How would you do the calculus at distances below the Planck Length?

How would you do the calculus at distances below the Planck Length?


Is the smallest integral possible the planck length?

>How would you do the calculus at distances below the Planck Length?
Give me one example where you would need to

it's equally valid to argue that you would or you wouldn't need to, but i'm just wondering if it's theoretically possible. been bugging me for a while.

i'm leaning towards yes, it is possible, but i have no evidence.

>i'm leaning towards yes, it is possible, but i have no evidence.

or anyone, apart from the denizens of this place to discuss it with for that matter

Well yes, it is possible to interpolate between two points. Does that answer your question? I'm struggling to see what you are asking here.

If you're already accepting the premise the planck length is a thing then you can't, because space is fuzzy below the planck length.

i'm entertaining the idea, really.

but it doesn't make sense, because if the planck length exists, that means infinity doesn't exist, we are just unable to properly measure the really big and really small

mathematical constructs aren't married to physical constructs and don't need to have a physical interpretation...


Soooo why not?

claude shannon bump

I love to speculate about whether the universe is continuous or discretized.

Also, if the smallest measurement of distance possible is the plank length, would the largest distance possible be upper limit of 1/(plank length)?

It just means that the universe is a simulation, because the computers we are running on have finite precision.

This isn't a question regarding the universe, it is a question regarding mathematics. If you are working within a complete field it is continuous, thus you can do the calculus to it.

In wildburger's number theory, to obtain numbers greater than the biggest dank number 10^200

Is the radius of the singularity of a black hole smaller than the planck length?

>If you are working within a complete field it is continuous, thus you can do the calculus to it.
Then the complete field you're working in does not have a planck length. As you saw earlier in the thread, the planck length is just a combination of universal constants, which have no relation or meaning in mathematics only in the universe. So you're question MUST be regarding the universe.

Can't be, if it was you'd get radiation of a wave length shorter than a planck length, which would cause huge problems. Of course it could be, and the planck length just might not exist.

>but it doesn't make sense, because if the planck length exists, that means infinity doesn't exist
no it doesn't

it just says that we don't know how to mathematically describe smaller distances. it says nothing about whether such smaller distances exist

This is what's known as abductive reasoning.

There are three types of rational thought: deductive, inductive, and abductive, listed in decreasing order of precision. Although the latter two are forms of fuzzy logic, all three feature rules of inference. One rule of inference in abductive reasoning -- the only rule, some would say (though it depends on what formal system you use) -- is Occam's razor.

You just violated it.

>It just means that the universe is a simulation, because the computers we are running on have finite precision.
Or it could mean that we were created by a God who decided that this would be the smallest measurement possible.

Both theories have equal grounds supporting it.

Nothing's stopping you from continuing to take integrals in terms of infinitesimals. Your answers will just be more precise than real life is.

plank lengths are now dank lengths. thank you user

>Is the smallest integral possible the planck length?

No. Math doesn't care about what we observe. Just because we can describe physical laws with the same language we use to describe mathematical ideas doesn't mean math is somehow bound by physical laws. That doesn't make sense.

Also if you limit yourself to the planck length you can't take integrals, so saying "smallest integral chunk" doesn't make sense when talking about non-infinitesimal finites.

That's a stupid answer to a stupid question.

>it just says that we don't know how to mathematically describe smaller distances

No it doesn't say that either. Quit replying to dumb shit with only slightly less dumb shit.