“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
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.
"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.
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.
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.
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. 🙂
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)...
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.
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.
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.
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.
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
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.
Placing a butterfly on a 2d sheet of paper with pins through it would probably reduce the chaotic nature of future events as well as putting a particle within a stadium weir. I hope this method of containment proves effective enough to produce useful advances. It probably won't for the butterfly, but maybe that's the chaos of a many particled stadium weir that would probably give rise to a Nascar race of emotionally scarred butterflies. Probably not w/o a multiverse. thanks doc
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.)
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.
My brain interpreted this as: Order (very small scales) -> Appears like chaos due to complexity of order (bigger scales) -> Order (macro scales) do I get a cookie?
I don't see how the linearity of QM prohibits chaos. That's like saying the linearity of Intergrable Systems prohibits chaotic behavior even though you could have a chaotic gas of solitons.
20 years ago I read a book about Chaos... And almost immediately understood Einstein's phrase "God does not play dice"... Time has given us the reason yet again.
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?
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.
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..
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.
My first thought was, that QM is only linear as long as a system evolves in some potential according to the Schrödinger Equation, but if you include the collapse (or partial collapse) of the wave function every now an then it leads to nonlinear behaviour.
Are you going to make a video about what you think of o3? I'd love someone like you to actually delve into the benchmarks. I was impressed by the SWE benchmarks (just issues taken from git, no simplifying the actual question etc, total human things). So would love to know what you think of the science, maths, etc parts. Might even be worth a long video
In my mind, the fact that quantum mechanical particles exist quantized shows how chaotic systems that allow a classical object to never return to the same position and create fractal like patterns couldn’t really be present in quantum systems. The quantized nature of quantum particles should not allow them to form chaotic patterns that insinuate they can be in any location in the given space.
Nobody understands quantum physics; it's not about the formalism, it's about the interpretation. That's the problem nobody truly understands quantum mechanics. Should it be viewed purely instrumentally as a tool for calculating probabilities, or ontologically, or perhaps as deterministic or non-deterministic? What is often ignored is that the Copenhagen interpretation, like any other interpretation, is not the truth. Statements about how "this or that" in the quantum world works are made based on the interpretation, but what gets overlooked is the interpretative nature of these claims. No, quantum mechanics is not formally difficult, it's the interpretation that is challenging. What does a wave function mean? You can't measure it, taste it, or smell it, what is it supposed to be? What is the correct interpretation of quantum mechanics? Should it be interpreted as having an ontological or epistemological reality, or perhaps none at all and merely a tool? I personally prefer the latter interpretation This is where it begins. Is the wave function just a mathematical tool for calculating probability distributions, or is it real? Or is it simply an absurdity that follows from the fact that we are limited beings who cannot see behind everything? Or what about the relational interpretation? It claims that states or wave functions always exist in relation to the observer, where we use language and formalism to form connections between our understanding and systems. But we have nothing, absolutely nothing, that tells us the quantum world is a certain way. It’s a matter of interpretation. And it annoys me that this is always left out. We don't know how the quantum world really is. We observe it through the lens of the Copenhagen interpretation Formalism, and that’s the point. Physicists, myself included in the past, often act as if the formalism equals reality. But it doesn’t. In the end, all this mathematical stuff could turn out to be something like the epicycle theory. There is nothing that excludes that possibility.
Watching the animations that show the building up of the Quantum scars made me think of the distribution of the CMB, Yes I know it's at a very large macroscopic scale, but at one time it wasn't. Could the CMB be an image of quantum scaring?
One talent of humans is to detect patterns in everything . So, we can see a face whilst looking at the Moon's surface. That doesn't mean it is actually a face. There are only so many patterns to find, so of course, some seem similar to others. It's actually a thing that paranoid people can have, they see patterns and try to make sense of them and then connect things in their mind that are actually not connected.
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.
Does the shape of the scar change based on where in the stadium the traveling particle is released? Or is it dependant purely on the shape of the stadium?
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?)
The insight from this experiment is that bounded systems develop their own internal order, and its been shown at all scales, not just the quantum. Vibrate a bowl of water.
Makes me think that the universe must have had a moment when it was the size of one planck-length (and one where it was one planck-time old). And there was a period when the whole universe must have been governed by quantom physics because it simply was so small. I guess that's what you mean - that the quantum scars from that period might have expanded into the cosmic web. I don't know if that's actually the case, but I would also like to know more about it. First question would be, of course, if a universe *is* governed by quantum physics when it is the size of a quantum object or if the huge mass (or whatever else) would mean the equations also fail to describe that state.
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.
Please give a look at Barandes’ research on the derivation of QM from indivisible stochastic processes. In that formulation the measurement problem doesn’t exist, I think.. but that comes at the expense of a non-Markov (indivisible) evolution.
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.
4:19 so could the scar be an outline for matter to share? Like a relative that shares with to become something. Imagine electricity shared with the differences of the battery and now potential increases. Maybe all is shared but chaos is when we don’t listen or can’t because we aren’t relative. I bet the quantum fluctuations can form the scar and it could share to form shapes in matter, like organs and metals and liquids, etc. i believe chaos is just us not able to understand so as we expand and share, we will be able to understand and become more relative with the infinite. Expansion doesn’t form into one but share with the many. Excellent video.
(I'm sure many people besides Sabine can answer this question, but I wouldn't be disappointed if Sabine did, even with a yes or no) Is the quantum chaos that Martin Gutzwiller wrote about the same as the (temporary but not real) quantum chaos you talk about here? I remember him making distinctions (and comparisons) between classical and quantum chaos, but I never remember him implying that quantum chaos was not chaos. Of course, it's been awhile since I read Gutzwiller. (BTW, I highly recommend his paper on the history of mathematical approaches to the Earth/Moon/Sun system. It's not a research paper, but it's an interesting historical summary)
I think they are resolving the realization of quantum chaos by studying ideas such as improved stationary wave intensities, dynamical localization, and spectral level repulsion. Examining universal statistical characteristics, the nearest-neighbor distribution (NND) as a gauge of quantum chaos, and Random Matrix Theory and related predictions. Recognize the roles of quantum scars, parametric dependence on the Hamiltonian, and finite-dimensional local Hilbert spaces in wavepacket dynamics
Is the N-body problem not considered an example of chaos in the quantum realm? I mean the development of quantum chemistry through the HF method was to sidestep this problem and approximate an answer, if there is no chaos and you could calculate exactly the interaction between a nucleus and two electrons then why has physics not developed an exact model for atoms other than hydrogen?
The caption reads "Scientists Uncover Hidden Pattern in Quantum Chaos." I know that English is not Sabine's first language, but the use of the word "hidden" is not appropriate. It's not hidden or it would be seen, observed, or found. Good enough is the phrase "Scientists Uncover Pattern in Quantum Chaos." Language is important, especially when discussing science.
The divergence between two probability distributions can grown exponentially, or not? E.g. KL divergence can go to infinite. Also you can have chaos in deterministic nonlinear bounded systems ...
So we applied probabilities to nano bits of "matter", giving us Quantum Mechanics. That's just math, and it seems like the math is defining its own limitations on what we measure. Strangly, when those irregularities show up in observations, not only do they back up the math we invented, they also seem to fit where the math isn't. Maybe we need to look at the quantum threshold as some sort of fractile definition/limitation.
Wow this is exactly what I'm preparing to study in grad school! My group has been looking at characterizing quantum chaos through nonlinear information scrambling and analyzing the growth of the OTOC (out-of-time-ordered correlator). Im hoping to propose a correspondence principle for my PhD but I have a lot of work to do first lol. For now the systems of interest are quite simple, Im not working on any ising-type model quite yet but that's the next step--spin chains, TFIM, Hubbard and bose-hubbard lattices. Ill let yall know what I find out!
Hmmm. Not sure about this one. On the one hand, I've heard QM equations called linear approximations of what may actual be an underlying non-linear reality. I don't know anywhere near enough to have a useful opinion but at least some people apparently think that true quantum chaos may be for real. Also, there are all sorts of famous chaotic systems where the values never exceed certain values. The famous period doubling chart contains values that, like probability, range from 0 to 1. The chaos is in the paths through these numbers.
3:55 that's my advisor, who said in the 90s "quantum mechanics works, we've know this for 70 years" (he was more involved with actual hard physics problems at the time).
It's fascinating that shape forms, it's possible that a quantum particle in a closed system caused that. --Chaos is unatural, reactions with other particles can't take place. It happens when they get stirred up by a greater force, then go back to orderly. There's no shape to it. Antimatter is an example. It's likely losing energy. The infinity sign is not chaotic, it's orderly.
I think folks have, as most findings with solid theory, popularized mis-concepts, since "chaos theory" was all about how, in reality, small things that were considered rounding errors actually are significant--our instruments just weren't/aren't sensitive enough to provide certainty about the quantities. A great way to deal with it since the term "chaos" implies something opposute of the theory is to demonstrate the changes in patterns generated just by measuring and keeping a few extra decimal points, whether the pattern is a fractal or a model of a hurricane: then think about the implications for e.g. modeling weather. The entire point of "a butterfly flapping its wings in one side of the world..." is that systems are NOT chaotic--they just seem to be because the level of detail needed to really umderstand the causal chain is vastly beyond han comprehension. I have never understood the discourse in public since it does not take much reading to figure this out--just a little *careful* reading. It's like insistence that quantum mechanics means the universe has no real determinism, then you do some digging and realize that idea is a school of interpretation of an interpretation of tge Copenhagen interpretation... And maybe I don't want to become an experimentalist in the era of "consensus" "science" since entire fields are gossip about ideas about whose origins the practitioners were apparently taught secondhand but did not read about. 😅
Uh no. Go study the early examples of chaos theory. For example the three equation weather examlple. No matter HOW many decimal points you approximate the REAL starting point, the model ALWAYS diverged. And once it does, it KEEPs diverging You need to study this more. I once created a Windows program where co workers could play with this until the understood it.
fractals emerge during phase transition in the form of avalanches and that's basically leading to chaos, and that's all I saw in this video, fractals and avalanches, so kind of a chaos.
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 ? 🙂
Wouldn't Heisenberg's equation of motion for any physical observable, usually not linear in quantum systems where one would expect to observe chaotic behavior (such as many-body systems), provide the "required" non-linearity?
Why can chaos not arise in quantum systems where the max. probability is 1? Considering that between 0 and 1 exist an infinite number of fractions (which aren't even limited by something like the Planck length), we, in principle, could mathematically also construct an infinite number of functions that return an infinite number of different 'points' on the scale between 0 and 1.
This is part of the more general topic of how to get the “classic limit”. Basically nobody knows exactly how classical mechanics arises from quantum mechanics. If you believe in many words your evolution as macroscopic object is not governed by a linear equation but by some stochastic process determining which copy of yourself and your surroundings you experience when you constantly branch out. This is, of course, part of QM but clearly not well understood mathematically.
“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
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…. ❤
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.
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.
The concept in The Elite Society's Money Manifestation ebook completely blew me away. It feels like finding a secret path to wealth
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.
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. 🙂
We all have that one friend with a P=3.5 of being late...
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.
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"?
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)...
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
The real chaos in quantum physics is the argument between the scientists about what's the next hypothetical particle going to be.
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....
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.
Dr Jacob Barandes has developed a locally real interpretation of QM.
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
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
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.
That conclusion is like totally unreal!
Placing a butterfly on a 2d sheet of paper with pins through it would probably reduce the chaotic nature of future events as well as putting a particle within a stadium weir. I hope this method of containment proves effective enough to produce useful advances. It probably won't for the butterfly, but maybe that's the chaos of a many particled stadium weir that would probably give rise to a Nascar race of emotionally scarred butterflies. Probably not w/o a multiverse. thanks doc
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.
this is Extremely useful, and important to know
mostly because it means developments can happen!
Thank you for the video.
Thank you for this
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.
My brain interpreted this as: Order (very small scales) -> Appears like chaos due to complexity of order (bigger scales) -> Order (macro scales) do I get a cookie?
1:29 in and my interpretation is how tv screens start off blurry then get sharper and clearer but the fractal nature is still there
those quantum scars eg 2:48 looks an awful lot like the pattern on the surface of the sun (not just the color obviously)
I don't see how the linearity of QM prohibits chaos. That's like saying the linearity of Intergrable Systems prohibits chaotic behavior even though you could have a chaotic gas of solitons.
Really interesting indeed! Thanks, Sabine! 😊
Merry Christmas!
Stay safe there with your family! 🖖😊
That's what I always say, there's a secret order in the chaos in my room!
Quick haircut Sabine 5:28 and no chaos 😂
new experiment throws chaos theory into itself!
Chaos =/= random.
We seem to insert "randomness" as an approximation.
Thanks a lot. It was interesting and very helpful.
Well that explains the scars on my heart . . .
20 years ago I read a book about Chaos... And almost immediately understood Einstein's phrase "God does not play dice"... Time has given us the reason yet again.
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?
You should have a chat with Steve Strogatz. He is a mathematician at Cornell who has certainly not ignored quantum chaos.
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.
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
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.
My first thought was, that QM is only linear as long as a system evolves in some potential according to the Schrödinger Equation, but if you include the collapse (or partial collapse) of the wave function every now an then it leads to nonlinear behaviour.
Hi Sabine, is there any relation between chaos attractors and quantum scars?
I actually know some people who's probability of being late is likely in the neighborhood of 3.5!
Sabine in this video here had superposition of 2 haircuts.
0:58 good for her.
Are you going to make a video about what you think of o3? I'd love someone like you to actually delve into the benchmarks. I was impressed by the SWE benchmarks (just issues taken from git, no simplifying the actual question etc, total human things). So would love to know what you think of the science, maths, etc parts.
Might even be worth a long video
In my mind, the fact that quantum mechanical particles exist quantized shows how chaotic systems that allow a classical object to never return to the same position and create fractal like patterns couldn’t really be present in quantum systems. The quantized nature of quantum particles should not allow them to form chaotic patterns that insinuate they can be in any location in the given space.
Nobody understands quantum physics; it's not about the formalism, it's about the interpretation.
That's the problem nobody truly understands quantum mechanics. Should it be viewed purely instrumentally as a tool for calculating probabilities, or ontologically, or perhaps as deterministic or non-deterministic?
What is often ignored is that the Copenhagen interpretation, like any other interpretation, is not the truth.
Statements about how "this or that" in the quantum world works are made based on the interpretation, but what gets overlooked is the interpretative nature of these claims.
No, quantum mechanics is not formally difficult, it's the interpretation that is challenging.
What does a wave function mean? You can't measure it, taste it, or smell it, what is it supposed to be? What is the correct interpretation of quantum mechanics? Should it be interpreted as having an ontological or epistemological reality, or perhaps none at all and merely a tool? I personally prefer the latter interpretation
This is where it begins. Is the wave function just a mathematical tool for calculating probability distributions, or is it real? Or is it simply an absurdity that follows from the fact that we are limited beings who cannot see behind everything?
Or what about the relational interpretation? It claims that states or wave functions always exist in relation to the observer, where we use language and formalism to form connections between our understanding and systems. But we have nothing, absolutely nothing, that tells us the quantum world is a certain way. It’s a matter of interpretation.
And it annoys me that this is always left out. We don't know how the quantum world really is. We observe it through the lens of the Copenhagen interpretation Formalism, and that’s the point. Physicists, myself included in the past, often act as if the formalism equals reality. But it doesn’t. In the end, all this mathematical stuff could turn out to be something like the epicycle theory. There is nothing that excludes that possibility.
"Physicists, myself included in the past, often act as if the formalism equals reality." Exactly!
Watching the animations that show the building up of the Quantum scars made me think of the distribution of the CMB, Yes I know it's at a very large macroscopic scale, but at one time it wasn't. Could the CMB be an image of quantum scaring?
One talent of humans is to detect patterns in everything . So, we can see a face whilst looking at the Moon's surface. That doesn't mean it is actually a face. There are only so many patterns to find, so of course, some seem similar to others. It's actually a thing that paranoid people can have, they see patterns and try to make sense of them and then connect things in their mind that are actually not connected.
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.
Does the shape of the scar change based on where in the stadium the traveling particle is released? Or is it dependant purely on the shape of the stadium?
This is a very nice report on this paper.
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?)
The insight from this experiment is that bounded systems develop their own internal order, and its been shown at all scales, not just the quantum. Vibrate a bowl of water.
"Quantum Scars" seem easily applied to the CMB or galactic superstructures. I thought for sure this is where you were headed, but no mention.
Makes me think that the universe must have had a moment when it was the size of one planck-length (and one where it was one planck-time old). And there was a period when the whole universe must have been governed by quantom physics because it simply was so small. I guess that's what you mean - that the quantum scars from that period might have expanded into the cosmic web. I don't know if that's actually the case, but I would also like to know more about it. First question would be, of course, if a universe *is* governed by quantum physics when it is the size of a quantum object or if the huge mass (or whatever else) would mean the equations also fail to describe that state.
Super interesting, all the best.
brilliant presentation. Merry Christmas.
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.
4:03 quantum scaring like when you tear muscles before they grow into stronger muscles increasing “power” or “efficiency”
Please give a look at Barandes’ research on the derivation of QM from indivisible stochastic processes. In that formulation the measurement problem doesn’t exist, I think.. but that comes at the expense of a non-Markov (indivisible) evolution.
Beautiful animation of the butterfly on the bobblehead.
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.
As a warehouse worker, I’ve always maintained: there is no such thing as chaos-only a different kind of order.
Nope. Weather.
Dibs on "Quantum Scar" as a character name in a novel. Can be both protagonist and antagonist at the same time!
seems useful for accelerated compute emulating quantum computing
4:19 so could the scar be an outline for matter to share? Like a relative that shares with to become something. Imagine electricity shared with the differences of the battery and now potential increases. Maybe all is shared but chaos is when we don’t listen or can’t because we aren’t relative. I bet the quantum fluctuations can form the scar and it could share to form shapes in matter, like organs and metals and liquids, etc. i believe chaos is just us not able to understand so as we expand and share, we will be able to understand and become more relative with the infinite. Expansion doesn’t form into one but share with the many. Excellent video.
(I'm sure many people besides Sabine can answer this question, but I wouldn't be disappointed if Sabine did, even with a yes or no) Is the quantum chaos that Martin Gutzwiller wrote about the same as the (temporary but not real) quantum chaos you talk about here? I remember him making distinctions (and comparisons) between classical and quantum chaos, but I never remember him implying that quantum chaos was not chaos. Of course, it's been awhile since I read Gutzwiller.
(BTW, I highly recommend his paper on the history of mathematical approaches to the Earth/Moon/Sun system. It's not a research paper, but it's an interesting historical summary)
I think they are resolving the realization of quantum chaos by studying ideas such as improved stationary wave intensities, dynamical localization, and spectral level repulsion. Examining universal statistical characteristics, the nearest-neighbor distribution (NND) as a gauge of quantum chaos, and Random Matrix Theory and related predictions. Recognize the roles of quantum scars, parametric dependence on the Hamiltonian, and finite-dimensional local Hilbert spaces in wavepacket dynamics
Is the N-body problem not considered an example of chaos in the quantum realm? I mean the development of quantum chemistry through the HF method was to sidestep this problem and approximate an answer, if there is no chaos and you could calculate exactly the interaction between a nucleus and two electrons then why has physics not developed an exact model for atoms other than hydrogen?
Its macroscopic
If I had to guess - the homogeneous stadium vibrates, or the inertia of interactions has resonance?
Wonderful, very interesting!
The caption reads "Scientists Uncover Hidden Pattern in Quantum Chaos." I know that English is not Sabine's first language, but the use of the word "hidden" is not appropriate. It's not hidden or it would be seen, observed, or found. Good enough is the phrase "Scientists Uncover Pattern in Quantum Chaos." Language is important, especially when discussing science.
Click bait
And you could learn how to write people's names correctly, but here we are.
@MsSonali1980 how to advertise the fact you don't know what is being discussed, 101.
@@MsSonali1980 Gland you are paying attention! You get five stars!
@@nosuchthing8 You presume and that is not good, especially in science.
The divergence between two probability distributions can grown exponentially, or not? E.g. KL divergence can go to infinite. Also you can have chaos in deterministic nonlinear bounded systems ...
Thanks Sabine.
So we applied probabilities to nano bits of "matter", giving us Quantum Mechanics. That's just math, and it seems like the math is defining its own limitations on what we measure. Strangly, when those irregularities show up in observations, not only do they back up the math we invented, they also seem to fit where the math isn't. Maybe we need to look at the quantum threshold as some sort of fractile definition/limitation.
2:35 Sabine, how would all this behave in a Penrose unilluminable room?
Wow this is exactly what I'm preparing to study in grad school! My group has been looking at characterizing quantum chaos through nonlinear information scrambling and analyzing the growth of the OTOC (out-of-time-ordered correlator). Im hoping to propose a correspondence principle for my PhD but I have a lot of work to do first lol. For now the systems of interest are quite simple, Im not working on any ising-type model quite yet but that's the next step--spin chains, TFIM, Hubbard and bose-hubbard lattices. Ill let yall know what I find out!
Can't ever unsee that butterfly doing the nasty to Einsteins head.
Linear Systems can of course be chaotic. 3 or more dimensions is all that is required.
Hmmm. Not sure about this one. On the one hand, I've heard QM equations called linear approximations of what may actual be an underlying non-linear reality. I don't know anywhere near enough to have a useful opinion but at least some people apparently think that true quantum chaos may be for real.
Also, there are all sorts of famous chaotic systems where the values never exceed certain values. The famous period doubling chart contains values that, like probability, range from 0 to 1. The chaos is in the paths through these numbers.
James Gleick is not going to be happy 😁
Chaos is just a word to describe what we don't understand.
Disruption causes collisions. When displacement can't be overcome by impaction force. Chaotically.
3:55 that's my advisor, who said in the 90s "quantum mechanics works, we've know this for 70 years" (he was more involved with actual hard physics problems at the time).
It's fascinating that shape forms, it's possible that a quantum particle in a closed system caused that. --Chaos is unatural, reactions with other particles can't take place. It happens when they get stirred up by a greater force, then go back to orderly. There's no shape to it. Antimatter is an example. It's likely losing energy. The infinity sign is not chaotic, it's orderly.
Perhaps the infinity sign is one dimensional matter moving in 4D space.
I think folks have, as most findings with solid theory, popularized mis-concepts, since "chaos theory" was all about how, in reality, small things that were considered rounding errors actually are significant--our instruments just weren't/aren't sensitive enough to provide certainty about the quantities.
A great way to deal with it since the term "chaos" implies something opposute of the theory is to demonstrate the changes in patterns generated just by measuring and keeping a few extra decimal points, whether the pattern is a fractal or a model of a hurricane: then think about the implications for e.g. modeling weather.
The entire point of "a butterfly flapping its wings in one side of the world..." is that systems are NOT chaotic--they just seem to be because the level of detail needed to really umderstand the causal chain is vastly beyond han comprehension.
I have never understood the discourse in public since it does not take much reading to figure this out--just a little *careful* reading. It's like insistence that quantum mechanics means the universe has no real determinism, then you do some digging and realize that idea is a school of interpretation of an interpretation of tge Copenhagen interpretation... And maybe I don't want to become an experimentalist in the era of "consensus" "science" since entire fields are gossip about ideas about whose origins the practitioners were apparently taught secondhand but did not read about. 😅
Uh no. Go study the early examples of chaos theory. For example the three equation weather examlple. No matter HOW many decimal points you approximate the REAL starting point, the model ALWAYS diverged. And once it does, it KEEPs diverging
You need to study this more. I once created a Windows program where co workers could play with this until the understood it.
fractals emerge during phase transition in the form of avalanches and that's basically leading to chaos, and that's all I saw in this video, fractals and avalanches, so kind of a chaos.
Sure. But that's microscopic. Her stadium and butterfly examples are super microscopic.
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 ? 🙂
Thank you 🙏
Wouldn't Heisenberg's equation of motion for any physical observable, usually not linear in quantum systems where one would expect to observe chaotic behavior (such as many-body systems), provide the "required" non-linearity?
Quantum theory may be linear, but gravity is not
Why can chaos not arise in quantum systems where the max. probability is 1?
Considering that between 0 and 1 exist an infinite number of fractions (which aren't even limited by something like the Planck length), we, in principle, could mathematically also construct an infinite number of functions that return an infinite number of different 'points' on the scale between 0 and 1.
The universe is classical. But superfluid dynamics are strange. And the fluid character induces quantization
Resonates amplify waves...
The scar it's self is the butterfly, it's all casualty.
This is part of the more general topic of how to get the “classic limit”. Basically nobody knows exactly how classical mechanics arises from quantum mechanics. If you believe in many words your evolution as macroscopic object is not governed by a linear equation but by some stochastic process determining which copy of yourself and your surroundings you experience when you constantly branch out. This is, of course, part of QM but clearly not well understood mathematically.
i had an understanding that if things happen with probability, therefore what happens is random, and to me that sounds pretty chaotic already
Could this observed pattern shape be explained by pilot wave theory?
And the stadium animation of "almost chaos" looks very much like pictures from the NJ "drone" incursion. 😮