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Classical Mechanics is a well-defined mathematical framework. Consequently, the word 'determinism' when applied to classical mechanical systems has a sharp mean

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 6y ago
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 6y ago
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 https://www.scottaaronson.com/blog/?p=5359

rrmm 6y ago

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 6y ago

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 https://www.scottaaronson.com/blog/?p=5359