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The explanation is that there seems to be a mathematical parallel between some wave equation used in quantum physics and the wave equation used in studying weat

The explanation is that there seems to be a mathematical parallel between some wave equation used in quantum physics and the wave equation used in studying weather patterns.

amelius 3y ago
Aren't quantum effects supposed to disappear in the macroscopic world? How is this explained?
- dekhn 3y ago
  https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
- stevenwoo 3y ago
  Not an explanation but the scientist who recognized the analogy of the quantum effect was also a physicist, seeing the parallel between particle movement and the fluid flow along the earth.Then another physicist was able to tweak Maxwell-Chern-Simons equations describing quantum particle movement and show they also applied to fluid flow topologies. It's not explained at all why this is so.
  - dekhn 3y ago
    See https://news.mit.edu/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729 https://news.mit.edu/2013/when-fluid-dynamics-mimic-quantum-... https://news.mit.edu/2014/fluid-systems-quantum-mechanics-0912 https://news.mit.edu/2014/fluid-systems-quantum-mechanics-09... and https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs My favorite is the images in https://thales.mit.edu/bush/wp-content/uploads/2021/04/Bush-AnnRev2015.pdf https://thales.mit.edu/bush/wp-content/uploads/2021/04/Bush-... of their experimental setup; more details in Harris's thesis: https://dspace.mit.edu/handle/1721.1/99068 https://dspace.mit.edu/handle/1721.1/99068
  - fnordpiglet 3y ago
    There are a lot of these things. You can explain water flow using V=IR. A simpler but salient demonstration of how these things can happen https://youtu.be/Z_s3TmYQAuc https://youtu.be/Z_s3TmYQAuc
- lisper 3y ago
  Just because two phenomena are described by similar equations doesn't mean they are driven by the same physical mechanism. Wave equations are ubiquitous in physics. Sound waves. Water waves. There is no connection between any of these and QM.
  - akasakahakada 3y ago
    So wave function is not a part of QM?
    - sidlls 3y ago
      It’s more that wave functions are ubiquitous in all areas of physics. It generally falls out of the fact that we can model tons of stuff with second order differential equations, which often result in models that have oscillator/wave-like behaviors
    - mannykannot 3y ago
      You are mixing up two different (but related) terms. The wave equation is a second-order partial differential equation which has some solutions in the form of waves. A QM wave function is a particular case of a wave equation, yielding a probability amplitude. One significant application of the wave equation in pre-quantum physics occurred when Maxwell was able to derive, from the electromagnetic theory he was developing, a wave equation having solutions in which electromagnetic waves propagate at the speed of light.
  - aeternum 3y ago
    First order differential equations generally govern diffusion where energy spreads out over an area. Second order are often waves where energy propagates but does not diffuse. Is pretty much everything described by those two classes? Any third-order differential equations in physics?
    - defrost 3y ago
      Good question. First & second order covers most cases, third order applications include things with 'jerk', sticky flows through small channels, .. There are other examples offered here: https://www.researchgate.net/post/Are_there_examples_of_third-order_linear_differential_equations_in_physics_or_applied_mathematics https://www.researchgate.net/post/Are_there_examples_of_thir... https://www.quora.com/Why-dont-differential-equations-of-physics-go-beyond-the-second-order https://www.quora.com/Why-dont-differential-equations-of-phy... https://math.stackexchange.com/questions/2167292/are-there-examples-of-third-or-higher-order-linear-differential-equations-in-p https://math.stackexchange.com/questions/2167292/are-there-e...
- blueprint 3y ago
  Quantum effects certainly do not disappear at macro scale. Everything at every scale aside from gravity is directly explained by quantum effects. The reason you don't see many weird things except in certain circumstances is related to 1. decoherence and 2. the wavelength that matter has. But everything is quantum even if you don't see weirdness. Certainty of probability and other "non-quantum" effects still fall within QM. For examples of macro scale quantum effects, see e.g. the Casimir effect and the HBT experiment aka photon bunching. There are many of them and scale doesn't really enter into it whatsoever. The key factor that underlies your question mainly is entanglement.
romusha 3y ago
When you put it that way, the "magic" disappears. Isn't this what category theory seeks? Relationship between distant/different mathematical structures? Whether this equation belongs to the same class with another even though they explain different physics?
ripperoni 3y ago
While it is correct, this oversimplifies the point. The finding was that certain wheather patterns can be modelled better than before by using a quantum physics equation. To further the point: The model of this quantum physics equation is also useful for quantum computers built with superconducting materials. Underlying is the question though, why does this equation apply to the earths wheather? There seem to be parallels in the quantum and "macro" model, like windings of electron and wheather currents. Maybe the right view to modeling the earth is about dynamics as much as it is about topoligical phenomenons. After all, topology is used for solving gravitational problems, too. Then why can the earth can be treated as a topoligical insulator and what implications does this have? Can we learn something from it that can be applied to other wheather phenomenons? Or maybe even to the earths core?
- MikePlacid 3y ago
  > why can the earth can be treated as a topoligical insulator I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about. So - what continuous deformations of Earth are you talking about?
  - deleted 3y ago
    [deleted]
  - zornthewise 3y ago
    [dead]
  - kergonath 3y ago
    That’s a culture difference issue. A topological insulator is a kind of material with specific properties (heavily simplified, that its inside is an electric insulator and its surface is an electric conductor). That’s where the topological aspect comes from. It has nothing to do with topology in mathematics except the name.

The explanation is that there seems to be a mathematical parallel between some wave equation used in quantum physics and the wave equation used in studying weather patterns.

amelius 3y ago

Aren't quantum effects supposed to disappear in the macroscopic world? How is this explained?

dekhn 3y ago
https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
stevenwoo 3y ago
Not an explanation but the scientist who recognized the analogy of the quantum effect was also a physicist, seeing the parallel between particle movement and the fluid flow along the earth.Then another physicist was able to tweak Maxwell-Chern-Simons equations describing quantum particle movement and show they also applied to fluid flow topologies. It's not explained at all why this is so.
- dekhn 3y ago
  See https://news.mit.edu/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729 https://news.mit.edu/2013/when-fluid-dynamics-mimic-quantum-... https://news.mit.edu/2014/fluid-systems-quantum-mechanics-0912 https://news.mit.edu/2014/fluid-systems-quantum-mechanics-09... and https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs My favorite is the images in https://thales.mit.edu/bush/wp-content/uploads/2021/04/Bush-AnnRev2015.pdf https://thales.mit.edu/bush/wp-content/uploads/2021/04/Bush-... of their experimental setup; more details in Harris's thesis: https://dspace.mit.edu/handle/1721.1/99068 https://dspace.mit.edu/handle/1721.1/99068
- fnordpiglet 3y ago
  There are a lot of these things. You can explain water flow using V=IR. A simpler but salient demonstration of how these things can happen https://youtu.be/Z_s3TmYQAuc https://youtu.be/Z_s3TmYQAuc
lisper 3y ago
Just because two phenomena are described by similar equations doesn't mean they are driven by the same physical mechanism. Wave equations are ubiquitous in physics. Sound waves. Water waves. There is no connection between any of these and QM.
- akasakahakada 3y ago
  So wave function is not a part of QM?
  - sidlls 3y ago
    It’s more that wave functions are ubiquitous in all areas of physics. It generally falls out of the fact that we can model tons of stuff with second order differential equations, which often result in models that have oscillator/wave-like behaviors
  - mannykannot 3y ago
    You are mixing up two different (but related) terms. The wave equation is a second-order partial differential equation which has some solutions in the form of waves. A QM wave function is a particular case of a wave equation, yielding a probability amplitude. One significant application of the wave equation in pre-quantum physics occurred when Maxwell was able to derive, from the electromagnetic theory he was developing, a wave equation having solutions in which electromagnetic waves propagate at the speed of light.
- aeternum 3y ago
  First order differential equations generally govern diffusion where energy spreads out over an area. Second order are often waves where energy propagates but does not diffuse. Is pretty much everything described by those two classes? Any third-order differential equations in physics?
  - defrost 3y ago
    Good question. First & second order covers most cases, third order applications include things with 'jerk', sticky flows through small channels, .. There are other examples offered here: https://www.researchgate.net/post/Are_there_examples_of_third-order_linear_differential_equations_in_physics_or_applied_mathematics https://www.researchgate.net/post/Are_there_examples_of_thir... https://www.quora.com/Why-dont-differential-equations-of-physics-go-beyond-the-second-order https://www.quora.com/Why-dont-differential-equations-of-phy... https://math.stackexchange.com/questions/2167292/are-there-examples-of-third-or-higher-order-linear-differential-equations-in-p https://math.stackexchange.com/questions/2167292/are-there-e...
blueprint 3y ago
Quantum effects certainly do not disappear at macro scale. Everything at every scale aside from gravity is directly explained by quantum effects. The reason you don't see many weird things except in certain circumstances is related to 1. decoherence and 2. the wavelength that matter has. But everything is quantum even if you don't see weirdness. Certainty of probability and other "non-quantum" effects still fall within QM. For examples of macro scale quantum effects, see e.g. the Casimir effect and the HBT experiment aka photon bunching. There are many of them and scale doesn't really enter into it whatsoever. The key factor that underlies your question mainly is entanglement.

romusha 3y ago

When you put it that way, the "magic" disappears. Isn't this what category theory seeks? Relationship between distant/different mathematical structures? Whether this equation belongs to the same class with another even though they explain different physics?

ripperoni 3y ago

While it is correct, this oversimplifies the point. The finding was that certain wheather patterns can be modelled better than before by using a quantum physics equation. To further the point: The model of this quantum physics equation is also useful for quantum computers built with superconducting materials. Underlying is the question though, why does this equation apply to the earths wheather? There seem to be parallels in the quantum and "macro" model, like windings of electron and wheather currents. Maybe the right view to modeling the earth is about dynamics as much as it is about topoligical phenomenons. After all, topology is used for solving gravitational problems, too. Then why can the earth can be treated as a topoligical insulator and what implications does this have? Can we learn something from it that can be applied to other wheather phenomenons? Or maybe even to the earths core?

MikePlacid 3y ago
> why can the earth can be treated as a topoligical insulator I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about. So - what continuous deformations of Earth are you talking about?
- deleted 3y ago
  [deleted]
- zornthewise 3y ago
  [dead]
- kergonath 3y ago
  That’s a culture difference issue. A topological insulator is a kind of material with specific properties (heavily simplified, that its inside is an electric insulator and its surface is an electric conductor). That’s where the topological aspect comes from. It has nothing to do with topology in mathematics except the name.