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Is nature granular, or discreet? – Is 0.999 =1.0?

by sans_souse·1y ago·15 comments·view on hn ↗

I am a complete novice in terms of the fields this relates to, but I found it surprising that I haven't seen it documented or heard reference to what I see as a pretty obvious connection between the "smooth" vs "granular" debate at sub-quantum (planck) scales and the proofs and resulting rule in mathematics that 0.999…=1.0 ... Is this already established, or presented somewhere?

Feel free to comment regardless, curious your takes.

15 comments

Planck length isn't an experimentally observable thing like Millikans oil drop shows quanta of charge, As I understand, it's a thing that "falls out of" all the other stuff we can measure and appears once we take values to their limits [0]. There's no reason to suppose space is actually discrete.

[0] https://physics.stackexchange.com/questions/316867/what-is-t...

Granular is hard to get one's head around. If you imagined the universe was like a grid at the Planck scale somebody traveling at a high speed would get a different idea of the structure of that grid because

https://en.wikipedia.org/wiki/Length_contraction

There was an effort to square that circle

https://en.wikipedia.org/wiki/Doubly_special_relativity

but it hasn't really advanced as a program. The question of "what is the meaning of the Planck length, time and energy?" is a big question in physics but doesn't have the urgency of "What is the neutrino mass term?", "Why is there so much matter but no antimatter?", "What the hell is the dark matter?" and such.

Not an expert, but shouldn't "materia snapping to a Planck length grid in space" be experimentally falsifiable? And could this imply there is no grid or that space is truly continuous?

It's thought the the "granularity of space" could manifest here

https://en.wikipedia.org/wiki/Greisen%E2%80%93Zatsepin%E2%80...

in particularly it is thought that very high energy cosmic rays would lose energy by interacting with CMB photons and that if space had some granularity the effect might be suppressed and let us see more energetic cosmic rays than we'd see otherwise.

Consider that lengths (and clocks) depend on your frame of reference, so a "Planck length grid" at one velocity wouldn't be one at another.

I like where your head is at tho

At Planck scales, things aren't so much "granular" as they are "fuzzy". Positions and such can be smeared out in a wave, rather than being discrete.

Measurements, however, are often discrete, and select a single [eigen]value from the smear.

Between the wave / and the measurement / falls the Shadow,

Could, is there talk about, nature being rational and not real (as in the number systems). Things could still being infinitely small but still discreet. As an armchair physicist I think this is a brilliant idea.

If we say reality is granular, and that infinitely smaller scales don't exist (more specifically, the planck limit holds true), does this not work in parallel with our mathematical proofs showing 1.0 is equal to 0.9 repeating?

Real numbers aren't based on measuring objects in space, they're an abstract construct that happens to work a lot like measuring space, at least on our scale.

You're free to reject the real numbers as a valid construct (intuitionist math), but you'd give up a lot else as well.

What do you give up when you stick to rational numbers apposed to real numbers when dealing with nature? I could see some things like pi would point to real numbers but in nature we will never get "exact" measurements anyway. Are there any physical models that only use rational numbers?

I am not a scientist. I do enjoy hearing about it though.

That's sort of from where I arrived at the propsed question as is; what examples of perfection exist so far as we can ascertain? Infinite in and of itself is a sort of "perfect" in its unobtainability, as is perfect 0° pure Kelvin, and with 0, we only ever can get infinitely closer. Perfection is in pi (I believe) perfect circles. It's what I call the undefinable quantity, or the unaccountable unit. None of this is novel but I think the connections are, between fields.

See N. Gisin's take on this

https://www.youtube.com/watch?v=oEWm3yPUosg

I found this very interesting! Thank you

you lose most square roots, for example