6 ms·

That would indeed by very unnatural. Fortunately that's nothing like what the Schrödinger equation says. The basics of quantum mechanics are: 1. Any system ca

by wnoise 6y ago

That would indeed by very unnatural. Fortunately that's nothing like what the Schrödinger equation says. The basics of quantum mechanics are: 1. Any system can be described in a linear "state space", whose basis vectors (roughly speaking) are each possible arrangement of the things being described (every thing's location). However, all possible states include (complex) linear combinations of these. This is usually described as the "wave function", you can plug in any value for coördinates of all your things and get a number back out. 2. States in a closed system evolve according to the (time-dependent) Schrödinger equation, -i h-bar d/dt (state) = E(state). This is sometimes phrased as "energy is the generator of time translation" (note that this phrasing holds true in the Hamiltonion formulation of classical mechanics too, but with different, related meanings). Actually calculating this can be difficult, and you might need to do various tricks such as decomposing in a convenient basis. No all-encompasing energy field binding and penetrating us needed, though the equation is non-local in the sense that it could depend on the entire world. (In fact, it's quasi-local in practice; energy is usually just a function of where things are (local), and how different that coefficient is on infinitesimally adjacent states (i.e. spacial derivatives of the wavefunction). But this does let changes propagate at any speed, including faster than light. Basic QM is not Einsteinian relativistic. It is perfectly Galilean relativistic in a very nice way though.) 3. If you measure a system, you're going to get results that are probabilistic with the probabilities proportional to the (absolute value of) the square of this wavefunction. After that, the state is reset to whay you measured, and evolution will proceed according to 2.

wizzwizz4 6y ago
You can actually skip 2, if you model yourself as part of the system as well (i.e. have an Ideal Observer who changes from “has XYZ knowledge of the system” to “observed ABC about the system” for all possible ABC, with respective amplitudes) – but then you're doing a lot of computation you're never going to use for prediction. (It's more elegant, though – even more so if you model yourself as a human, though this'll take more computational power than we have.)
- wizzwizz4 6y ago
  I meant skip 3. Skipping 2 is like making a laptop without a processor.
bollu 6y ago
And why is this "natural"? I find the collapse to be the strangest axiom, the rest I can handle.
- SiempreViernes 6y ago
  Well one definition of "natural" could be that it "came from nature", and as the Schrödinger equation perfectly describes non-relativistic events in nature arguably it came from nature just as much as newtons laws of motion. Another measure of naturalness is "simplicity", and the Schrödinger equation is a fairly simple expression. You might argue that it's results don't feel very intuitive, and therefore it is not natural. But then I why you think its intuitive that levers work.
- jfengel 6y ago
  Collapse isn't actually an axiom. It doesn't appear in the Schroedinger Equation at all. It comes in when you treat the measurement apparatus as separate from the thing being measured. When you do that, collapse flows naturally from that assumption. It's a valid approach, and very useful, but many people find it philosophically awkward. An approach that's philosophically easier, but less pragmatic, is to treat the masurement apparatus as part of the system. Now you've got one single enormous quantum system. The math of that is far too complex to actually run, and more importantly, too enormous to hold itself in an unstable equilibrium. It must fall into a more stable equilibrium. The tricky part is when there's more than one stable state. The measurement apparatus exists in both of those states, and returns opposite results. The states are in local equilibria, and don't exchange significant amounts of state with each other. You can call that "splitting universes", if you want, though I think that's needlessly messianic. Like the first one, it's perfectly valid. And pragmatically it acts just like collapse. There's a philosophical question about whether the other states "actually exist but can't be reached" or "don't exist at all since we can't prove it except by inference from the fact that this one exists and follows the Schroedinger Equation so closely". That's "philosophical" in the sense that there is no physical difference between the two, but just one of your mental model. That's a lot of words; sorry about that. But the point is that you don't need a collapse axiom, and if you choose to add one, it's not strange.

by wnoise 6y ago

wizzwizz4 6y ago

You can actually skip 2, if you model yourself as part of the system as well (i.e. have an Ideal Observer who changes from “has XYZ knowledge of the system” to “observed ABC about the system” for all possible ABC, with respective amplitudes) – but then you're doing a lot of computation you're never going to use for prediction. (It's more elegant, though – even more so if you model yourself as a human, though this'll take more computational power than we have.)

wizzwizz4 6y ago
I meant skip 3. Skipping 2 is like making a laptop without a processor.

bollu 6y ago

And why is this "natural"? I find the collapse to be the strangest axiom, the rest I can handle.

SiempreViernes 6y ago
Well one definition of "natural" could be that it "came from nature", and as the Schrödinger equation perfectly describes non-relativistic events in nature arguably it came from nature just as much as newtons laws of motion. Another measure of naturalness is "simplicity", and the Schrödinger equation is a fairly simple expression. You might argue that it's results don't feel very intuitive, and therefore it is not natural. But then I why you think its intuitive that levers work.
jfengel 6y ago
Collapse isn't actually an axiom. It doesn't appear in the Schroedinger Equation at all. It comes in when you treat the measurement apparatus as separate from the thing being measured. When you do that, collapse flows naturally from that assumption. It's a valid approach, and very useful, but many people find it philosophically awkward. An approach that's philosophically easier, but less pragmatic, is to treat the masurement apparatus as part of the system. Now you've got one single enormous quantum system. The math of that is far too complex to actually run, and more importantly, too enormous to hold itself in an unstable equilibrium. It must fall into a more stable equilibrium. The tricky part is when there's more than one stable state. The measurement apparatus exists in both of those states, and returns opposite results. The states are in local equilibria, and don't exchange significant amounts of state with each other. You can call that "splitting universes", if you want, though I think that's needlessly messianic. Like the first one, it's perfectly valid. And pragmatically it acts just like collapse. There's a philosophical question about whether the other states "actually exist but can't be reached" or "don't exist at all since we can't prove it except by inference from the fact that this one exists and follows the Schroedinger Equation so closely". That's "philosophical" in the sense that there is no physical difference between the two, but just one of your mental model. That's a lot of words; sorry about that. But the point is that you don't need a collapse axiom, and if you choose to add one, it's not strange.