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As far as we know, the universe is made up of discrete units and any other type of math is an abstraction over discrete math.
by yunwal 1y ago
As far as we know, the universe is made up of discrete units and any other type of math is an abstraction over discrete math.
- Keyframe 1y agoI thought it was a smooth continuous manifold
- datameta 1y agoTo what extent are the Planck length and Planck second confirmed smallest discrete units?
- Keyframe 1y agoI 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.
- datameta 1y agoWhere could you recommend I read more about how they are derived scales?
- Keyframe 1y agoWikipedia 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 https://simple.wikipedia.org/wiki/Planck_units
- datameta 1y agoI suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.
- Keyframe 1y agoyou received a link to simplified wikipedia, which is not wikipedia. https://simple.wikipedia.org/wiki/Simple_English_Wikipedia https://simple.wikipedia.org/wiki/Simple_English_Wikipedia
- thot_experiment 1y agoI'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.
- datameta 1y agoIs that because we see no way to bootstrap equipment down so many magnitudes of scale, not even close - or is it something else?
- narnarpapadaddy 1y agoAny 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.
- narnarpapadaddy 1y agoOne 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.
- giardini 1y agoAs far as we know, the universe is a single unity, and any discrete units and any other type of math are human distinctions overlaid upon that unity.
- random3 1y agoCan you explain what you mean here? I mean yes there’s a universe so it can be see as a unit. There’s also quantum mechanics, telling us we can only distinguish discrete objects at the bottom of the scale. Can you give an example of a non-human distinction, or explain what you mean by that concept?
- IAmBroom 1y agoI assume the post is missing its "/s".
- giardini 1y agoYes. It was a parody of yunwal's post (which I possibly should have cc'ed). . Reread yunwai's post and mine together and you will understand. Endless "unity...discrete" discussions have arisen in both science and philosophy since the beginning.
- giardini 1y agoFWIW my use of the phrase "human distinction" was merely for emphasis: I make no claims about non-humans. In any case, any distinction I have interest in or speak of would be human, whether made by a human or otherwise.