[HN Gopher] Alternative interpretations of classical physics (2019)
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Alternative interpretations of classical physics (2019)
Author : JPLeRouzic
Score : 91 points
Date : 2021-03-23 09:44 UTC (13 hours ago)
(HTM) web link (journals.aps.org)
(TXT) w3m dump (journals.aps.org)
| prof-dr-ir wrote:
| Classical Mechanics is a well-defined mathematical framework.
| Consequently, the word 'determinism' when applied to classical
| mechanical systems has a sharp meaning. For example, the dynamics
| of a finite set of point masses with a smooth potential function
| is 'deterministic' in the sense that there are mathematical
| theorems proving that initial conditions can be uniquely evolved
| forward for some finite amount of time.
|
| The paper wants to argue for general non-determinism, but can
| only do that by changing the definition of determinism to
| something more fuzzy. It then proposes a new set of mathematical
| axioms to incorporate this definition, but the question that the
| paper does not answer is whether all this _buys_ us anything or
| not. I think that any reasonable physicist would say that there
| is nothing foundational left to do for classical mechanics purely
| in itself, so it must be that possible applications can only lie
| in the search for a more fundamental theory of nature.
|
| But then I am very pessimistic. We understand quite well how
| classical mechanics arises as a limit from quantum mechanics,
| which in turn emerges from relativistic quantum field theories.
| Together with general relativity, it is the latter that are the
| most fundamental (experimentally confirmed) theories. Therefore,
| trying to uproot the mathematics of classical mechanics feels
| like starting completely at the wrong end to me.
| rrmm wrote:
| In the abstract, the authors say
|
| """ Building on recent information-theoretic arguments showing
| that the principle of infinite precision (which translates into
| the attribution of a physical meaning to mathematical real
| numbers) leads to unphysical consequences, we consider possible
| alternative indeterministic interpretations of classical
| physics
|
| """
|
| which seems to be the jumping off point to disregard strict
| determinism in that sense. So I guess it'd buy you out of the
| unphysical consequences.
|
| Don't have aps access though so I can't say more (probably
| couldn't even with aps access :D)
| kurthr wrote:
| Agreed. One of the first things I learned early in Physics was
| to choose your model wisely. There are many models, some will
| be accurate for the problem you are solving, while others will
| not (or will not be tractable). Often a simplification (simple
| harmonic oscillation, thermodynamics, etc) gives excellent
| insight and results, and in others a change of perspective
| (lagrangian dynamics, state-space) are helpful. Although there
| are cases strikingly close to Classical (photon optics, charge
| quantization, etc) where quantum effects become significant and
| useful, they are rare. It is mostly in the realm of (sub)atomic
| and interstellar where obviously quantum and relativistic
| effects (other than magnetism) become necessary to consider.
|
| As much as I dream of understanding the non-local modifications
| necessary for quantum gravity, it doesn't seem like inserting
| non-determinism into classical physics has many useful effects
| (hah, showing I'm an engineer at heart!). I know that a lot of
| pop-sci goes into understanding "reality" and wave-function
| collapse, but I find Scott Aaronson's take on the difficulty of
| over-interpretation more seriously.
|
| https://www.scottaaronson.com/blog/?p=5359
| johndoe42377 wrote:
| > Physics without determinism
|
| What does this even mean? The whole universe and life itself are
| possible precisely because there is determinism, which is
| captured in what we call logic, (and arithmetic).
|
| Sects, fucking sects everywhere.
| mseepgood wrote:
| The universe and biology are stochastic.
| johndoe42377 wrote:
| Oh, really? Molecular biologists and Pfizer scientists would
| disagree.
| tsimionescu wrote:
| The turn of phrase is probably bad, but determinism can exist
| even in a fundamentally undeterministic universe. All that is
| required for the universe to be undetermimistic is for SOME
| events to lack a cause. For example, a universe in which once
| every billion years a particle appears out of thin air
| somewhere in the universe and flies off in a random direction
| is, on the whole, non-deterministic, even if every other
| interaction works according to simple mechanistic rules.
| Garlef wrote:
| What I dislike about clickbaity paper titles like this is the
| following:
|
| Using a general term like "determinism" in the title of a paper
| might be fine for an expert audience: They will know that the
| paper deals with a specific definition inside a specific
| discussion.
|
| But the general public will pick up on this and incorporate it
| into their superstitions. In the end this could (indirectly,
| through a funnel of regurgitations) strengthen some persons
| believe in pseudoscience resulting in them not vaccinating their
| kids or treating cancer with homeopathy because "everything is
| connected on the quantum level".
|
| Scientists should be more responsible with the choice of their
| titles.
|
| I think adding a discriminatory suffix to terms like
| "determinism" would provide a solution. Something like "Physics
| without infinite precision determinism: [...]" is much less
| likely to be misinterpreted.
| magicalhippo wrote:
| Published in 2019.
|
| Requires subscription, preprint is here:
| https://arxiv.org/abs/1909.03697
| magicalhippo wrote:
| Seems this paper was cited by this[1] Quanta article which was
| discussed here[2].
|
| [1]: https://www.quantamagazine.org/does-time-really-flow-new-
| clu...
|
| [2]: https://news.ycombinator.com/item?id=22848766
| ceceron wrote:
| I've been always taught that classical (Newtonian) physics
| doesn't have to be interpreted as deterministic. However, the
| reason was simpler than the lack of the "infinite precision".
| Basically, some classical systems can have several solutions,
| e.g. the famous Norton's dome
| https://en.wikipedia.org/wiki/Norton%27s_dome .
| leephillips wrote:
| Norton's dome is intriguing; other departures from determinism
| in classical physics include "space invaders": in some many-
| particle systems a particle can develop an infinite velocity,
| which sends it "out of world"; then time reversibility means it
| can enter the world unpredictably. I mention both of these in
| an article about unsolved problems in classical physics:
| http://arstechnica.com/science/2014/08/the-never-ending-conu...
| jayd16 wrote:
| >which sends it "out of world"
|
| Wouldn't any system have to include this "out of world"
| particle? Doesn't its inclusion mean "the world" simply grows
| at that infinite rate?
| cozzyd wrote:
| At least a few of these seem to be cases where the concept of
| a point particle breaks down.
|
| There are similar problems in E&M at caustics that are solved
| by remembering that E&M waves have non-zero wavelength.
| martincmartin wrote:
| Doesn't conservation of energy preclude this? If all
| particles start with finite energy, and only finite energy is
| added to the system, won't the total energy stay finite? Or
| are you assuming an infinite potential somewhere, e.g.
| gravity from a point "planet"?
| leephillips wrote:
| The examples I know of all involve gravitational or similar
| potentials, so there is unbounded negative energy available
| from 1/r. But you can still get singularities without
| collisions: Xia, Annals of Math. 135 411-468 (1992).
| selimthegrim wrote:
| Norton doesn't understand the principle of virtual work and
| should go back and read D'Alembert and Lanczos.
| twic wrote:
| > Take a simple bottle of milk like the ones pictured here,
| with a cylindrical section below a tapering segment.
|
| Those bottles are rectangular!
| leephillips wrote:
| They are rectangular cylinders. The shape works for the
| problem under discussion.
| wodenokoto wrote:
| I thought you where making up words, saying "rectangular
| cylinder", but apparently it's a thing:
|
| https://www.quora.com/Geometry-What-is-a-rectangular-
| cylinde...
| leephillips wrote:
| A cylinder can have any cross section.
| sudosysgen wrote:
| I find this write-up enlightening :
| https://blog.gruffdavies.com/2017/12/24/newtonian-physics-is...
|
| It seems the equations given by Norton really are unphysical,
| so actually it's not a proof on indeterminism, but simply
| incompleteness - newtonian physics cannot model some really
| really fucky situations - its incomplete.
| randphys wrote:
| I can recommend taking this blog post with a grain of salt.
| I'm a physics masters student and after working through the
| math myself I believe the Lipschitz continuity violation that
| Gruff rejects as a red herring is actually the real source of
| the nondeterminism, and is not just some mathematical fluff.
|
| The first law and stitching arguments he makes appear to both
| be flawed. Having non-zero derivatives of force in
| combination with zero velocity and zero force is perfectly in
| accordance with Newton's first law. And in his frictionless
| ball counterexample, his equation is incorrect because it
| violates Newton's second law, not because two solutions are
| stitched together.
|
| Lipschitz continuity is required for guaranteed uniqueness of
| differential equation solutions, and non-uniqueness can
| appear as nondeterminism or incompleteness.
|
| I think he reaches the right conclusion but his reasoning is
| flawed.
| leephillips wrote:
| That's a brilliant analysis of the Norton's dome; thank you.
| ceceron wrote:
| Thanks. It's a great piece of writing!
| selimthegrim wrote:
| Why is virtual work not taught anymore?
| leephillips wrote:
| Who says it's not? I suspect most courses in advanced
| classical mechanics still cover it, although probably
| briefly.
| IgorPartola wrote:
| Link to actual explanation from Norton:
| http://www.pitt.edu/~jdnorton/Goodies/Dome/
| jayd16 wrote:
| Are these kinds of math tricks less likely to be a lack of
| modeling than nondeterminism, ie, does the fact that one
| mathematical model produces a non-deterministic result mean
| that the actual situation is non-deterministic?
| leephillips wrote:
| No, it doesn't, as you suspect. The article that sudosysgen
| links to up above treats this question nicely.
| codeulike wrote:
| This seems to overlap with that Wolfram thread from yesterday
| https://news.ycombinator.com/item?id=26544651
| mensetmanusman wrote:
| One interesting thing about the universe is that it tends to hide
| infinities.
|
| Black holes are wrapped in event horizons. The digits of pi would
| require all the energy of the universe to calculate. Calculating
| the brain with sufficient accuracy (using our current
| computational framework) would require a computer so large it
| would generate a black hole...
| simiones wrote:
| > Black holes are wrapped in event horizons.
|
| Not really - the event horizon is the effect of the black hole,
| not something separate from it. Also, from one perspective
| there is nothing mysterious about it - an observer passing
| through it would not notice any kind of border there (though an
| observer who is not passing through it would see it as some
| kind of barrier emitting Hawking radiation).
|
| Also note that physicists do not believe that there is any
| infinity at the center of a black hole. With a theory of
| quantum gravity we may even be able to describe the structure
| of the core of a black hole (though it would remain forever an
| un-testable model). Just like classical mechanics allows a
| particle to gain unbounded speed, GR allows a mass to gain
| unbounded gravity, but that is likely incorrect, we just don't
| know how to describe the limit yet.
|
| > The digits of pi would require all the energy of the universe
| to calculate.
|
| This makes no sense - pi has an infinite number of digits, so
| all of the energy in the universe can't possibly be enough to
| compute it.
|
| > Calculating the brain with sufficient accuracy (using our
| current computational framework) would require a computer so
| large it would generate a black hole...
|
| I find this hard to believe. Regardless, there is no infinity
| in the human brain.
|
| Note that in general infinity is an inherently non-scientific
| concept - there is no way to experimentally distinguish an
| infinity from a quantity larger than the largest possible
| experiment.
| ddxxdd wrote:
| >pi has an infinite number of digits, so all of the energy in
| the universe can't possibly be enough to compute it.
|
| If the universe is also infinite, then you could calculate Pi
| with X% of the universe's energy, where X is an arbitrarily
| small positive number.
| andrewflnr wrote:
| > Also note that physicists do not believe that there is any
| infinity at the center of a black hole.
|
| This is my impression as well, but do you have a good source
| for it? If I'm talking with people about black holes, it
| would be nice to have something to point to besides my vague
| impression from watching physics lectures.
| leephillips wrote:
| Any physics equations have limits of applicability. If a
| singularity appears in the solution to the equations, that
| is a sign that you have found one of these limits, not that
| there is an actual infinity there.
| GoblinSlayer wrote:
| Just calculate digits of pi in base pi, it's 1.0 exactly.
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