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Chubbybrot!!! not gonna lie that looks cute!!!

So basically Chaos theory?

Quantum information theorists have a way to understand electron spin that we explain in our book, "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit" Oxford UP (2024) and I’ll summarize it here. According to Einstein, special relativity (SR) is a "principle theory," i.e., a theory whose formalism follows from an empirically discovered fact. For SR that empirically discovered fact is the light postulate - everyone measures the same value for the speed of light c, regardless of their relative motions. Since c is a constant of Nature according to Maxwell's electromagnetism, the relativity principle (the laws of physics are the same in all inertial reference frames) says it must be the same in all inertial reference frames. And, since inertial reference frames are related by uniform relative motions (boosts), the relativity principle tells us the light postulate must obtain, whence the Lorentz transformations of SR. Likewise, quantum information theorists have rendered quantum mechanics (QM) a principle theory and its empirically discovered fact is called Information Invariance & Continuity (Brukner & Zeilinger, 2009). In more physical terms, Information Invariance & Continuity entails that everyone measures the same value for Planck's constant h, regardless of their relative spatial orientations or locations (let me call that the "Planck postulate"). Since h is a constant of Nature according to Planck's radiation law, the relativity principle says it must be the same in all inertial reference frames. And, since inertial reference frames are related by relative orientations or locations in space (rotations or translations), the relativity principle tells us the Planck postulate must obtain, whence the finite-dimensional Hilbert space of QM. Electron spin is just a consequence of the Planck postulate, since the measurement of electron spin is just a measurement of h (Weinberg, 2017). Quantum superposition is one consequence of the Planck postulate, as we can illustrate with electron spin. Suppose you send a vertical spin up electron to Stern-Gerlach (SG) magnets oriented at 60 deg relative to the vertical. Since spin is a form of angular momentum, classical mechanics says the amount of the vertical +1 angular momentum that you should measure at 60 deg is +1*cos(60) = 1/2 (in units of hbar/2). But the SG measurement of electron spin constitutes a measurement of h, so everyone has to get the same +/- 1 for a spin measurement in any SG spatial orientation, which means you can't get what you expect from common sense classical mechanics. Instead, QM says the measurement of a vertical spin up electron at 60 deg will produce +1 with a probability of 0.75 and it will produce -1 with a probability of 0.25, so the average is (+1 + 1 + 1 - 1)/4 = 1/2. In other words, QM says you get the common sense classical result on 'average only' because of the observer-independence of h. Give up your dynamical bias for QM (just as is done for SR) and physics makes perfect sense. As we explain in our book, this principle account of QM solves the mystery of entanglement without violating locality (as in Bohm’s pilot wave), statistical independence (as in superdeterminism or retrocausality), intersubjective agreement (as in QBism), or the uniqueness of experimental outcomes (as in Many Worlds).

Why would you need to know this? Just a question cause i’m curious on the uses

Doesn't the Riesz representation only work for BOUNDED linear functionals? If not then it shouldnt be the "dual space" but the "algebraic dual space"

Woah

Neat

whaaaat

Nonlinear mechanics❤

The one you left out is retrocausality. But Many Worlds, superdeterminism, and retrocausality are all just crocks of crap. Non-locality is MUCH easier to accept, especially when you recognize that spacetime isn't fundamental in the first place.

The bottom line is that Einstein's assumption 3 was wrong. The particles, before either is measured, do not HAVE individual quantum states. The only quantum state in play at that time is the singlet state that describes THE SYSTEM, not either particle individually. So sure - we did not perform a measurement on particle 2. But we did perform a measurement on THE SYSTEM, and that CHANGES THE QUANTUM STATE of the system. Assuming particle 1 measured "up," we get this: |01> + |10> ---measurement---> |10> Clearly, particle 2 now has a 100% certainty of being down. That's all there is to it, and the fact that they're separated in a space-like way simply DOES NOT MATTER. The locality assumption is WRONG, full stop. The fundamental assumption that leads into this mess is that spacetime is a "container" that holds "everything." That's simply not the case. Spacetime isn't fundamental at all - you can completely formulate the dynamics of nature using only functions of time alone. If you then assume that at least one conserved quantity exists (that's the ONLY assumption you need to make, and it doesn't matter what the conserved quantity is), then the laws of physics come rolling out, and, more importantly, spatial dimensions EMERGE from the dynamics. All that means is the dynamics that unfold can be THOUGHT OF as occurring within a spatial manifold. Thinking of it that way allows the dynamics to be organized in a very efficient way - so efficient, in fact, that we have actually EVOLVED to view the dynamics of reality in this way. Space is something we PERCEIVE - not something that existed in the first place. Some aspects of the dynamics fit snugly into this spatial presentation, and those aspects are local and subject to the "c speed limit." Other aspects, though, like entanglement corellation, Einstein Rosen bridges, and so on, do NOT fit into the spatial presentation and are subject to no such speed limit. Once you recognize that space isn't fundamental, everything just falls into place. The singlet state no longer describes the system after you make that first measurement. So you can't point to it and say "this doesn't tell us that particle 2's spin is down." I mean, you can point and say that, but it's meaningless. It's no longer the correct state.

As far as I'm concerned John Bell GOT a Nobel prize, in 2022. All of that work was based on HIS insights. He was the one that really deserved the prize. But he was dead, and they have their rules. So they couldn't. That's just how the cookie crumbles. But I have NO DOUBT that he would have been in the group, or possibly would have received the prize individually and alone, had he still been living. The 2022 prize was the best step they could take toward recognizing the man's greatness.

How long does it take to diverge if you were to just use floats for one, and doubles for the other with the same initial value?

Chaos theory and Lorentz Butterflies are pretty.

whats app do you use?

It's worth noting that this doesn't mean chaotic systems aren't deterministic, they're just impossibly hard for us to predict.

LOOK AN MULTIBROT MORPH

Wat

Sorry - Bells theorem doesn't and cannot rule out the initial state of the particles. I say the initial state of the particles is set at the moment of entanglement. The claim that a particle has no properties until measured is just wrong. They are simply unknown until measured. This does NOT mean superposition isn't real. Until the initial state is either predictable or influenced or forced - no one can claim that entangled particles communicate anything at all after being entangled. Convince me that I'm wrong...

I think he means the running sum of the distance, which can exceed the distance between the 2 masses. He's asserting the difference in that sum between blue/magenta, as time increases, is chaotic. It IS bounded, thats why when he keeps changing scale size, you don't lose either distance sum

Are you sure about the units? [S] =J/K [kT]=J

Wow

so, whats the best book and resources to explore whatever the hell is going on here? list of unpretentious prereqs as well (unpretentious prereqs means enough to play and explore the world but not enough to pass formal rigorous examination... in other words, enough to understand just enough to be extremely dangerous if relied upon on the subject. enough to "use" the library but not "write" it if you get my drift?

i believe that we are just assuming that it’s unpredictable. if you had every value and every detail of the situation, to an extremely extremely minute precision, you’d be able to predict the path it takes

How can there be an upward trend when the sum of the distances is clearly bounded?

This is so good, criminally underrated. Keep up and you will garner a significant audience. Subscribed 👍

Problem with this sim is the bounce calculation isn’t modelling the exact moment the ball is bouncing and is just doing it on a frame by frame basis (hence they bounce to higher points than they start). This is going to introduce just as much choas in itself

This is why we rather study a million harmonic oscillator then 1 double pendulum 😂

I feel like I’m way to stupid to have this in my recommended shorts, also what the hell is a theta

Could this help solve the three body problem

what constitutes as a "slight change" in the starting conditions?

If you do z^2 + c^1.25 it looks like it has 2 heads

Such a master piece ... subbed

Beautiful animations. Great!

If all contributing factors are known it is entirely predictable. If any is not known that is when predictions become much less likely.

9:40 😺

First

I love the song based off this theory, Laplace's Angel by Will Wood which makes fun of determinism by sarcastically saying that if there is no free will than there is no evil and everything should be legal

I don't know a oot about double pendulums. Is it a total coincidence that the areas covered by the pendulums in the theta 1, theta 2 graphs are in the shape of a rectangle?

crystal clear big dog thank you

There’s a channel that I haven’t seen in a while that makes art like this. He puts down a canvas and stabs a hole in the bottom of a paint bucket on a string on the ceiling and it creates patterns like this. They’re beautiful pieces.

So neat and beautifully demonstrated

What a fantastic presentation of the double pendulum, I have seen this topic described before but never with such high-quality animations. Also seen the angle plots together with the animation is great. Thanks for letting the beautiful figure complete at 8:50, the animation-voice over timing was perfect.

Can we talk about the prefect timing at 8:50? So satisfying you stopped the plot just the right time

Please give details of the lecture referenced at minute 5:10 of this video. I can’t quite hear the name or where to find it. Thank you.

This is such a good video to have in the youtube catalogue. Will probably use as a reference if I ever need to explain a double pendulum, or chaos tbh. Also, if you're open to suggestions. I think it would be interesting to see how different approximation schemes (RK4, Verlet, etc.) affect the double pendulum. I'm almost finished with a video covering the subject, on Simple Harmonic Oscillators though, but I think the double pendulum would be a really interesting medium to explore the topic. Again, really great video, thanks for making it!

Happy to see this video. Great effort in explaining the Stronger Uncertainty Relations. Really appreciated. -Arun Pati

Ngl, this felt like the non answer equivalent of an explanation.