[HN Gopher] Schrodinger equation emerges mathematically from cla... ___________________________________________________________________ Schrodinger equation emerges mathematically from classical mechanics (2012) Author : pcwelder Score : 97 points Date : 2023-12-22 16:29 UTC (6 hours ago) (HTM) web link (www.researchgate.net) (TXT) w3m dump (www.researchgate.net) | hughw wrote: | I have not yet read the linked paper, but seismologists have used | the Schroedinger wave equation in seismic imaging since at least | the 1970s [1], certainly a "classical" system. | | [1] https://pubs.geoscienceworld.org/geophysics/article- | abstract... | ndsipa_pomu wrote: | Okay, the abstract clearly had english words in there, but I've | got no idea what they mean. Does anyone have an overview that | would make sense to a non-expert? | leeoniya wrote: | Turbo Encabulator? | | https://en.wikipedia.org/wiki/Turbo_encabulator | | https://www.youtube.com/watch?v=Ac7G7xOG2Ag | denton-scratch wrote: | Yup. "Metaplectic" is a new one on me. Wikipedia isn't much | help: | | https://en.wikipedia.org/wiki/Metaplectic_group | lr1970 wrote: | A Big missing part is the wave function and superposition | principle that Classical Physics cannot emulate.The paper is at | best a mathematical curiosity. | aleph_minus_one wrote: | > A Big missing part is the wave function and superposition | principle that Classical Physics cannot emulate. | | I am not a physicist, but doesn't the Schrodinger equation | decribe the wave function? | Racing0461 wrote: | I believe that's that he's saying. thats why we needed the s | equation. | bluish29 wrote: | I don't know if there is a rule about science papers links, but I | think using the journal paper link [1] is more suitable. The | paper is open access, so no need for research gate. | | [https://iopscience.iop.org/article/10.1088/1742-6596/361/1/0...] | JadeNB wrote: | I'd say the gold standard is DOI, though, for many journals, | that's easily derived from the URL: | | https://doi.org/10.1088/1742-6596/361/1/012015 | ben_WG wrote: | The Schrodinger equation emerges from classical mechanics most | closely (well ok that's a bit subjective) from the Hamilton | Jacobi frame work, and it was indeed here that Schrodinger saw, | in hindsight, because in the beginning he pretty much guessed it, | the biggest connection to classical dynamics. This is also | related to the optic-mechanical relation that abstracts mechanics | to the point it becomes comparable to optics. | | Hamilton Jacobi theory: | https://en.m.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equa... | | Optic-mechanical analogy: | https://en.m.wikipedia.org/wiki/Hamilton%27s_optico-mechanic... | | Schrodinger equation from HJ theory: | https://www.reed.edu/physics/faculty/wheeler/documents/Quant... | patcon wrote: | > in the beginning he pretty much guessed it | | Ah, you've given me a thought I'm grateful for. Thanks! | | I'm someone who's had a gut feeling about something in some | random niche of science for several years. I've spent that time | slowly gathering evidence from the literature to validate my | hunch. It feels less like a "guess" and more like a high | dimensional observation (of a form that's hard to cite or trace | origins for) that first needs to be re-grounded in "real | research". | | Though maybe it DID feel like a guess to Schrodinger...! but if | he didn't say it that way, I'd assume it's not quite so | accurate a framing :) though it is an entertaining way to | communicate it, and I appreciate that it lends a sense of | serendipity and happenstance and luck, which is perhaps the | most important thing to telegraph about how science happens... | to take a swing at the false inevitability and certainty that | has its hooks in our histories! | _a_a_a_ wrote: | wat? | i_am_a_squirrel wrote: | I'm guessing mushrooms and/or some sort of stimulant. | mlyle wrote: | Thinking about where ideas come from is valuable. | | This thing that I'm intuiting, but don't have a firm | logical path to prove or explain: | | - Is it actually grounded in subconscious observations of | real things, and things that I'm learning but cannot yet | articulate? | | - Or is it just something that I made up and I'm pursuing | uncritically? | | Being able to tell the difference more of the time saves | a lot of effort. | glompers wrote: | GP is saying that there are hunches that are not ready for | primetime but which are creative thought nonetheless, and | which need to be worked with before they can become | workable. It's a good thought, echoed by quotes from other | designers like Alden Dow, as well as theologians, | scientists, and engineers. Not an encouraging way of | letting GP know you encountered difficulty in engaging the | nonstandard phrasing. GP was trying to discuss the | phenomenon without disclosing his or her hypothesis | directly. | _fizz_buzz_ wrote: | It was a guess in a sense, but a very educated guess. | Schrodinger didn't get lucky, he was hard working, talented | and very educated in his field. He was already one of the | most revered physicist at the time he came up with the | Schrodinger equation. | NotSuspicious wrote: | And in the Christmas spirit, he made his big discovery | while cheating with his wife on a Christmas retreat in | 1925-1926 | | >A few days before Christmas, 1925, Schrodinger, a | Viennese-born professor of physics at the University of | Zurich, took off for a two-and-a-half-week vacation at a | villa in the Swiss Alpine town of Arosa. Leaving his wife | in Zurich, he took along de Broglie's thesis, an old | Viennese girlfriend (whose identity remains a mystery) and | two pearls. Placing a pearl in each ear to screen out any | distracting noise, and the woman in bed for inspiration, | Schrodinger set to work on wave mechanics. When he and the | mystery lady emerged from the rigors of their holiday on | Jan. 9, 1926, the great discovery was firmly in hand. | | https://www.nytimes.com/1990/01/07/books/the-lone-ranger- | of-... | | He was also an admitted pedophile. It is possible that that | "mystery girlfriend" he was with while coming up with his | revolutionary perspective on quantum physics was an | underage girl he was grooming | | https://www.irishtimes.com/life-and-style/people/how- | erwin-s... | | https://www.forbes.com/sites/rebeccacoffey/2022/01/24/schrd | i... | kridsdale1 wrote: | Sounds like a stretch if she was described as "an old | girlfriend" (as in, much time has passed, not that she is | old). But she may have been significantly young in their | first relationship, who knows? | danbruc wrote: | _I 've spent that time slowly gathering evidence from the | literature to validate my hunch._ | | That is most likely the wrong way to go about this, you | should probably look for evidence that your hunch is wrong, | that it is in conflict with established physics. | exe34 wrote: | It can mean the same thing - when I have a hunch I think of | as many ways of shooting it down as possible - but that | often involves predicting something starting from the hunch | and then testing that prediction against nature/existing | literature. I'd still call it "trying to validate this | hunch". | jdewerd wrote: | Right, in fact it's very much "a thing" for bored/retired | engineers (or otherwise physics-adjacent) to guess a new | physics principle and convince themselves that it must be | correct without actually doing the boring and difficult | work of checking it against existing known-good principles | / data and coming up with experiments that prove it to be | usefully differentiated. You know, the difficult parts of | science. | | This is the source of a steady stream of crackpots that | regularly pester the physics community. Don't be one of | them. If your trajectory doesn't include a bunch of | graduate level physics classes, a literature review, and a | big math slog, you are at risk. Existing techniques are | _very_ powerful and you need to know them well before you | know what counts as a genuine addition. | | https://www.youtube.com/watch?v=11lPhMSulSU | i_am_a_peasant wrote: | Meh, I wish I'd had taken the physics path. But life | happened. Too late to change now. Maybe I can at least | make a lot of money by making something useful. | jdewerd wrote: | The fact that physical theory has such good coverage of | everyday circumstances is really tough news if you want | to do physics, but it's excellent news if you want to do | engineering :) | danilor wrote: | If I wanted to know what the community thought of a particular | paper, is there a place where I can find a discussion of it? I | thought maybe researchgate was the place, but I usually don't see | discussion on the paper submission there. I know sometimes you | can find the peer reviewer comments before the paper got | published, but what I mean is comments from other scientists. | bowsamic wrote: | As a physicist, no, that's not a thing, at least not that I | know of. Beyond whatever you can find from a simple google | search is unknown to us | | Best you can do is look for papers that cite this paper. | bjelkeman-again wrote: | So are the only informal discussions done in person, or via | email? | mseri wrote: | Both I'd say. More recently also online | calls/conferences/seminars, and (way more rarely but it | happens) on twitter/mastodon/... | staunton wrote: | Maybe math overflow or physics overflow might work in rare | cases... For most papers, I don't think there's really much a | layperson can actively do to find out what experts think. | leephillips wrote: | Scientists comment on papers by writing papers. For a paper | that just appeared, wait a year or so, and check Google Scholar | for papers that cite this paper. Check again every few months. | | If you know physicists with an interest in this field, you can | ask them if they've seen the paper and what they think of it. | If they have an opinion they'll probably share it with you | freely, but they won't write it down anywhere. | rsp1984 wrote: | I created a platform to solve exactly this problem: | https://gotit.pub/ Let me know if you have any feedback, always | happy to chat! | AndrewKemendo wrote: | https://gotit.pub/view/1e023g4l3o6b3t1f1q625c4g | | I made a link cause I didn't see one via search | throwaway81523 wrote: | physicsforums.com is kind of ok sometimes, though I don't go | there myself. | magicalhippo wrote: | Reminds me of a paper by by Hardy[1] where he introduces five | reasonable axioms (his words). Classical and quantum probability | theory obeys the first four. However the fifth, which states that | there exists continuous transformations between pure states, is | only obeyed by the quantum theory. | | In that sense he argues that quantum theory is in a sense more | reasonable than classical theory. | | There's also an interesting link between this and entanglement[2] | which seems to rule out other probability theories, leaving only | quantum theory able to exhibit entanglement. | | Not my field at all though, just find these foundational things | interesting to ponder. | | [1]: https://arxiv.org/abs/quant-ph/0101012 | | [2]: https://arxiv.org/abs/0911.0695v1 | fsckboy wrote: | isn't it more likely that classical mechanics emerges from the | Schrodinger equation? | monadINtop wrote: | it's not more likely, it just does. If we couldn't re-derive | all known laws of classical mechanics and thermodynamics from | the large scale limit of quantum mechanics, than we would have | rejected quantum mechanics as wrong (or incomplete) decades | ago. | | This paper seeks to show that some of the mathematical | framework of quantum mechanics "pops out" of some intuitive | (depends on your perspective i guess) machinery from classical | mechanics. It doesn't really mean much fundamentlly, and | doesn't really reflect the historical derivations of the | equations, but it is interesting to look in retrospect how | readily some of these equations pop out from seemingly basic | frameworks. | | Its also interesting to consider the actual historical | discovery of these concepts, or any scientific concept that | generalised existing theories to a far deeper and more unifying | result (e.g classical -> quantum mechanics, newtonian mechanics | -> general relativity). You are required to somehow develop a | theory that not only extends beyond horizons currently seen, | but also one that correctly replicates the theory it seeks to | supercede. Its like a literary character trying to write the | story it is embedded in. | | Of course, there are always hints to the keen observer, | especially tucked away at the foundations: much of special | relativity unravelled itself directly from the laws of | electromagnetics, since in the equation the speed of light is | never specified, and the naive galilean assumption that | everyone made - that time and space are absolute speeds must be | specified relative to observers - was the veil obscuring our | vision. If you take the courage to abandon the absoluteness of | time and space, and to declare that the speed of light doesn't | need to be specified in terms of some preferred reference | frame, since the speed of light is invariant for all observers | everywhere throughout all of space an time, the intractable | gulfs seperating what we know from what we don't vanish like a | mirage, and meld together naturally into a more fundamental | unified theory. | | And we can take the same step again, by noticing the strange | coinicdence that in Newton's theory of gravitation and | mechanics, the inertial mass happens to exactly equal the | gravitational mass, magically cancelling each others | contribution. If we declare that these two phenomena are infact | exactly the same, and we realise that the apparant difference | between somebody accelerating and somebody falling is an | illusion, obscuring the fact that both are simply bodies taking | the shortest path through the warped 4-dimensional manifold of | spacetime, we once again unify all of our observations into a | stunningly elegant, geometric theory of immense power. | danbruc wrote: | Not a physicist and only read the abstract, but that does not | sound right. One frequently hears that one can recover classical | mechanics from quantum mechanics in the limit of Planck's | constant becoming zero but not even that seems to be [completely] | true [1] as a quick search shows. The other way around, as this | paper claims, seems even more unlikely. As they mention a couple | of mathematical tools that went into this analysis, maybe they | accidentally introduced the relevant differences between | classical and quantum mechanics with them. Or maybe just reading | the abstract is not good enough and they claim something | different than what I think they claim after reading the | abstract. If they actually claim that one can recover important | aspects of quantum mechanics from classical mechanics without | introducing additional concepts or assumptions, then I am highly | skeptical. | | [1] | https://physics.stackexchange.com/questions/32112/classical-... | alecst wrote: | Schrodinger's reasoning was remarkable. | | The high-level description of classical mechanics was formulated | by Hamilton, who was starting from optics. He saw a mathematical | analogy between the equations for light and the equations for | mechanics. The principle of least time (Fermat's principle) for | light became the principle of least action for mechanics. | | But the principle of least time does not predict diffraction, | just the geometric path of a light ray. It fails when the | wavelength of the light is large compared to whatever it's | interacting with. | | At the time, the equations for mechanics were clearly failing for | small systems. Here's where Schrodinger had his incredible | insight: what if mechanics broke in _the same way_ as optics? | Could matter itself display a kind of "diffraction" when its | "wavelength" was similar in size to the objects it was | interacting with? Could this explain the success of de Broglie's | work, which treated small particles like waves? | | The Schrodinger equation followed right after that. | | It's worth reading the original paper if you have a physics | background -- probably grad-level (just being realistic.) I've | been wanting to write a blog post about this because the physics | lore is something like "Schrodinger just made a really good | guess" but that totally undersells the depth of his reasoning. | ahartmetz wrote: | Yeah, I've been taught that Schrodinger basically made a guess | as well... Very interesting how it really happened. | transfire wrote: | Is my impression correct -- if you introduce fundamental | (quantized) randomness, classic physics turns into quantum | physics. Or is that an over simplification? ___________________________________________________________________ (page generated 2023-12-22 23:00 UTC)