4 ms·

then you are interested in a version of physics that doesn't exist, even though some might choose to supress the details at low level

ajkjk 2y ago
Er? No I'm describing actual physics. Physics does not care about rational vs reals. Nothing is measured to infinite accuracy anyway.
- afiori 2y ago
  One thing that is used a lot in physics are known as Dirac Deltas[0] that is, in very informal terms, the derivative of the function f(x) = 0 for negative x otherwise f(x) = 1. Physics are very good at working with concepts and abstraction before any formal mathy justifications can be found, but the only way to formaly work with a dirac delta that makes sense formally is defining it in terms of measures [0] https://en.wikipedia.org/wiki/Dirac_delta_function https://en.wikipedia.org/wiki/Dirac_delta_function
  - ajkjk 2y ago
    That is not true, it is not the 'only way' to formally deal with them. A better way to think of them is as the vector space dual of functions (/forms) under the pairing given by integration. No measures required. The measure theoretic explanation is very much "fitting delta functions into our existing machinery" rather than any sort of inherent requirement. Actually an even better way to think of delta functions is just as a geometric object, a point (or line/plane/etc). Which is somewhat related to the measure theoretic version, but much more simple to think about.
    - staunton 2y ago
      You need measures to define the vector spaces that those (what you call "forms", and others call "distributions") act on... Not that it would be impossible to define everything without measures (or even without real numbers), but it's really not clear how to go about it.
- tsimionescu 2y ago
  Even if accuracy is finite, the fact that, for example, circles aren't polygons is definitely relevant to physics. You might be able to get all of the relevant physics you need without the continuum by working with several disjoint sets of numbers (the rationals, the rationals-multiplied-by-pi, the rationals-multiplied-by-e, etc) but I'm not even sure of that.
  - rbanffy 2y ago
    If you look close enough, from the physics point of view, all circles are polygons, and, also, they aren’t really flat. Zeroes and infinities are problematic in physics. Physics and math aren’t the same discipline, and it’s dangerous to conflate them. I’m pretty sure there will be a point where you’ll have a light-emitting superconductor on your way to an infinite current.

ajkjk 2y ago

Er? No I'm describing actual physics. Physics does not care about rational vs reals. Nothing is measured to infinite accuracy anyway.

afiori 2y ago
One thing that is used a lot in physics are known as Dirac Deltas[0] that is, in very informal terms, the derivative of the function f(x) = 0 for negative x otherwise f(x) = 1. Physics are very good at working with concepts and abstraction before any formal mathy justifications can be found, but the only way to formaly work with a dirac delta that makes sense formally is defining it in terms of measures [0] https://en.wikipedia.org/wiki/Dirac_delta_function https://en.wikipedia.org/wiki/Dirac_delta_function
- ajkjk 2y ago
  That is not true, it is not the 'only way' to formally deal with them. A better way to think of them is as the vector space dual of functions (/forms) under the pairing given by integration. No measures required. The measure theoretic explanation is very much "fitting delta functions into our existing machinery" rather than any sort of inherent requirement. Actually an even better way to think of delta functions is just as a geometric object, a point (or line/plane/etc). Which is somewhat related to the measure theoretic version, but much more simple to think about.
  - staunton 2y ago
    You need measures to define the vector spaces that those (what you call "forms", and others call "distributions") act on... Not that it would be impossible to define everything without measures (or even without real numbers), but it's really not clear how to go about it.
tsimionescu 2y ago
Even if accuracy is finite, the fact that, for example, circles aren't polygons is definitely relevant to physics. You might be able to get all of the relevant physics you need without the continuum by working with several disjoint sets of numbers (the rationals, the rationals-multiplied-by-pi, the rationals-multiplied-by-e, etc) but I'm not even sure of that.
- rbanffy 2y ago
  If you look close enough, from the physics point of view, all circles are polygons, and, also, they aren’t really flat. Zeroes and infinities are problematic in physics. Physics and math aren’t the same discipline, and it’s dangerous to conflate them. I’m pretty sure there will be a point where you’ll have a light-emitting superconductor on your way to an infinite current.