[HN Gopher] Schrodinger equation emerges mathematically from cla...
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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?
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