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Why Quantum Mechanics?

scottaaronson.blog

11–20 of 248 posts

Re: Why Quantum Mechanics?

#12
post #6

I've always liked these kinds of questions. Myself, I always wondered why specifically three dimensions. (Please don't start telling me about string theory.)

I wondered that for a long time myself and recently stumbled on what I believe is (or at least is a good candidate for) the correct answer: planetary orbits are stable in three dimensions, but not any other dimensions. The anthropic principle therefore selects for three-dimensional slices/subsets of the wave function.

They're really not stable in two dimensions? Hmm [1], and another answer [2] (mentioned by Hawking apparently) but that's less convincing since there could be a 2D universe with intelligent organisms that just have their digestive systems on the outside...

1. https://www.reddit.com/r/askscience/comments/q8fmo/what_woul...

2. http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Di...

Re: Why Quantum Mechanics?

#13

The answer to these questions is one of those things that are beyond human understanding. It's like asking why does probability work? Why does predicate logic work? They are axioms. We have never looked beyond these axioms nor will we ever in your lifetime. I mean we may find a deeper mathematical model for quantum mechanics but the question of "why?" will never be answered. It may not even be the right question.

Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right?

Not exactly. It's only true in flat euclidean geometry. If General Relativity holds then we're only in a flat spacetime if the total energy content of the universe is in some range of values, otherwise the universe could be the 3d equivalent of a sphere or it could be a hyperbolic shape. In neither of these configurations do right triangles behave the way you learnt in primary school.

So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect.

Re: Why Quantum Mechanics?

#15
post #11

Randomly found a link to this video on super determinism from his blog and found it super interesting. 100% agree, what is 'free will' anyways? A concept with no scientific definition. Why is it even used to explain anything in quantum mechanics? https://www.youtube.com/watch?v=ytyjgIyegDI

I think the question of free will is even simpler. It doesn't come down to determinism vs indeterminism because either way it's not "you" making a decision. At the lowest level (neuron or whatever) when a decision is "made" it is either deterministic (determinism) or probabilistic (indeterminism) based on physics but either way, where is the "you" in the process? Only way free will makes sense is if something supernatural is involved.

Re: Why Quantum Mechanics?

#16
post #6

I've always liked these kinds of questions. Myself, I always wondered why specifically three dimensions. (Please don't start telling me about string theory.)

I wondered that for a long time myself and recently stumbled on what I believe is (or at least is a good candidate for) the correct answer: planetary orbits are stable in three dimensions, but not any other dimensions. The anthropic principle therefore selects for three-dimensional slices/subsets of the wave function.

Actually in 2d they are but there are other problems in 2D. There are actually quite a few special properties of 3D+1

interesting reading https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensio...

Re: Why Quantum Mechanics?

#17
post #6

Earlier quoted context omitted.

I wondered that for a long time myself and recently stumbled on what I believe is (or at least is a good candidate for) the correct answer: planetary orbits are stable in three dimensions, but not any other dimensions. The anthropic principle therefore selects for three-dimensional slices/subsets of the wave function.

They're really not stable in two dimensions? Hmm [1], and another answer [2] (mentioned by Hawking apparently) but that's less convincing since there could be a 2D universe with intelligent organisms that just have their digestive systems on the outside... 1. https://www.reddit.com/r/askscience/comments/q8fmo/what_woul... 2. http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Di...

Right hand rule only works in 3d and 7d

Re: Why Quantum Mechanics?

#18

> why complex values amplitudes? If you multiply the left and right sides of schrodingers equation by its complex conjugate, do you still get an equation that the real valued square of the wave function solves? Can you do QM with just the real valued probability distribution? If you can, why not say that that’s the “real” thing, and factoring it is just a convenient way to solve it, same as imaginary solutions to qua…

> Can you do QM with just the real valued probability distribution?

You can't. The key fact is that other observables, such as momentum, depend on the complex part of the wave function.

Re: Why Quantum Mechanics?

#19
post #11

Randomly found a link to this video on super determinism from his blog and found it super interesting. 100% agree, what is 'free will' anyways? A concept with no scientific definition. Why is it even used to explain anything in quantum mechanics? https://www.youtube.com/watch?v=ytyjgIyegDI

I think the question of free will is even simpler. It doesn't come down to determinism vs indeterminism because either way it's not "you" making a decision. At the lowest level (neuron or whatever) when a decision is "made" it is either deterministic (determinism) or probabilistic (indeterminism) based on physics but either way, where is the "you" in the process? Only way free will makes sense is if something superna…

Physics is based on what can be measured objectively. In other words the probability could be an approximate description of a real (and perhaps knowable) yet un-objectively-measurable process.

The idea "everything that is natural can only be everything we can objectively measure" should be problematic right? Of course whatever out there that is unmeasurable is rife with confusion, messiness, lies etc but that shouldn't mean it doesn't exist at all.

The old confounding variables problem. It's silly to believe there must be none, yet that's what the physics = everything worldview amounts to.

EDIT: I love Scott Aaronson. Of course he predicted this type of answer explicitly and is looking for a more nuanced one :)

Re: Why Quantum Mechanics?

#20
post #11

Randomly found a link to this video on super determinism from his blog and found it super interesting. 100% agree, what is 'free will' anyways? A concept with no scientific definition. Why is it even used to explain anything in quantum mechanics? https://www.youtube.com/watch?v=ytyjgIyegDI

I think the question of free will is even simpler. It doesn't come down to determinism vs indeterminism because either way it's not "you" making a decision. At the lowest level (neuron or whatever) when a decision is "made" it is either deterministic (determinism) or probabilistic (indeterminism) based on physics but either way, where is the "you" in the process? Only way free will makes sense is if something superna…

> At the lowest level (neuron or whatever) when a decision is "made" it is either deterministic (determinism) or probabilistic (indeterminism) based on physics but either way, where is the "you" in the process?

It's a matter of scale. At the highest level, of the individual, if you present them with two options, they will chose one of the options. At that level, the question is a trivial: yes, obviously they have "the capacity [] to choose between different possible courses of action unimpeded."[1] Your description was just an explanation of how they choose. If you then ask if the individuals also have "the capacity to do otherwise"[2] then that depends on whether things are deterministic or probabilistic. If they're probabilistic, then yes, otherwise no.

In all three cases, yours and my two, the question is answered trivially and uninteresting. The real question philosophers are asking, I'm told, is whether people have moral responsibility or not. It's interesting psychologically too, should you really feel guilty if you couldn't have done differently?

1. https://en.wikipedia.org/wiki/Free_will

2. https://plato.stanford.edu/entries/freewill/#FreeDoOthe

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