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Chaos: The Real Problem With Quantum Mechanics
🕑 Added 2022-05-28 12:00:04 +0000 UTC[This is a transcript of the video.]
You’ve probably seen a lot of headlines claiming that quantum mechanics is “strange”, “weird” or “spooky”. In the best case it’s “unintuitive” and “no one understands it”. Poor thing. In this video I will try to convince you that the problem with quantum mechanics isn’t that it’s weird. The problem with quantum mechanics is chaos. And that’s what we’ll talk about today.
Saturn has 82 moons. This is one of them, its name is Hyperion. Hyperion has a diameter of about 200 kilometers and its motion is chaotic. It’s not the orbit that’s chaotic, it’s the orientation of the moon on that orbit.
It takes Hyperion about 3 weeks to go around Saturn once, and about 5 days to rotate about its own axis. But the orientation of the axis tumbles around erratically every couple of months. And that tumbling is chaotic in the technical sense. Even if you measure the position and orientation of Hyperion to utmost precision, you won’t be able to predict what the orientation will be a year later.
Hyperion is a big headache for physicists. Not so much for astrophysicists. Hyperion’s motion can be understood, if not predicted, with general relativity or, to good approximation, with Newtonian dynamics and Newtonian gravity. These are all theories which do not have quantum properties. Physicists call such theories without quantum properties “classical”.
But Hyperion is a headache for those who think that quantum mechanics is really the way nature works. Because quantum mechanics predicts that Hyperion’s chaotic motion shouldn’t last longer than about 20 years. But it has lasted much longer. So, quantum mechanics has been falsified.
Wait what? Yes, and it isn’t even news. That quantum mechanics doesn’t correctly reproduce the dynamics of classical, chaotic systems has been known since the 1950s. The particular example with the moon of Saturn comes from the 1990s (details here).
The origin of the problem isn’t all that difficult to see. If you remember, in quantum mechanics we describe everything with a wave-function, usually denoted psi. There aren’t just wave-functions for particles. In quantum mechanics there’s a wave-function for everything: atoms, cats, and also moons.
You calculate the change of the wave-function in time with the Schrödinger equation, which looks like this. The Schrödinger equation is linear, which just means that no products of the wave-function appear in it. You see, there’s only one Psi on each side. Systems with linear equations like this don’t have chaos. To have chaos you need non-linear equations.
But quantum mechanics is supposed to be a theory of all matter. So we should be able to use quantum mechanics to describe large objects, right? If we do that, we should just find that the motion of these large objects agrees with the classical non-quantum behavior. This is called the “correspondence principle”, a name that goes back to Niels Bohr.
But if you look at a classical chaotic system, like this moon of Saturn, the prediction you get from quantum mechanics only agrees with that from classical Newtonian dynamics for a certain period of time, known as the “Ehrenfest time”. Within this time, you can actually use quantum mechanics to study chaos. This is what quantum chaos is all about. But after the Ehrenfest time, quantum mechanics gives you a prediction that just doesn’t agree with what we observe. It would predict that the orientations of Hyperion don’t tumble around but instead blur out until they’re so blurred you wouldn’t notice any tumbling. Basically the chaos gets washed away in quantum uncertainty.
It seems to me that some of you are a little skeptical. It can’t possibly be that physicists have known of this problem for 60 years and just ignored it? Indeed, they haven’t exactly ignored it. The have come up with an explanation which goes like this.
Hyperion may be far away from us and not much is going on there, but it still interacts with dust and with light or, more precisely, with the quanta of light called “photons”. These are each really tiny interactions, but there are a lot of them. And they have to be added to the Schrödinger equation of the moon.
What these tiny interactions do is that they entangle the moon with its environment, with the dust and the light. This means that each time a grain of dust bumps into the moon, this very slightly changes some part of the moon’s wave-function, and afterwards they are both correlated. This correlation is the entanglement. And those little bumps slightly shift the crest and troughs of parts of the wave-function.
This is called “decoherence” and it’s just what the Schrödinger equation predicts. And this equation is still linear, so all those interactions don’t solve the problem that the prediction doesn’t agree with observation. The solution to the problem comes in the 2nd step of the argument.
Physicists now say, okay, so we have this wave-function for the moon with this huge number of entangled dust grains and photons. But we don’t know exactly what this dust is or where it is or what the photons do and so on. So we do what we always do if we don’t know the exact details: We make guesses about what the details could plausibly be and then we average over them. And that average agrees with what classical Newtonian dynamics predicts.
So, physicists say, all is good! But there are two problems with this explanation. One is that it forces you to accept that in the absence of dust and light a moon will not follow Newton’s law of motion.
Ok, well, you could say that in this case you can’t see the moon either so for all we can tell that might be correct.
The more serious problem is that taking an average isn’t a physical process. It doesn’t change anything about the state that the moon is in. It’s still in one of those blurry quantum states that are now also entangled with dust and photons, you just don’t know exactly which one.
To see the problem with the argument, let me use an analogy. Take a classical chaotic process like throwing a die. The outcome is an integer from 1 to 6, and if you average over many throws then the average value per throw is 3.5. Just exactly which outcome you get is determined by a lot of tiny details like the positions of air molecules and the surface roughness and the motion of your hand and so on.
Now suppose I write down a model for the die. My model says that the outcome of throwing the die is either 106 or -99 each with probability 1/2.
Wait, you say, there’s no way throwing a die will give you minus 99. Look, I say, the average is 3.5, all is good. Would you accept this? Probably not.
Clearly for the model to be correct it shouldn’t just get the average right, but each possible individual outcome should also agree with observations. And throwing a die doesn’t give minus 99 any more than a big blurry rock entangled with a lot of photons agrees with our observations of Hyperion.
Ok but what’s with the collapse of the wave-function? When we make a measurement, then the wave-function changes in a way that the Schrödinger-equation does not predict. Whatever happened to that?
Exactly! In quantum mechanics we use the wave-function to make probabilistic predictions. Say, an electron hits either the left or right side of a screen with 50% probability each. But then when we measure the electron, we know it’s, say, left with 100% probability.
This means after a measurement we have to update the wave-function from 50-50 to 100-0. Importantly, what we call a “measurement” in quantum mechanics doesn’t actually have to be done by a measurement device. I know it’s an awkward nomenclature, but in quantum mechanics a “measurement” can happen just by interaction with a lot of particles. Like grains of dust, or photons.
This means, Hyperion is in some sense constantly being “detected” by all those small particles. And the update of the wave-function is indeed a non-linear process. This neatly resolves the problem: Hyperion correctly tumbles around on its orbit chaotically. Hurray.
But here’s the thing. This only works if the collapse of the wave-function is a physical process. Because you have to actually change something about that blurry quantum state of the moon for it to agree with observations. But the vast majority of physicists today think the collapse of the wave-function isn’t a physical process. Because if it was, then it would have to happen instantaneously everywhere.
Take the example of the electron hitting the screen. When the wave-function arrives on the screen, it is spread out. But when the particle appears on one side of the screen, the wave-function on the other side of the screen must immediately change. Likewise, when a photon hits the moon on one side, then the wave-function of the moon has to change on the other side, immediately.
This is what Einstein called “spooky action at a distance”. It would break the speed of light limit. So, physicists said, the measurement is not a physical process. We’re just accounting for the knowledge we have gained. And there’s nothing propagating faster than light if we just update our knowledge about another place.
But the example with the chaotic motion of Hyperion tells us that we need the measurement collapse to actually be a physical process. Without it, quantum mechanics just doesn’t correctly describe our observations. But then what is this process? No one knows. And that’s the problem with quantum mechanics.
Comments
I just migrated here from being a supporter on youtube. Please make more physics videos! Especially I would love to see more of your ideas and critical analysis of QED and single electron-photon interaction.
Terry Bollinger
From YouTube: >>The Strandbeest Universe<< chrslb (YouTube): I really didn't get this one. Isn't there a computational limit that applies in practice to chaotic systems, even if they're not maybe technically chaotic because they are for example simulated on a computer? Terry Bollinger: Yes. The founding fathers of both quantum mechanics and relativity were pre-computer continuum-math devotees, and thus had almost no appreciation for the severe precision limits that finite local energy imposes on both the physical world and our models of that world. This caused a century of perplexity in which infinities popped up constantly in our math due to inattention and indifference to this issue. For example, the simplest definition of quantum mechanics is that it is the limit of resolution possible given the finite energy resources of our material world. chrslb: Thank you! Are you talking about some kind of finite computation model of reality? It would be interesting to hear more about this. I wonder if naively this means that our world behaves as if it were simulated on a computer. Terry Bollinger: It's a finite computation model, but the computer and the software are one and the same, with the behaviors we call physics emerging as the parts interact and constrain each other. Strandbeests are a better analogy: https://youtu.be/LewVEF2B_pM [In fact,] that may become the title for a seriously technical Apabistia paper: "A Strandbeest Universe". Why "seriously technical?" The components of this... quantum strandbeest?... necessarily extend below the structure of both spacetime and the particles of the Standard Model. The analogy gets surprisingly specific. For example, the three colors of the strong force, when fused irreversibly with the fractional electric charges associated with them in all real particles, become three of the most important near-ground (possibly at ground) orthogonal construction units of the... hmm, how about "quandbeests"?... Yeah, that works better. A tight dance of such "color bar" units gives the fundamental fermions of the Glashow cube, while a more loosey-goosey dance on the same cube gives the mesons and hadrons. As with Strandbeests, sufficiently large collections of smaller quandbeests (QBs, pronounced "queue-bees"?) collectively self-orient and begin moving in a single consensus direction. We like to call that direction "time." As Einstein envisioned until he was later overruled by Minkowski, the time units of this universal quandbeest (UQB?) are not continuous. They are more like ticks of a clock, providing the individual steps of the universal quandbeest as it moves across the sands of time. So... again, chrslb, thanks. I like this analogy. When one is taking an, um, different :) approach to interpreting a huge body of very standard, well-proven physics data, it helps to have a clear visual analogy in your head. That's just the way our brains are built. [2022-05-29.18.36 EDT Sun] Terry Bollinger CC BY 4.0 https://sarxiv.org/apa.2022-05-29.1836.pdf
Terry Bollinger
From YouTube: >>Wave Functions of the Universe are Just Dumb Math Errors<< Steve Zara (YouTube): This is a rare video that actually shocked me. If quantum mechanics has a problem with a moon, how can some physicists talk of "the wave function of the universe"? Terry Bollinger: They cannot. All variants of universal wave functions include the mathematical concept of splicing together two or more functions "piecemeal." This enables them to model locality in a way that is infinitely differentiable and thus compatible with the infinite-precision continuum school of mathematics. There are two problems with this. The first is that one side of the splice always goes to infinity, which requires infinite computational capacity even if it looks smooth to human eyes. The second is that this kind of smoothness is incompatible with how the light cones of quantum events operate in the real world. These cones create finite edges that limit both the smoothness and the maximum details of expanding wave functions before they grow large enough to merge with all of the other wave functions in the universe. Everett's many-worlds idea is the least plausible and most egregious example of this kind of impossible-smoothness thinking since it assumes a universal wave function that, due to light-cone limits, cannot exist in the physical world. [2022-05-28.10.06 EDT Sat] Terry Bollinger CC BY 4.0 http://sarxiv.org/apa.2022-05-28.1006.pdf
Dr. Arne Babenhauserheide
Similar effects could happen for lone planets that are only visible temporarily and mostly non-interacting between those measurements.
Dr. Arne Babenhauserheide
A way to test this assumption would be to find a region of space that is almost completely empty *and* far from all masses around it, but still just bright enough that we can detect objects. What I described would predict that in such regions massive objects would behave closer to quantum mechanics than in strongly interacting regions. If there were very rare blips of light there — for example from remote supernovae — these could allow gathering enough data to check whether the motions between the measurements correspond to classical mechanics or quantum mechanics.
Dr. Arne Babenhauserheide
I wish I had taken the time during studying physics to get deep enough in quantum mechanics to answer in equations. Because there is something in your explanation that bothers me: You assume that the wave function has to collapse everywhere at the same time. Can the wave function collapse differently for the different interacting particles? Can the wave function collapse partially such that for some particles only part of the wave function collappses, because too weak interaction only measures part of it?
I think those two scientists wrote a book about Constructor Theory.
Hi Sabine, Nice job explicating the logical difficulties that QM has in moving from a math formalism (the wavefunction) to the physical implications (if any) of that formalism. Much of the problem stems from this rather casual assumption that seems to lack any sound logical justification: "But quantum mechanics is supposed to be a theory of all matter." That most QM theorists believe this may be a fact, but that doesn't make the supposition true. It is in trying to reconcile that supposition with reality that the difficulties with QM can be seen. Those difficulties transcend the epistemological conceit underlying the misguided belief that smaller "stuff" is more fundamental than bigger "stuff". The predilection of theoretical physicists to cast laboratory derived relationships as "universal laws" is a big part of the problem attending the current "crisis of physics", the other part being the prevalence of the mathematicist philosophy in academic science. In the latter case it is simply the belief that QM formalisms can be meaningfully stretched to account for individual classical scale phenomena when in fact those formalisms can't even account for individual quantum scale events, except statistically. As you described it: "So we should be able to use quantum mechanics to describe large objects, right?" This illustrates a major blind spot of theoretical physics. Matter-energy relationships that exist on one scale are not known to translate to vastly different scales, at least not without the invocation of empirically baseless free parameters. Our solar system scale gravitational models do not work on galactic scales, let alone the extra-galactic cosmos without the ad hoc addition of dark matter and dark energy. Classical mechanics does not scale to the quantum level any better than quantum behavior scales to the classical level. Scale matters in physical reality but theoretical physics spends untold amounts of time trying to make "universal laws" out of local systems relationships. Scale matters in physics. Here is a recent Quanta article about a group of "physicists" who are tying themselves in mathematical knots trying to rewrite the "fundamental law" of entropy in terms of QM, or generate entropy from QM, or something (in theory at least): https://www.quantamagazine.org/physicists-trace-the-rise-in-entropy-to-quantum-information-20220526/#comments I certainly agree with you on the problem with QM being that the wavefunction doesn’t describe a physical process. Unless of course you employ the framework of Bohmian mechanics where both the wavefunction and the charged particle are physical entities in themselves. It seems to me the Bohmian model is so widely disfavored only because its physical description is too logically coherent.
Rad Antonov
Hi Tracey. Ironically, what came out was different from what I was initially planning to say. I think the key to bridging our explanations of reality at various scales is finding the right question. For that we need experimental guidance. Perhaps recent advances, such as coupling phonon modes in macroscopic membranes to SQUIDs or atomic physics measurements of gravitational Aharanov-Bohm effect can show discrepancies with garden variety quantum mechanics. Absent that, i don’t see how theorists can come up with anything that supplants what we already have.
Happy Saturday, Tracey! Thanks for those links. I am not arguing against quantum mechanics explaining solar radiation, long distance entanglement or that we persist and don't meld into other "solid" things. And the demonstration of superposition using large molecules (https://www.accessscience.com/content/demonstration-of-quantum-superposition-using-record-breaking-large-molecules/BR1023191) does appear to indicate that those molecules did indeed exhibit quantum effects, as the article stated the molecules created wave interference patterns. However, that article stated that "[t]he wave function is said to collapse upon measurement to a single, discrete value, such as for a particle's location, momentum, or energy." Therefore, that a "classical" object can have its location, momentum or energy determined would seem to indicate that its wave function is always collapsed, as the article states: "The models that serve to reconcile quantum and classical interpretations of the world suggest that the rate of a particle's wave-function collapse is proportional to the square of the particle's mass, thus relegating heavier particles (or the objects they comprise) to increasingly definite, classical-like states." I think that that says what I'm trying to say better than my competency allows me to. I really appreciate this forum! It provides for a better level of discussion than any I've found yet. Enjoy your weekend!
Interesting, thanks. Enjoy your supper chaos-free!
I was going to eat a bit of supper, but then I saw your post, Colleen, and I have now learned, upon looking for some relevant papers, that Pluto's small moons and Neptune's moon Nereid also behave just like Hyperion. The Poincare cross sections for all of these moons show very tiny islands of stability. I think you are right that the rotation could "tip" into a stable regime, but it looks to be a very low probability. If Hyperion ever found itself in a stable rotation state, I suspect it would be short-lived.
Thing being, since this is Chaos, Hyperion's rotation might reach a tipping point and flip a phase-change into a nice, steady pattern, amIright?
Rad, you've put into words exactly what I've been struggling with all day. Quantum mechanics was never my thing when I was getting my degree, but it is interesting now to see the struggle to bridge quantum reality with classical reality -- the crux of the measurement problem.
Rad Antonov
I’ve been thinking about this episode for awhile now and still don’t know if I fully grasp the point. Is it that there is a yet to be discovered mechanism by which the wave function collapses upon measurement/interaction and that it is ultimately this unknown mechanism, which prevents the Schrödinger equation from describing the dynamics of Hyperion for a period longer than the Ehrenfest time? I would’ve thought the difficulty is in coming up with a Hamiltonian that accurately captures all the dynamics. But it seems your point is that no matter the Hamiltonian, the Schrödinger equation eventually settles down into some periodic motion, while Hyperion is perpetually chaotic. Whatever that mechanism is, I guess it would have to be non-linear. Furthermore, wouldn’t it also imply that the wave function itself is an entity that should in theory be observable, given that its collapse has a visible impact on the motion of Hyperion. In practice though, we count particles, measure energies, filter polarizations and detect interference patterns, never a wave function. Even the STM pictures that look like wave functions are just IV graphs. For all those cases, a quantum mechanical description with the Schrödinger or Dirac equation gives the best approximation for what we observe. Granted, we have a hard time understanding how some macroscopic properties emerge from these equations, e.g. band structure but still, quantum mechanics works really, really well. I am hard pressed to say there is a problem with it just because my intuition struggles with the implications. Still, if measurement collapse is the path to finding new physics, sign me up.
Hi Jeffery, I think the de Broglie wavelength is the answer to your last question: lambda = h/p where h is Planck's constant and p is momentum. Since lambda is super tiny for "big" things, their quantum effects are immeasurably small. Sabine has a couple videos about quantum mechanics not being just for small things: https://www.youtube.com/watch?v=HSIvPUMX1pk and https://www.youtube.com/shorts/eFWvGW8WjY4. I am interested in Sabine's answer to the rest of your philosophical question.
Hmm, a bit surprised to see that Sean Carroll wrote an article about Hyperion that basically concluded that measurement process must be physical: https://www.discovermagazine.com/the-sciences/quantum-hyperion
Maybe, observability would require Heisenberg time which makes it hard, instead of Ehrenfest time?
But I have to admit one argument seems questionable to me, namely the contradiction between a linear phase space description like Schroedinger eq. and nonlinear classical motion. Liouville Operator is linear and describes chaotic motion. Where exactly is the point? Please allow another question: You say, after Ehrenfest time, QM has a problem. Are there experimental efforts to measure such effects?
What empirical evidence implies that quantum dynamics has anything to do with the macro world? While any measurement of a subatomic particle will affect its state, the same doesn't hold true for macro objects. For example, I can record the position of a car on a road and determine its position, speed and velocity with precision because it reflects light that I can see. With respect to Hyperion, there is chaos because there are motions caused by past impacts and the gravitational effects of the other orbiting objects and Saturn itself that simply cannot be accurately accounted for, but again, as it is visible, measurements would not affect it. It therefore seems that attempting to extend quantum mechanics to macro objects is invalid because a macro object's wave function is always collapsed. Someone must have looked into this and come to that conclusion with some empirical evidence that there is a limit to the application of quantum mechanics due to the size of the object.
Dear Sabine, great video concerning the argument that the collaps of the wave function must be a physical process, this is what I always "believed", yes, since I am not aware of a theory for it.
