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Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by datameta on Saturday June 21, 2025 @12:35PM (#44338834)
To what extent are the Planck length and Planck second confirmed smallest discrete units?
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by Keyframe on Saturday June 21, 2025 @04:44PM (#44340602)
I was referring to spacetime in GR is modeled as smooth continuous manifold. In case you're serious though, planck length are not some fine-grained pixels/voxels in the cartesian 3d world, at least not confirmed; in-fact planck units are derived scales.
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by datameta on Sunday June 22, 2025 @11:21AM (#44347646)
Where could you recommend I read more about how they are derived scales?
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by Keyframe on Monday June 23, 2025 @06:56AM (#44354368)
Wikipedia is a good start, but if it's too terse/advanced there's always simple wikipedia which seems to have an explanation as well https://simple.wikipedia.org/wiki/Planck_units
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by datameta on Monday June 23, 2025 @10:34AM (#44356214)
I suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by Keyframe on Monday June 23, 2025 @12:17PM (#44357293)
you received a link to simplified wikipedia, which is not wikipedia. https://simple.wikipedia.org/wiki/Simple_English_Wikipedia
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by datameta on Monday June 23, 2025 @08:58PM (#44361839)
I can't tell now if you're being intentionally condescending.
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by Keyframe on Wednesday June 25, 2025 @10:38AM (#44377861)
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by thot_experiment on Saturday June 21, 2025 @07:41PM (#44341552)
I'm not a physicist, but I think those are the smallest units in the sense that they are the smallest units we could theoretically interact with/measure, not some hard limit. It's just that it's moot to consider anything smaller because there's no way for us to ever know.
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by datameta on Sunday June 22, 2025 @11:23AM (#44347664)
Is that because we see no way to bootstrap equipment down so many magnitudes of scale, not even close - or is it something else?
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by narnarpapadaddy on Sunday June 22, 2025 @04:43PM (#44350125)
Any given model has less fidelity than reality. An atlas map of the US has less detail than the actual terrain. The Planck constants represent the maximal fidelity possible with the standard model of physics. We can’t model shorter timeframes or smaller sizes, so we can’t predict what happens at scales that small. Building equipment the can measure something so small is difficult too… how do you measure something when you don’t know what to look for?

It may be that one day we come up with a more refined model. But as of today, it’s not clear how that would happen or if it’s even possible.

Imagine going from 4K to 8k to 16k resolution and then beyond. At some point a “pixel” to represent part of an image doesn’t make sense anymore, but what do you use instead? Nobody currently knows.

Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by narnarpapadaddy on Sunday June 22, 2025 @08:06PM (#44351298)
One addendum / clarification:

It may also be that "space" and "time" are emergent properties, much like an "apple" is "just" a description of a particular conglomeration of molecules. If we get past Planck scales it may turn that out that there are no such things as "space" and "time" and the Planck constants are irrelevant. We currently don't know but there _are_ a few theoretical frameworks that have yet to be empirically verified, like string theory.