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Reality as a Vector in Hilbert Space

arxiv.org

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Re: Reality as a Vector in Hilbert Space

#41

Post by vlmutolo »

drdeca wrote: post #16

Someone asked in a deleted comment, something along the lines of "Which Hilbert space?", pointing out that a Hilbert space is just a vector space which has an inner product, and is complete under the metric induced by the norm. I wrote a response to this, and while the initial comment was deleted (presumably by the author of the comment), I think my response might still be informative to others who have the same ques…

This question is addressed directly by Griffiths in his “Introduction to Quantum Mechanics”. It’s in a footnote at the beginning of chapter 3, “Formalisms”.

Basically he says that when physicists say “Hilbert space”, they’re actually referring to a specific Hilbert space, namely the set of all square integrable functions, sometimes referred to as “L2”.

Re: Reality as a Vector in Hilbert Space

#42

Post by nabla9 »

linconcr wrote: post #32

Schrödinger equation does not even account for relativistic effects (even though the author pointed out the opposite in the text)... anyone who has read basic texts on philosophy of science knows that this kind of proposition, "it explains reality", is completely "out of reality". it cannot be done by the simple fact that we do not know if any theory will remain as the best explanation for a bunch of experimental fac…

See:

Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space, CJ Cao, SM Carroll - Physical Review D, 2018 https://journals.aps.org/prd/pdf/10.1103/PhysRevD.97.086003

Re: Reality as a Vector in Hilbert Space

#43

Post by xwolfi »

aeneasmackenzie wrote: post #18
nitrogen wrote: post #14

Earlier quoted context omitted.

You should read Anathem or Permutation City some time.

What will he get from Permutation City? It's a work of fiction, entirely supposition.

But it helps you realize there's nothing obvious about reality. We can question everything, even that maybe we're experiencing reality in a time based manner due to a fluke but theres actually no evolution - we're a static map of space time, and us idiots pretend we evolve and change direction.

Re: Reality as a Vector in Hilbert Space

#44

Post by xwolfi »

PeterWhittaker wrote: post #40
afturkrull wrote: post #15

“ .. the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian. The structure of our observed world, including space and fields living within it, should arise as a higher-level emergent description .. ” Wha¿

It's a statement of pure materialism: Nothing exists outside solutions to that equation. All subjective human "artifacts" we struggle to identify, e.g., consciousness, are emergent properties of their material substrates. Souls, if they exist (heh), are subject to the same physical laws as bubbles, sand, and frogs.

Souls? What is this religious idiocy even doing here. There s no if, ofc information doesnt continue to evolve coherently after it's thinking processor disappears.

Why would there be an immortal information processor centered around continuing human thoughts ? So we can debate MAGA politics with Cro-Magnons?

"Souls" psch

Re: Reality as a Vector in Hilbert Space

#46

Post by User23 »

PeterWhittaker wrote: post #40
afturkrull wrote: post #15

“ .. the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian. The structure of our observed world, including space and fields living within it, should arise as a higher-level emergent description .. ” Wha¿

It's a statement of pure materialism: Nothing exists outside solutions to that equation. All subjective human "artifacts" we struggle to identify, e.g., consciousness, are emergent properties of their material substrates. Souls, if they exist (heh), are subject to the same physical laws as bubbles, sand, and frogs.

Emergence is a handwave of colossal proportions that is easily revealed by asking "what is this emergence and where does it come from?" If you're going to be a pure materialist you don't get to just say oh it magically comes from nowhere, you have to show the mechanism. The cellular automata guys can be seen as giving that an intellectually honest shot, but I bet plenty of them are actually dualists anyhow.

Re: Reality as a Vector in Hilbert Space

#47

Post by nine_k »

websitejanitor wrote: post #13

This is idealism getting lost in the sauce to the highest degree. If you ever find yourself thinking "reality is just math", you must remember: the map is not the territory .

Imagine living in a virtual reality and hearing that the reality is just a computation.

Would it be metaphysical? Not really, because it does not speak about anything but the computation which, by construction, is the reality of such universe. It claims no knowledge of the computer implementation details which are mot reflected in the computation, like its power consumption or the color of the chassis, or even the fact that a chassis might exist.

I think that sticking to intuitive and customary notions of reality when experimental data contradict them is not scientific. Science is all about building a better model that fits more and more experimental data points as tightly as possible. If such model introduces notions that the mundane experience entirely lacks, while still describing these mundane phenomena perfectly, it's time to admit that the reality is indeed "weird", and it's your mundane intuitions which are wrong (or, rather, apply narrowly).

Also, the end result of science is the math that fits the experiments, that is, the model of reality, the language of it is math. You can ask whether there's something behind that math, like you might ask whether there's something behind the computations in a virtual reality universe. I assume we can't see past this border with scientific means, only with metaphysical.

Re: Reality as a Vector in Hilbert Space

#49

Post by nitrogen »

websitejanitor wrote: post #29
nitrogen wrote: post #14

Earlier quoted context omitted.

You should read Anathem or Permutation City some time.

I have read Anathem. It's math as occult magic riffing on harry potter.

Pretty much anything can be dismissed with an adlib of the form "It's [boring subject] as [thing I don't like] riffing on [some other thing]." It never captures the nuance, or why X as Y riffing on Z might still be interesting or enlightening.

Re: Reality as a Vector in Hilbert Space

#50

Post by powerset »

hprotagonist wrote: post #4

Arisibalt trudged to the kitchen and busied himself at the keg. "I'd better fortify myself," he explained, to no one in particular, "as I am condemned to spend the remainder of the evening drawing light bubbles."

For some reason most of my comment contributions here are references to N.S. Glad to see I'm not the only one who immediately thought of this.
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