Analytics wrote: ↑Mon Jun 10, 2024 11:08 pm
For a given system, QM provides some wave functions. Those wave functions evolve deterministically from moment to moment. If the waves are "observed" at any point in time then you'll end up seeing some sort of discrete thing that is like the wave function randomly collapsing on a single value, but that observation event doesn't actually effect the underlying wave function that keeps on going on its deterministic way.
Is that more or less the way it works?
No, the observation does affect the wave function. It collapses it to a new wave function that gives 100% probability to the result that you just measured. Or at least it's going to seem like that. If you measure something, and then immediately measure the same property of the same system again, the second measurement result is always exactly the same as the first one. If instead you wait a while between measurements, then the second result might be different, depending on exactly what you measured and exactly what the system is doing while you're not measuring it.
For instance if you measure the velocity of an isolated particle flying through vacuum, then you can wait as long as you like between measurements, and the second result will still be the same, because isolated particles flying through vacuum don't change their velocity. If instead what you measured was the position of the particle, though, then your first measurement will pin down the particle's location, and if you look again right away, it will still be right where you saw it the first time. The longer you wait, though, the more likely it becomes that the particle will have drifted away from its first location by the time you look again.
Measurement seems just to be a sort interrupt call on normal physics, like one of those weird card games where you can play a special card to invoke a wild special rule. That's the rule, and it works. In practice it's not mysterious or ambiguous because it's normally obvious when a measurement happens. We have to go far out of our way to make a measurement, deliberately concocting some device that will enormously amplify tiny signals so that we can notice microscopic states and events. We understand how to make amplifiers like that, and we understand how they work—but only at an engineering level. We can make them and use them, but we don't understand the amplifiers themselves at anything like the fundamental level on which we understand the simple, tiny systems that we study by means of the amplifiers. We peer at the bright laser spot through strong lenses; shadowy monsters hold the lenses in place.
The quantum measurement problem is a bit like the problem of consciousness. We think we understand subatomic particles and stuff, but we don't have any real idea at all what it means for us to understand anything. We rely in practice on a crude "there's a little sprite in my head" model of consciousness that would have been state of the art in 400 BC. In principle consciousness itself is also a phenomenon of particles and forces, like superconductivity or lasing, which we should be able to understand microscopically. It's just too hard for us to do that, at this point, so we rely on that ancient theory of mind to be a sufficient description of everything that happens up to a human particle physicist pushing the start button. We drop in the modern theory of particles to describe the experiment itself, and then we let it hand back off to the ancient theory when humans interpret the signals. We hope that the joints between crude theories and fine theories don't mess things up too much.
In fact there's no need to drag consciousness into particle physics like that—or particle physics into consciousness. The same kind of handing-off between precise and crude theories happens without even worrying about human beings, when we just hand off from quantum field theory to the crude theory of quantum measurement and our crude understanding of amplifying detectors. All quantum measurement devices rely crucially at some point on some process which is thermodynamically irreversible. Measurement must create entropy. No doubt that's profound, but it's damning, because entropy and thermodynamics are vaguely defined concepts from the 19th century. That's how badly our understanding of quantum measurement is lagging our understanding of fundamental quantum fields themselves.
I definitely do not want to use our ignorance about quantum measurement as a gap in which to hide God. My point is rather that if someone claims to have disproven God with physics, but their claim rests on aspects of our current understanding of quantum measurements, then this is a really shaky claim, even though parts of current physics are really solid. Quantum measurement is a really big weak point.
If you really want to understand quantum mechanics then I really think it's best not to start with particles moving in space, but instead with the much simpler scenario of a bit-world: a radically simplified universe in which there are only two possible cases. Even a single particle in three dimensions is enormously more complicated than that, because a universe that consists of one particle in infinite empty space still has a different possible case for every point in that space (namely the case that the particle is at that point). The bit-world is so simple that you might not think it could be anything more than a dumbed-down teaching example, but in fact it's enough to get you up and running on quantum information theory, and a lot of real current experiments effectively create little bit-worlds by isolating a bit of the world, like the spin of an electron.
And the problem with thinking instead about single particles moving in space is that this is very apt to be profoundly misleading. It's not too hard to get an intuitive picture of a quantum particle as a fuzzy, ripply blob that kind of drifts around in space, like Caspar the Friendly Ghost. And that picture would fit pretty well with a lot of what you can read about quantum mechanics. There's not much going on with just one particle, though. Even for an atom, you need at least two particles. So how do two particles look in quantum mechanics? Two of those ghostly blobs drifting through space?
Nope. They're just one ghostly blob, drifting through six dimensions. With three particles, the fuzzy blob is in 9D. And so on, until there's still just one fuzzy blob for the whole entire universe—fuzzing and drifting in an abstract space of unthinkably many dimensions. The quantum wave function—which is one way of expressing the quantum state vector—does not propagate in space-as-in-three-dimensional-space. It propagates in the abstract space of all possible states of the system. If your system is one particle, then you can label its states with three numbers, (x,y,z). If your system is two particles, then you need six numbers—three for each particle. And so on.
This global-view aspect of quantum mechanics isn't actually special to quantum mechanics. There's a way of formulating good-ol' classical mechanics that is similarly global, with a function in global state-space. The weird new things about quantum mechanics are the simple but strange rules about what changes in time and what it means, and you can learn these weird rules in the simple context of a bit-world; they then extend to high-dimensional spaces straightforwardly. Learning quantum mechanics by learning about fuzzy blobs in 3D space, on the other hand, is a bit like learning Chinese by learning the game of Go, and then imagining that life in China is all about black and white things on a grid.
There are basically an infinite number of possible configurations of the system that would allow Jesus to walk on water at time t (and the number of configurations where he sinks is closer to infinity squared). Of those infinite configurations where he walks on water for that instant, some of them would allow Jesus to walk on water at t + 1. Of that much smaller but still near-infinite set, a subset would allow him to walk on water at t + 2, etc. Your speculation is that there is probably a specific configuration where Jesus wins the lottery 1,000 times in a row, resulting in successfully walking on water for a few seconds. If we could figure out that specific configuration, we could then roll the formulas back in time to come up with an initial configuration that would cause this long series of unlikely events to unfold on cue.
Is that more or less your perspective?
Yes, that's it. Just two comments.
1) The small set of molecular configurations where Jesus wins so many times in a row, with the water molecules, is an awfully tiny fraction of the set of all possible states of the sea of molecules. Every single actual state of the sea, though, is an even tinier fraction of that set. Getting a royal flush in poker isn't harder than getting a jack-high hand because of any repulsive force between kings and aces of the same suit, or anything like that, but just because there are more ways to get jack-high than royal flush. So you have to rig the deck carefully. The water-walking would be a miracle of precise fine tuning, not of actually violating any natural law (probably).
2) The fact that all kinds of weird things could apparently happen for the right initial conditions is not some currently puzzling detail on the fringes of science. It's the Law and the Prophets of science, the core theory within all core theories so far. If human understanding ever closes this loophole, it won't be because science in anything like the form we know it advances, but because history goes from ignorance to science to X, where X is the whole new thing that removes initial conditions. That could happen, but there's no reason to expect it, at this point.
I was a teenager before it was cool.
