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I thought it was a smooth continuous manifold


To what extent are the Planck length and Planck second confirmed smallest discrete units?


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.


Where could you recommend I read more about how they are derived scales?


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


I suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.


you received a link to simplified wikipedia, which is not wikipedia. https://simple.wikipedia.org/wiki/Simple_English_Wikipedia


I can't tell now if you're being intentionally condescending.



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.


Is that because we see no way to bootstrap equipment down so many magnitudes of scale, not even close - or is it something else?


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.


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.




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