Analytics wrote: ↑Fri Jun 07, 2024 4:50 pm
My understanding is that our ignorance is based on the underlying nature of reality and not a function of not having precise-enough and subtle-enough instruments to detect things without disturbing them. Isn’t the real point of the uncertainty principle that to the extent that a particle’s position is known, its speed is fundamentally unknowable? This unknowableness is intrinsic to the math and isn’t really talking about our ignorance per se, isn’t it?
I like to explain this point in lectures by asking students to think about a robot orchestra playing robot music. The robot players can be incredibly precise. But can even a perfect robot orchestra play a perfect 440 Hz A note at a particular nanosecond? No, because the precise frequency of exactly 440 Hz means a pattern of air pressure that repeats every 1/440 of a second. To even say that the pattern repeats itself that way needs at least a couple of 440ths of a second, meaning that the pattern has to extend over millions of nanoseconds. To say exactly when that pattern begins, to a nanosecond, isn't just physically impossible: it's logically impossible.
The impossibility of position and velocity both being precisely defined is just like that impossibility of having frequency and time both precisely defined. Moreover this isn't just a qualitative analogy. The mathematical relationship between time and frequency really is exactly the same as the mathematical relationship between position and velocity. Why that should be is not at all clear. To our intuition, velocity and position aren't related that way at all. Quantum mechanics just says that in fact they are related that way, as an axiom.
This is the thing about "quantum indeterminacy". It's only an indeterminacy if one tries to fit it into the more intuitive framework of classical mechanics, in which momentum and position are completely independent quantities. A basic fact of classical mechanics is that the laws of nature are differential equations of second order, so that position and momentum at any one time, separately, are necessary and sufficient inputs in order to say what happens through all time. Limitations on how well one can possible know both position and momentum count in classical mechanics as limitations on what we can say about anything. Quantum mechanics, however, is a radically different framework. You can see how different it is by talking about simpler systems than particles, with their position and velocity, and instead just discussing two-state systems, like heads-or-tails coins or zero-or-one bits. That's why my first quantum lectures are about bits rather than particles.
In its own way quantum mechanics is utterly deterministic. Its kind of determinism just doesn't map simply onto classical determinism. In fact it's kind of crazy, with this deterministically evolving "amplitude" whose practical meaning seems hard to pin down. At some point you back quantum mechanics into a corner and force it to say what that weird amplitude thing actually means, concretely, when for example you measure something. Then it pulls out a probability knife.
The quantum state evolves deterministically. What it means for measured properties, however, is only a probability distribution. Neither can we say that the quantum state actually is nothing but a probability distribution, however. The rule for deducing the probability distribution from the quantum state is simple but that's the problem. It's literally just squaring two things and adding them. The problem is that this isn't logic.
If you insist on trying to fit this into the logic of classical mechanics, then in many cases it's kind of as if quantum mechanics has this extra randomness. That's not really what quantum mechanics is like, though. Quantum mechanics is this simple rotation in a higher-dimensional space, with nothing random at all. The randomness only comes from trying to describe it in classical terms.
Including trying to measure it with big, clunky meters whose arrows swing around their dials classically. That's the problem of quantum-classical correspondence.
It does come out looking like randomness. Quantum states evolve with perfect determinism, however, that is even of a particularly simple form—until we measure them. This is a perverse, naïve picture that gives a special role to humans and our measurement devices, even though these are just big lumps of atoms like everything else. Unfortunately, though, we still can't do anything better. We've come from Bohr's crude model of quantised orbits to the renormalisable relativistic quantum field theory of the Standard Model, but we haven't been able to improve on Bohr's old measurement axiom at all.
Anyway: I said that a particular quantum state of the universe must have an image under reverse time evolution through 14 billion years. The particular state could be a state in which Jesus's feet are held up against gravity by an atypical proportion of upward strikes from molecules. My statement wasn't a guess or a wish. It's exact. Any state has such an image, and that image state is no more or less unlikely than any other particular state having the same global features like charge and energy.
We’re not merely asking the universe to provide a state where Jesus walks on water at time t. We are also asking for that state to lead to another state at t + 1 where he is walking on water again. And that needs to be true again and again and again for billions of different nanoseconds so that the feat of walking on water persists for a few seconds.
You're quite right about this, and it does raise the stakes enormously. Even when you or I step into water, half the time the random molecular strikes on our feet are going to hold us up a bit more than they do on average—by definition. It amounts to a delay in our sinking of at most a few picoseconds, I'd guess, depending on how we measure this delay; the reduction in how far we sink is probably much less than the uncertainty in how to define the water surface level, given that water is really a bunch of molecules whose spatial extent is also uncertain. For walking on water, even for a few seconds, that luck in molecule strikes has to hold for what counts as an enormously long time on molecular scales.
If we were talking about a human effort to design a controlled swimming pool for Elon Musk to walk across, this would be a decisive point. It's not clear to me that it has any weight at all in a discussion of God. It is in principle possible to keep on walking on water for a while. God could nail that. Maybe there are limits on how long the water-walking could last that even God couldn't surpass without revising the laws of physics. Are there limits too short to support a story of water-walking? Maybe, but it's not obvious. For what it's worth, I'd bet not.
(I'd bet a beer; maybe a bottle of wine, but not so much more than that. I actually think it's very unlikely that Jesus walked on water. I'm just using it as a thought experiment to point out that he maybe could have, in principle. I think the story is a garbled account that was probably based on an episode in which he walked by on shore while his disciples struggled to land in a storm, if it wasn't simply made up completely, or copied from some other story, by people who thought it was totally the kind of thing that would have happened with Jesus.)
My original thought was that there couldn't exist an early state of the universe that necessarily leads to that. This state not existing was driven by my sensibilities regarding the granular and stochastic nature of reality, chaos theory, and the 2nd law of thermodynamics.
This is a sensible thought, but it's not actually supported by our current understanding of reality, chaos, or the Second Law. That's not because you in particular have somehow failed. It's because these are things that nobody really understands now. We understand some great things about all those things, but we don't understand them enough.
It makes me think of a supernatural meddler in reality who is making extreme measures to create the illusion that the world works according to natural law and takes extreme measures to be unknown and unknowable, when the underlying reality is the exact opposite. It’s a disturbing thought.
I think this is overly pessimistic, because I think of the theorem that the most efficient encoding of information produces random signals. We should not expect God to be deliberately hiding from us by making things look random. We should, however, expect a God who has far more knowledge and power than us to do things that look random to us.
I was a teenager before it was cool.
