What's the difference between:
1) A sphere.
2) A circle rotating along a diameter in a three dimensional space at an infinite speed.
No such thing and not in terms of "that can't be" (we're talking about a 2d shape taking up 3d volume by rotation, being impossible in a real world sense isn't a factor) but because it doesn't make sense. Infinite isn't a quantity.
At an arbitrarily large speed?
One is a solid body and the other is a rotating 2D shape.
As for what differences this makes, think in terms of stuff like density and mass.
momentum implies mass right? this is more of the idea of both shapes.
>no such thing as infinite speed
>arbitrary large speed
different than what i mean.
>one is a solid body and the other is a 2d shape
outside of a temporal dimension, yes.
>think in terms of density and mass
I'm thinking of massless concepts in a non-physical abyss. *tips fedora*. not sure what the term is for what i'm talking about lol.
>safe to touch
no such thing as touching or fingers in this situation.
idk.. the rotating circle seems more tangible and easily applied to a mathematical format.
again, kind of my question.
Well... Here goes nothing..
a sub-question would be "how fast would the circle have to be rotating for it to be mathematically indistinguishable from a sphere?"
This one I thought about pretty hard tbqh. But given the "infinite speed", you couldn't really slow it down. Right? Idk.
I think I didn't do what you're saying justice
>infinite isn't a quantity
you're right, but why doesn't it make sense? if i said that "as the rotating circle's speed approaches infinity, it becomes indistinguishable from a sphere" that would imply some kind of acceleration. These two things have existed forever, and the rotating circle has been going the same speed forever. how would one differentiate the two?
Mathematically theyre the same, you dont need the infinite speed bullshit if youre not thinking pseudo physics. Circle is the boundary of a flat ball(disk), rotation of the circle just adds one dimension to the ball. A sphere can be defined by a rotating circle as this boundary of the ball.
Physically the difference would be in what happens if you bring two such objects together. An atom is a good example, by itself you could confuse it for a very small solid but by its interactions it clearly not.
That's why I said an arbitrarily large speed (which should actually be angular velocity, but w/e).
It doesn't make sense to use infinity as a quantity because it isn't one. It's like if someone asks how many cookies you want and you answer "enlightenment". This is especially true in situations like this where you're talking about concepts that are impossible in the first place. But notice that I didn't just pedantically say it doesn't make sense because I knew what you were talking about, corrected that terminology bit, then went ahead to answer.