum Chaos" is a short-hand for "the study of the quantum mechanics of classically chaotic systems". So, it isn't quite accurate to say "quantum chaos doesn't exist" simply because qm is a linear theory. There are definitely differences in the qm properties of classically chaotic systems when compared to classically integrable systems (e.g., the distribution of the spacing of energy eigenvalues). These differences make it a field that both exists and is worth understanding.
The paper might be irrelevant to an expert like you, but it's fascinating to a novice like me.
@@nosuchthing8 The paper is not irrelevant. It's an interesting result. I just don't think that Sabine put it in the correct context or represented the field of Quantum Chaos entirely correctly.
@goodspellr1057 I agree with you.
Why the condition for chaos changes from 0:55 small differences in initial state result in vastly different outcomes to 2:25 particles smear out evenly ? Funnily, the second condition, as one could understand it, is met for both quantum and classical, as in the quantum case, wave function "smears out evenly" too in the sense that regardless of the initial state for the given confined space, the resulting pattern is the same.
4:41 okay, the funniest part about the quanta is it is spiritual. The whole thing is spiritual. I've seen many of your videos and you singing and I know you are spiritual. I didn't realize that the Germans were extremely spiritual in the past and I would assume still. I got to show this stuff. It's really amazing and you could explain it to my wife Maria. Thank you very much Sabine for helping me❤
What
4:03 quantum scaring like when you tear muscles before they grow into stronger muscles increasing “power” or “efficiency”
The concept in The Elite Society's Money Manifestation ebook completely blew me away. It feels like finding a secret path to wealth
Probability is a pragmatic way to hide an unknown law of chaos, precisely smoothing away the difference of chaos and random.
Sabine, I must immediately disagree with your statement that "Linear theories cannot be chaotic".
Indeed, it was a long held belief that only non-linear operators can be chaotic. But that turned out to be so wrong that mathematics currently has an entire field called "Continuous linear chaotic operators". The easiest example is the right shift operator on l^2. That operator is continuous, linear and not only chaotic but hypercyclic (a stronger property)
Curious, with no degree or training in higher math, making questioning comment:
Perhaps its only a matte of nomenclature in the specified field of math study, but anything labelled "hypercyclic" would be reasonably expected to be high-frequency patterns, or patterns repeating extremely often, and not in congruence with non-regular, irregular, chaos. No? (language issue or terms of art nomenclature issue?)
@gregrice1354 Well, not quite. Indeed, nomenclature in mathematics is often misleading.
A point of a vector space is called hypercyclic with respect to an operator if applying that operator arbitrarily many times onto that point will eventually bring it arbitrarily close to any other point in the vector space. Which means that by simply starting at one point and following its path under the operator, you will eventually traverse the entire vector space in the sense that you will have gotten arbitrarily close to each and every point somewhere along your path. And an operator is called hypercyclic if it has a hypercyclic vector
When we talk about chaos in quantum systems governed by unitary evolution, we should consider it from the multiworld point of view: the wave function exists in a space of very large dimensionality; its value at each point is very small like 10^(-1000); thus, these two-dimensional examples are not relevant at all. Yes, maybe if we consider a closed system in the infinite timeframe, the chaos does not exist, but in real life this small timeframe of our life is totally suppressed by a huge dimensionality, and we can say (effectively) that the chaos exists.
This reminds me of the classical Buffon's needle experiment, where you randomly throw needles on a striped paper. The ratio of the needles that touch the line to the needles that do not is approximate Pi. The more needles you through the closer you get to Pi. Theoretically, if you throw infinite needles the ratio will be exactly Pi.
There is no room for randomness in our universe, it is just patterns that we are not yet smart enough to recognize.
The fact that reality is ordered and described by elegant mathematical laws is extraordinary. There is a mental source for it indeed.
Reality is certainly ordered. I do think that the full ordering of the universe is likely beyond the ability of the human mind to comprehend, though.
How do you go from a simple abstract probability exercise to conclude that randomness does not exist? And how do you define "randomness"? You are describing an effect of statistical aggregation (LLN) in a clean symmetric completely abstract case. Try to think if instead of parallel strips (note that the concept itself of parallelism requires a postulate) you had a more complex shape. A Sierpiński triangle or whatever. Would you still get pi ? 🙂
@@W-HealthPianoExercises Randomness is the absolute absence of any predictable pattern. Order is the existence of these patterns, simple or complex.
The absence of randomness is a belief of mine, but it is based on current knowledge. Many phenomenal were thought to be random until there is a theory that describes it comes along. Often this theory makes extra predictions about more patterns of nature.
Mathematical laws describe everything we know about physics so far, from statistical patterns in QM to deterministic patterns in CM and GR
Nope. Weather. Chaotic.
@@AiethingI think you are using your own current personal definitions of reandomness. The statement 'randomness is the absolute absence of any predictable pattern' oversimplifies the concept and does not accurately describe the nature of randomness. It is not defined by a lack of predictability. In fact, randomness can manifest in highly varying degrees depending on distributional properties. For instance, if I presented you with any chart of stock prices, you would likely be able to identify trends or patterns within what may appear to be random fluctuations. This illustrates that randomness is not a binary concept; it operates on a spectrum that includes both deterministic and stochastic behaviors. Moreover, you can even define randomness as a layer on top of fuzziness or deterministic chaos. Mathematical models are just our attempt to frame reality, but reality has no obligation to comply to our imagination nor has an obligation to be of mathematical nature at all. As in fact so far there is a greater evidence that math alone is not capable to capture reality. Think of consciousness. Think of life. Where is the math ? 🙂
Kudos to your graphics department for providing Einstein with a helmet. He must be protected at all costs! 😁
it's really crazy how nobody is talking about the book the hidden path to manifesting financial power
No it isn't, I have it and it's really bad and misleading, a money making scam one could say :/
Sabine, so where does quantum tunneling fit into this? Is it chaotic or not?