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Let's assume if in reality, Planck's length is the smallest possible length and Planck's time is smallest possible time. Do we still need infinite divisibility of length or any quantity in our mathematics for any type of calculation, knowing fully well that nature does not follow infinite divisibility?

Qmechanic
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Abdullah Khan
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    Does this answer your question? Does the Planck scale imply that spacetime is discrete? – AccidentalFourierTransform Jan 12 '20 at 22:23
  • @AccidentalFourierTransform Actually my question is related to side effect of discrete spacetime assuming it is real, if we assume it is real, what would be effect on mathematical calculations which we normally do by assuming infinite divisibility , would we still need to do it that way , because nature wouldn't be following infinite divisibility. – Abdullah Khan Jan 12 '20 at 22:25
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    In general, physics cannot answer the question "what would happen if the rules of physics were different?". – AccidentalFourierTransform Jan 12 '20 at 22:40
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    @AccidentalFourierTransform The question is not "what would happen if the rules of physics were different?". It is a question about the consequences, for the known physics, of a possibility which cannot be excluded on the base of existing experiments. It is quite different from an uncontrolled change of the known physical laws. Moreover, the answers to the previous question you cited in your first comment do not address directly the present question which is not on the existence of a limit to infinite divisibility, but on the possible consequences. – GiorgioP-DoomsdayClockIsAt-90 Jan 12 '20 at 23:44
  • Accident transform. You totally blew by a legit question to be rude and condescending. We appreciate your knowledge and achievement, but your attitude sucks. Read the question again. – RaSullivan Jan 13 '20 at 00:21
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    @RaSullivan How is it rude or condescending to say physics cannot answer the question "what would happen if the rules of physics were different?" ? Or are you referring to the 1st comment, which was posted automatically as part of the duplicate closure vote process? – PM 2Ring Jan 13 '20 at 09:46
  • Pm2Ring....because that is not what was asked. The question posed illuminated a valid point and deserved an answer, not a sidestep. Questioning leads to discovery, even in the face of criticism. Review the history of Dirac and the nutrino, for example. Closed minds created by the illusion one is knowledgeable are all around. – RaSullivan Jan 16 '20 at 18:14

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Your question is very interesting because it goes to the heart of the way we use mathematics to model the physical world.

My answer is that a possible discover of a physical limit to divisibility would not modify the way we use mathematics for modeling reality at length scales quite far from the minimum distance. It is not something new in physics. Even if we know that there are atoms, this does not imply that continuum physics has become obsolete or useless. It simply implies that we do not expect that at the scale of a few angstroms we could use a continuum description. But at a micron scale or upper, there is no doubt about the usefulness of a continuum approach.

Another example can be found in electromagnetism where the existence of an elementary charge does not hamper the usefulness of modeling the source of the electric field as a continuous charge density.

The basis for such an independence on the finest scale details is the concept of modeling through mathematical structures which are close enough to the modeled phenomenology. Here, close enough means that the difference is well below the unavoidable experimental uncertainty.

GiorgioP-DoomsdayClockIsAt-90
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