> > This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory.
> What does "a way similar to quantum theory" mean?
I'm not an expert (though I have studied undergraduate physics). I imagine what he's trying to reference is that while the equations of quantum mechanics relating to states are entirely deterministic, the measurements we make are probabilistic in nature (I am careful to not say "non-deterministic" -- because it would not be correct to phrase it that way). I've skimmed through the paper and I see no reason that this peculiar nature of quantum mechanics (which we still don't understand) applies to a mathematical reformulation of classical mechanics.
I imagine the reason the author mention quantum mechanics is that they have published the paper in the quantum mechanics section of arXiv...
But personally my biggest issue with the abstract is this:
> Since a finite volume of space can't contain more than a finite amount of information, I argue that the mathematical real numbers are not physically relevant.
This conflates several concepts from different fields in a single sentence and is utterly ludicrous. The author appears to be talking about the Bekenstein bound (which states that there is a maximum amount of entropy for a given region of space with a given amount of energy -- otherwise you could violate thermodynamics by placing such a system into a black hole). But he is conflating the concept of entropy (or "information") from thermodynamics with his own concept of "number information". If this conflation was accurate then one could assume that the amount of entropy in a system is related to the decimal expansion of variables related to that system -- which is just a ridiculous thing to argue (especially if you consider that you can change the decimal expansion of a number by changing units).
> What does "a way similar to quantum theory" mean?
I'm not an expert (though I have studied undergraduate physics). I imagine what he's trying to reference is that while the equations of quantum mechanics relating to states are entirely deterministic, the measurements we make are probabilistic in nature (I am careful to not say "non-deterministic" -- because it would not be correct to phrase it that way). I've skimmed through the paper and I see no reason that this peculiar nature of quantum mechanics (which we still don't understand) applies to a mathematical reformulation of classical mechanics.
I imagine the reason the author mention quantum mechanics is that they have published the paper in the quantum mechanics section of arXiv...
But personally my biggest issue with the abstract is this:
> Since a finite volume of space can't contain more than a finite amount of information, I argue that the mathematical real numbers are not physically relevant.
This conflates several concepts from different fields in a single sentence and is utterly ludicrous. The author appears to be talking about the Bekenstein bound (which states that there is a maximum amount of entropy for a given region of space with a given amount of energy -- otherwise you could violate thermodynamics by placing such a system into a black hole). But he is conflating the concept of entropy (or "information") from thermodynamics with his own concept of "number information". If this conflation was accurate then one could assume that the amount of entropy in a system is related to the decimal expansion of variables related to that system -- which is just a ridiculous thing to argue (especially if you consider that you can change the decimal expansion of a number by changing units).