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Reality as a Vector in Hilbert Space
- exdsq 6y agoCan someone try to ELI5 this for me?
- deleted 6y ago[deleted]
- db48x 6y agoThere is a very excellent tutorial on this subject in Anathem, but Neal Stephenson. Great book too; definitely worth reading.
- exdsq 6y agoThanks, I'll check it out!
- Rebelgecko 6y agoJust a heads up, the analog in Anathem is called "Hemn spaces"
- codezero 6y agoThey are attempting to describe physical reality with a single wave equation, and have constructed one with a lot of interesting properties, and their goal is to break the hamiltonian down into independent components to describe physical systems. The system is a finite-dimensioned Hilbert space (but it's large, like, almost infinite, but being finite is an important feature according to the paper) - and each dimension can be described by an energy spectrum, it's that energy which gives rise to physical reality via fields (and the properties that emerge from those fields). They propose basically a needle-in-the-haystack approach to finding mathematical solutions to the individual energy dimensions, I guess.
- newobj 6y agodidn't read it - and certainly wouldn't understand it if i did - but it does gel nicely with my internal pseudoscientific ponderings about the universe. nice! (this is part tongue-in-cheek and part serious; i often wonder: "what if we are simply tumbling along some "existential gravity" in a higher dimension?")
- hprotagonist 6y agoArisibalt 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."
- powerset 6y agoFor 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.
- hprotagonist 6y agoit comes with the username :)
- orphean 6y agoSomeone just finished reading Neal Stephenson’s Anathem...
- krastanov 6y agoThis abstract also describes a central plot point to Greg Egan's "Schild's Ladder".
- codezero 6y agoIs this a, uh, thing that's going around? I'm a physics undergrad who published, and the idea of boson field(s) being the source of all physics has been really top of mind. Maybe it's just a consequence of Higg's being discovered finally.
- deleted 6y ago[deleted]
- raziel2701 6y agoThere's no pictures in the pre-print, how am I supposed to understand this? I need to see what an eigenspectrum looks like!
- deleted 6y ago[deleted]
- websitejanitor 6y agoThis 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.
- nitrogen 6y agoYou should read Anathem or Permutation City some time.
- aeneasmackenzie 6y agoWhat will he get from Permutation City? It's a work of fiction, entirely supposition.
- xwolfi 6y agoBut 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.
- websitejanitor 6y agoI have read Anathem. It's math as occult magic riffing on harry potter.
- nitrogen 6y agoPretty 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.
- ravi-delia 6y agoI may be risking sounding like a fool here, but isn't there kind of a real distinction between saying that there are underlying mathematical patterns in a reality that behaves like a state machine, and saying that literally this function and starting condition are isomorphic to the universe? Like if on a low level it turns out that everything is, I don't know, cellular-automata-based, that would be a more useful frame than wandering vectors in a Hilbert space. But if we get to the end of physics and found that, in fact, you could rederive everything from that one explanation, it wouldn't be unfair to say that the universe is that vector, and perhaps some functions. I guess really I'm wondering if it matters more how the universe is 'computed' or what it's 'computed on'. In a non-simulated universe, of which it seems there must exist at least one, there would at some point just have to be laws without causes. If those laws corresponded to some simple bit of math, it wouldn't be wrong to merge map and territory. edit: That's not to say that I actually think the paper is correct. I'm definitely not far enough along in my education to be 100% sure, but there are enough suspicious features and a high enough bar that I'm doubtful. I just meant to mount a general defense of 'what if it's all math' type explanations.
- afturkrull 6y ago“.. 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¿
- PeterWhittaker 6y agoIt'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.
- xwolfi 6y agoSouls? 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
- User23 6y agoEmergence 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.
- drdeca 6y agoSomeone 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 question. It is as follows: All countably infinite dimensional Hilbert spaces are isomorphically isometric. Pick an orthonormal basis for it, and that gives you an isomorphism with \ell^2(\mathbb{N}) (which preserves the metric). As such, some people will sometimes just refer to "the Hilbert space", to refer to any countably infinite dimensional Hilbert space over the complex numbers. If the Hilbert space in question is countably dimensional, then this is "the" one they mean. I think there are some reasons that some people say one might have to use one with an uncountable dimension? I don't understand these reasons. I think they are connected to quantum field theory? My impression is that it is somewhat controversial whether one with uncountably infinite dimension is ever necessary to model physics. Wikipedia has more to say about this question. Because I don't understand it, you would be better off reading it on wikipedia than reading me trying to summarize something written on Wikipedia which I don't understand. edit : upon actually reading more of the link, I might see why the comment I meant to reply to was deleted : the paper answers their question, saying that the Hilbert space is determined by the dimension. So, my comment is a bit redundant. edit2: 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.
- nonameiguess 6y agoThe paper itself says the dimension of the Hilbert space is e^(e^123), so very big but not infinite, countably or otherwise. That said, I also do not remotely understand this paper. I think I at least grasp the basics of quantum theory itself modeling the very small world as a Hilbert space that collapses to a single real-valued vector upon being measured and the math checks out according to what it predicts and what we actually measure, but after reading this I cannot tell why this should have any consequences for ontology. I think I understand the basic desire physicists have to include an ontology in their theories. Old-school billiard ball physics and even general relativity have very obvious and intuitive analogies to basic geometric objects we can envision. We definitely get a map with the math and at least a clear allusion to the territory by reifying these geometric analogies. With quantum physics, nothing at all comes out as some clear candidate for a territory. So this guy is just going galaxy brain and proposing maybe there is no territory at all and the most ontologically basic thing from which all observable phenomena we actually experience arises is just the math itself. I don't really see a justification in the paper, but that's kind of the nature of philosophy. At the most fundamental level, nothing can be justified.
- byzn7 6y agoGrandiose paper from a joke "scientist". This definitely not science, it's a poorly argued metaphysical proposition.
- optimalsolver 6y agoSean Carroll is a highly respected physicist. Not sure what you're on about.
- mjfl 6y agoI make my experimental apparatus. I send an electron through a double slit. Hilbert space tells me it goes through both, and keeps going through both for all eternity. I only see one flash. The whole of the electron is found to have hit that part of the screen, and nowhere else. This interpretation just kicks the can down the road, to the "emergence of consciousness", in order to explain simple experimental results.
- Diederich 6y agoThe author is https://en.wikipedia.org/wiki/Sean_M._Carroll https://en.wikipedia.org/wiki/Sean_M._Carroll Shortly after Covid19 started last year, he started a series of videos called "The Biggest Ideas in the Universe", playlist here: https://www.youtube.com/watch?v=HI09kat_GeI&list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX https://www.youtube.com/watch?v=HI09kat_GeI&list=PLrxfgDEc2N... I've watched quite a lot of this so-called 'popular' hard science material on youtube, and this series was by far the best I've run across. His approach is a bit different from most others, and his presentation is engaging, approachable but also fairly substantial. Specifically, he doesn't elide all of the relevant math, but doesn't get too deep at the same time. You'll see a lot of integrals, derivatives and graphs. For example, he talks about an hour on the big idea of 'Change', and another "Space". Perhaps even more interesting are the followup Q&A videos, which are as long as and perhaps even more detailed than the source. Do give the linked six minute intro video a watch.
- linconcr 6y agoSchrödinger 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...
- nabla9 6y agoSee: 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 https://journals.aps.org/prd/pdf/10.1103/PhysRevD.97.086003
- memming 6y agoI love the second quote: In Hilbert space, nobody can hear you scream. – Aharonov & Rohrlich (2005)
- jtsiskin 6y agoRelevant XKCD: https://xkcd.com/505/ https://xkcd.com/505/