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Comment by hvidgaard | Hacker News Reader

Re: infinities and continuities, to my understanding, it has been proved than interaction with the world is inheriently discrete determined by Planks constant - I am not a physicist, so may be wrong.

If we cannot interact with arbitrarily precision and can only ever observe a finite universe, does it make sense to even ask if the it is any other way? Should it be figure out how to interact with the world using some new fundamental mechanic, other than a wave bound by C and h, it opens the question.

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Even if the world is fundamentally discrete, that does not mean that continuous models are not valuable. They are.

We are used to doing discrete approximations to continuous problems, but the other way around works too. For example, evaluating the sum

1 + 1/4 + ... + 1/n^2

is quite hard. On the other hand, we may approximate by the integral over x^2, which remarkably has an easy formula.

Continuous and discrete models complements each other, they are not mutually exlusive.

I wasn't trying to say that continues models are not valuable, only that the question "is the world continues?" does not make sense if we can only interact with it in a discrete way.

We don't interact with complex numbers but "Are quantum 'probabilities' complexL" is still a meaningful question.

That is simply a rewording of the question: is it useful to use continuity to model the world.

This is getting quite philosophical now. It depends on the intrepetation of "world". If we mean the universe then no, it is to our current understanding of it, not useful to model it's entirety using continuity, if we can only messure it discretely. If by world we mean a subset of the universe, then it makes perfect sense, because the world might be on the macro level where this "discretness" is far smaller than we ever want to go.

I think you should concentrate on the world model in my sentence rather than world. I have something I want to analyse. How is it useful to think about it and what techniques do I want to use?

Planck's constant arises in continuous theories of quantum mechanics, such as Bohmian mechanics and its QFT extensions.

There are limitations to how much we can know, but not limits to what can be.

I haven't studied Bohmian mechanics to any reasonable degree, so I cannot comment on it. But preliminary reading has me sceptical because it relies on infinity. Time will tell I suppose.

Then read "The Cellular Automaton Interpretation of Quantum Mechanics" by Gerard 't Hooft (https://en.wikipedia.org/wiki/Gerard_%27t_Hooft), which tries to formulate a superdeterministic version of quantum mechanics based on cellular automata (i.e. much more discrete):

> https://arxiv.org/abs/1405.1548

EDIT: also cf. https://link.springer.com/book/10.1007%2F978-3-319-41285-6

There is some light bedtime reading for a decade or two... Thanks for the link, I actually look forward to dive into the topic.

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