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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

#31

Post by rrmm »

websitejanitor wrote: post #27
rrmm wrote: post #23

Earlier quoted context omitted.

Right, but his whole point is to defend the idea of saying, "what if the math is the reality, what happens then?" It's sort of the same jump that pushed QM forward in the first place of discarding all the assumptions about particles and orbits and just went purely to what was necessary directly in the math. In the paper he advocates going farther and saying, there's no independent "space" just the vector and space(ti…

>what if the math is the reality, what happens then? Magic. Reversing the relationship between reality and our interpretation of it literally means bending reality with ideas. In this case magic is matrix multiplication.

Yeah. I think the downside is that you end up even further into the "shut-up and compute" paradigm of physics that we are already in.

But if you get predictions from the theory that turn out to be true in the end (like entanglement, Bell's inequality, etc) then it gives you a lot of confidence in your theory.

I don't know how it'll turn out. At this point people are throwing stuff against the wall to see what sticks to get physics out of the local minima it seems to have found itself in.

I don't think Carroll or anyone else is naively wandering into this endeavor from a philosophical standpoint though.

Re: Reality as a Vector in Hilbert Space

#32

Post by linconcr »

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 facts in the future (in a way, the equation mentioned did not predict even spin or antiparticles). there is just no way to prove this, it is a futile and useless exercise of futurology masked as complex linguistic mumbo-jumbo and not at all impressive physics knowledge...

Re: Reality as a Vector in Hilbert Space

#33

Post by Rebelgecko »

exdsq wrote: post #12
db48x wrote: post #9

Earlier quoted context omitted.

There is a very excellent tutorial on this subject in Anathem, but Neal Stephenson. Great book too; definitely worth reading.

Thanks, I'll check it out!

Just a heads up, the analog in Anathem is called "Hemn spaces"

Re: Reality as a Vector in Hilbert Space

#34

Post by bjornsing »

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…

> Oh, and, furthermore, the article says that in a bounded region, we have reason to expect the dimension of the space to be finite dimensional? This surprises me.

Does it? Iirc a classic basis for a countably infinite Hilbert space is a Fourier series. If you have a finite space to describe, and a maximum frequency you need to represent (which I would say is reasonable to assume), then you only need a finite dimensional space.

Re: Reality as a Vector in Hilbert Space

#35

Post by ks1723 »

rrmm wrote: post #31
websitejanitor wrote: post #27

Earlier quoted context omitted.

>what if the math is the reality, what happens then? Magic. Reversing the relationship between reality and our interpretation of it literally means bending reality with ideas. In this case magic is matrix multiplication.

Yeah. I think the downside is that you end up even further into the "shut-up and compute" paradigm of physics that we are already in. But if you get predictions from the theory that turn out to be true in the end (like entanglement, Bell's inequality, etc) then it gives you a lot of confidence in your theory. I don't know how it'll turn out. At this point people are throwing stuff against the wall to see what sticks…

I fully agree to the last point. He had (and probably/hopefully continues to have) very interesting discussions on all kinds of topics ranging from physics to biology to philosophy to psychology to social topics to ... in his mindscape podcast https://www.preposterousuniverse.com/podcast/

Re: Reality as a Vector in Hilbert Space

#36

Post by morpheos137 »

mayagerard0 wrote: post #28
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 .

Sure, but I think the analogy breaks down in this case.Here the map contains precisely the same amount of information as the territory, no reduction of dimensionality,no loss of resolution. Everything that can be said of the territory can be said of the map and we're left with a case in which the only unique non-shared property of the territory is "physical existence", whatever that is.

Yeah imagine instead of a map you have a 3d model of space time. At a certain degree of granularity the model becomes isomorphic to "reality."

Re: Reality as a Vector in Hilbert Space

#37

Post by strogonoff »

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 .

> If you ever find yourself thinking "reality is just math", you must remember: the map is not the territory.

What makes you think your perception of reality is not the map in this dichotomy?

Re: Reality as a Vector in Hilbert Space

#39

Post by drdeca »

bjornsing wrote: post #34
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…

> Oh, and, furthermore, the article says that in a bounded region, we have reason to expect the dimension of the space to be finite dimensional? This surprises me. Does it? Iirc a classic basis for a countably infinite Hilbert space is a Fourier series. If you have a finite space to describe, and a maximum frequency you need to represent (which I would say is reasonable to assume), then you only need a finite dimensi…

I guess the maximum frequency is the surprising thing to me?

Idk, I guess I thought maybe the limited information was, not really limiting the dimension?

Or, maybe I thought because of no clean objective separation between the observable universe, and the rest of it, that that would cause an issue? Not really sure what I was thinking.

I guess it makes sense that it would be finite dimensional.

Hm, actually, I am confused about what counts as the observable universe. Is it that which is in our past light cone, or, that which is in a future light cone of our past light cone, or?

Also, there’s the issue of time in different reference frames. If the state of the observable universe, is supposed to be given by a vector in the same Hilbert space at each time t, uh, well, that appears to depend on the reference frame. Like, the points in space time that are “simultaneous” depends on the reference frame.

So, a vector which describes the state of the universe in a given time slice in a given reference frame, I don’t see how it would also describe it for a different reference frame.

Re: Reality as a Vector in Hilbert Space

#40

Post by PeterWhittaker »

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.

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