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?
Asked
Active
Viewed 148 times
1 Answers
4
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-89
- 39,465
- 9
- 53
- 119