14 ms·

Chaotic gravitational systems and their irreversibility to the Planck length

77 points by seventhtiger 3y ago

seventhtiger 3y ago
Does having inherently unpredictable phenomena have philosophical implications?
- widea 3y ago
  The variation of philosophical implications are possibly unpredictable by themselves...
  - richardfey 3y ago
    Ha! Gödel would be so proud of this conjecture
- jbotz 3y ago
  Certainly. One of the most fundamental philosophical questions is about the nature of time, precisely because all of our "laws" of physics are time reversible, so from the perspective of physics time doesn't really exist or is just a space-like dimension (no arrow). And so the Universe should be perfectly deterministic and with enough computing power and precise enough knowledge of the initial conditions everything should be perfectly predictable and the future should be "fixed". In some way or another probably most of philosophy is arguing about whether or not this is true and what it means. This paper claims that 5% of 3-body systems in the Universe can't be predicted even in principle, because you would need to measure initial conditions to greater precision than the planck length, which is impossible. And of course N-body systems where N > 3 are even more unpredictable, and the whole of the Universe is an N-body system, so if correct it would mean the end of determinism. For a good treatment of this topic for a lay audience see Lee Smolin's recent book "Time Reborn".
  - lordfrito 3y ago
    > And of course N-body systems are even more unpredictable, and the whole of the Universe is an N-body system, so if correct it would mean the end of determinism. I read this as the systems are, for all intents and purposes, practically unpredictable, not fundamentally unpredictable. Just because we can't measure beyond the plank length doesn't mean there aren't deterministic rules down there. So my take is that the universe could still be deterministic, but that can't be knowable to us since we'd have to be able to peer below the plank length. Maybe I'm reading this wrong.
    - nine_k 3y ago
      "Fundamentally"as in "QM forbids this". If our universe were different, a simpler kind which Laplace dealt with, it could be completely predicable, as theories of 18th century stated.
      - simonh 3y ago
        I think an appeal to quantum mechanics is a different argument from the one under discussion, which is based on discrete physics.
        TheOtherHobbes 3y ago
        It's a different view of the same problem.
        mannykannot 3y ago
        I'm not sure it is a different argument, given its dependence on the Planck length.
    - layer8 3y ago
      Indeed. The evolution of the universal wave function as described by the Schrödinger equation is perfectly deterministic. If you believe in that as the fundamental description of reality (which also means not believing in wave-function collapse), the result is the many-worlds interpretation of QM. Similarly, hidden-variable theories are deterministic.
- daxfohl 3y ago
  See Norton's Dome as an example of nondeterministic behavior in classical mechanics. No quantum or chaos etc required. https://en.m.wikipedia.org/wiki/Norton%27s_dome https://en.m.wikipedia.org/wiki/Norton%27s_dome
  - tsimionescu 3y ago
    Note that this is not an actual physical experiment - it only works with an infinitely accurate and smooth shape of the dome, which contradicts all of the models of how matter exists at least since the ancient greeks. Any dome made up of atoms, even if arranged perfectly accurately up to the position of each individual atom, does not exhibit any kind of non-deterministic behavior in classical mechanics.
mikewarot 3y ago
It's also possible that inertia is quantized[1], which further complicates things. There is an experiment launching soon which may offer some evidence either way. [1] https://physicsfromtheedge.blogspot.com https://physicsfromtheedge.blogspot.com
- seventhtiger 3y ago
  Maybe the universe is digital after all.
  - layer8 3y ago
    Quantization does not imply discreteness: https://physics.stackexchange.com/questions/206790/difference-between-discretization-and-quantization-in-physics https://physics.stackexchange.com/questions/206790/differenc...
    - finite_depth 3y ago
      To give a concrete example, a free particle can have any energy it likes - it's only bound states that have discrete spectra. Mathematically, this corresponds to solutions to a particular differential equation existing for particular values of energy (which appears as a constant in the equation). To use a simpler DE for an example: dx/dt = kx has solutions Ce^kt for all k, but a more complicated DE might only have solutions for some k.
    - mjburgess 3y ago
      And neither alone imply computable (or 'digital'). You'd need determinism. Some reply was (improperly?) flagged, but computability requires determinism. All computable functions are functions from the integers to the integers
      - MrRolleyes 3y ago
        [dead]
      - 3y ago
mjburgess 3y ago
> we conclude that up to 5 per cent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable. Hence, incidentally, classical physics is itself non-deterministic and non-computable.
- AnotherGoodName 3y ago
  Feels like it's just another way quantum mechanics non determinism bubbles up into the larger world. So not that all that insightful right?
  - mjburgess 3y ago
    I don't think it requires any QM to see. I used to have an argument that you could derive non-determinism from the resolution to Zeno's paradox, but i've forgot the steps. Roughly, you need to measure infinitely precisely to give an infinitely precise value to a variable. Via Zeno, continuous time precludes infinite measurement precision (there are no 'moments') and hence infinite precision in measurement. All chaos is doing here is giving us a bound on the actual lack of precision reality has -- I take it, via a zeno-ish argument above, that reality has to have such a bound. Relevantly, none of this requires any reasoning from QM premises or observations. This paper adds-to-the-pile cases where (classical) chaotic systems require measurement beyond-possible spatio-temporal resolution to be deterministic.
    - daxfohl 3y ago
      Classical mechanics does have nondeterministic cases even without appeals to mathematical paradoxes. See https://en.m.wikipedia.org/wiki/Norton%27s_dome https://en.m.wikipedia.org/wiki/Norton%27s_dome as the most well-known example.
      - mjburgess 3y ago
        It's unclear whether that's a concequence of poorly specified premises of the classical mathematical framework. Here, I mean that 'classical reality' as specified in a framework of basic applied mathematics, with no QM premises, produces non-determinism -- via only showing that (classical) chaotic systems exist

77 points by seventhtiger 3y ago

seventhtiger 3y ago

Does having inherently unpredictable phenomena have philosophical implications?

widea 3y ago
The variation of philosophical implications are possibly unpredictable by themselves...
- richardfey 3y ago
  Ha! Gödel would be so proud of this conjecture
jbotz 3y ago
Certainly. One of the most fundamental philosophical questions is about the nature of time, precisely because all of our "laws" of physics are time reversible, so from the perspective of physics time doesn't really exist or is just a space-like dimension (no arrow). And so the Universe should be perfectly deterministic and with enough computing power and precise enough knowledge of the initial conditions everything should be perfectly predictable and the future should be "fixed". In some way or another probably most of philosophy is arguing about whether or not this is true and what it means. This paper claims that 5% of 3-body systems in the Universe can't be predicted even in principle, because you would need to measure initial conditions to greater precision than the planck length, which is impossible. And of course N-body systems where N > 3 are even more unpredictable, and the whole of the Universe is an N-body system, so if correct it would mean the end of determinism. For a good treatment of this topic for a lay audience see Lee Smolin's recent book "Time Reborn".
- lordfrito 3y ago
  > And of course N-body systems are even more unpredictable, and the whole of the Universe is an N-body system, so if correct it would mean the end of determinism. I read this as the systems are, for all intents and purposes, practically unpredictable, not fundamentally unpredictable. Just because we can't measure beyond the plank length doesn't mean there aren't deterministic rules down there. So my take is that the universe could still be deterministic, but that can't be knowable to us since we'd have to be able to peer below the plank length. Maybe I'm reading this wrong.
  - nine_k 3y ago
    "Fundamentally"as in "QM forbids this". If our universe were different, a simpler kind which Laplace dealt with, it could be completely predicable, as theories of 18th century stated.
    - simonh 3y ago
      I think an appeal to quantum mechanics is a different argument from the one under discussion, which is based on discrete physics.
      - TheOtherHobbes 3y ago
        It's a different view of the same problem.
      - mannykannot 3y ago
        I'm not sure it is a different argument, given its dependence on the Planck length.
  - layer8 3y ago
    Indeed. The evolution of the universal wave function as described by the Schrödinger equation is perfectly deterministic. If you believe in that as the fundamental description of reality (which also means not believing in wave-function collapse), the result is the many-worlds interpretation of QM. Similarly, hidden-variable theories are deterministic.
daxfohl 3y ago
See Norton's Dome as an example of nondeterministic behavior in classical mechanics. No quantum or chaos etc required. https://en.m.wikipedia.org/wiki/Norton%27s_dome https://en.m.wikipedia.org/wiki/Norton%27s_dome
- tsimionescu 3y ago
  Note that this is not an actual physical experiment - it only works with an infinitely accurate and smooth shape of the dome, which contradicts all of the models of how matter exists at least since the ancient greeks. Any dome made up of atoms, even if arranged perfectly accurately up to the position of each individual atom, does not exhibit any kind of non-deterministic behavior in classical mechanics.

mikewarot 3y ago

It's also possible that inertia is quantized[1], which further complicates things. There is an experiment launching soon which may offer some evidence either way. [1] https://physicsfromtheedge.blogspot.com https://physicsfromtheedge.blogspot.com

seventhtiger 3y ago
Maybe the universe is digital after all.
- layer8 3y ago
  Quantization does not imply discreteness: https://physics.stackexchange.com/questions/206790/difference-between-discretization-and-quantization-in-physics https://physics.stackexchange.com/questions/206790/differenc...
  - finite_depth 3y ago
    To give a concrete example, a free particle can have any energy it likes - it's only bound states that have discrete spectra. Mathematically, this corresponds to solutions to a particular differential equation existing for particular values of energy (which appears as a constant in the equation). To use a simpler DE for an example: dx/dt = kx has solutions Ce^kt for all k, but a more complicated DE might only have solutions for some k.
  - mjburgess 3y ago
    And neither alone imply computable (or 'digital'). You'd need determinism. Some reply was (improperly?) flagged, but computability requires determinism. All computable functions are functions from the integers to the integers
    - MrRolleyes 3y ago
      [dead]
    - 3y ago

mjburgess 3y ago

> we conclude that up to 5 per cent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable. Hence, incidentally, classical physics is itself non-deterministic and non-computable.

AnotherGoodName 3y ago
Feels like it's just another way quantum mechanics non determinism bubbles up into the larger world. So not that all that insightful right?
- mjburgess 3y ago
  I don't think it requires any QM to see. I used to have an argument that you could derive non-determinism from the resolution to Zeno's paradox, but i've forgot the steps. Roughly, you need to measure infinitely precisely to give an infinitely precise value to a variable. Via Zeno, continuous time precludes infinite measurement precision (there are no 'moments') and hence infinite precision in measurement. All chaos is doing here is giving us a bound on the actual lack of precision reality has -- I take it, via a zeno-ish argument above, that reality has to have such a bound. Relevantly, none of this requires any reasoning from QM premises or observations. This paper adds-to-the-pile cases where (classical) chaotic systems require measurement beyond-possible spatio-temporal resolution to be deterministic.
  - daxfohl 3y ago
    Classical mechanics does have nondeterministic cases even without appeals to mathematical paradoxes. See https://en.m.wikipedia.org/wiki/Norton%27s_dome https://en.m.wikipedia.org/wiki/Norton%27s_dome as the most well-known example.
    - mjburgess 3y ago
      It's unclear whether that's a concequence of poorly specified premises of the classical mathematical framework. Here, I mean that 'classical reality' as specified in a framework of basic applied mathematics, with no QM premises, produces non-determinism -- via only showing that (classical) chaotic systems exist