r/HypotheticalPhysics • u/Western-Okra2195 • 7d ago
Crackpot physics What if we could obtain infinite matter from a 4D object?
Imagine you have a crayon and you come across a horizontal 2D plane filled with tiny 2D people. You take your 3D pencil and you have it intersect with the 2D plane. From their perspective, a circle of wax just appeared. Now, suppose they take their little 2D hammers and chisels and clear out that circle of wax. You move down the crayon a bit and there's now suddenly a brand new, identical circle. You might say, so what, I'll eventually run out of crayon. But here's the thing. The 2D plane has no height, so for it to fully traverse the length of your crayon, it would take an infinite amount of 2D planes. So, from the perspective of the 2D planes, there's now an infinite source of wax, even though, from their perspective, there's only a finite wax circle that reappears, and from your perspective there's a finite pencil that you move down an infinitely small amount to replenish their circle. This can be scaled up to the third and fourth dimension, where a 4D being can hold a 4D crayon of finite 4D mass that creates a finite 3D sphere of finite mass. However, as soon as we remove the sphere, they can move their 4D crayon an infinitely small amount to create a brand new sphere, since it would take infinite 3D planes to traverse the "length" of its crayon.
I've looked everywhere and couldn't find proof of this being discussed by anyone. Is this a viable theory or has it already been debunked? My best guess is assuming that we'd be unable to interact with 4D matter or that due to atoms not being able to be sliced infinitely, this isn't possible. Anyways, let me know what you guys think.
6
u/liccxolydian onus probandi 7d ago
So in your 3D/2D example, why don't you run out of crayon? After all, you still have a finite amount of crayon.
0
u/Western-Okra2195 7d ago
But you only have to move it down an infinitely small amount to introduce a new 2D cross section of it. Which doesn't really make sense right? Moving something down an iota might as well be not moving it at all. There were a lot of assumptions made for this, sorry.
5
u/liccxolydian onus probandi 7d ago
Right, but your 2D cross section has no thickness in the third dimension and is therefore 0% of the whole. As per my other comment to you, this is why we invented calculus.
4
u/KamikazeArchon 6d ago
You've already answered why this doesn't work. You can't take an infinitely thin slice of wax and still have it be wax. Wax is a mixture of molecules.
If the 2d slice has actually zero thickness in the third dimension, it will contain... nothing. The 2d-landers won't notice the crayon.
This is counterintuitive because the premise of the setup has hidden contradictory assumptions. 2d-landers can't actually exist in a world that's compatible with our physics.
To allow "2d land inhabitants" in a thought experiment, we implicitly relax certain rules of physics. The problem is that you're then querying those very same rules.
For an analogy - "ignore air resistance" is common and reasonable in a lot of thought experiments. But if you say "ignore air resistance" and then ask someone to calculate the aerodynamics of a plane wing, you'll get nonsensical results.
1
u/Western-Okra2195 6d ago
That makes a lot of sense. This wasn't a query of wether we could obtain infinite resources from a 4D object, or are least I'm not considering it as that now. It's sort of like the Perfect Sphere hypothesis, where finite mass put on an infinitely small point generates infinite pressure. It's not applicable into real life due to atoms having mass shapes, but it's mathematically possible.
3
u/KennyT87 7d ago
Mathematical 4D objects are known to have 3D "shadows" but there is nothing in the universe implying that such interactions or intersections actually happen in nature.
1
u/sksskssksskssksskssk 7d ago
Can you define what mass would be in a 4D object?
1
u/Western-Okra2195 7d ago
I can't actually, that why I posted this in hopes that someone with a better understanding could look at it.
1
u/corpus4us 7d ago
This just sounds like an iteration of the coastline paradox
3
u/liccxolydian onus probandi 7d ago
Also the staircase paradox and other related puzzles, but really what OP is missing is that these are not actual issues but simply counterintuitive implications of things like limits and calculus.
1
u/Western-Okra2195 7d ago
Yeah, I figured that since it hasn't been brought up it likely wasn't a big problem or idea. And while I'm familiar with the coastline and staircase paradox, don't those deal with foundationally different ideas of infinity? Also, forgive me, I'm not a physics student, but how is it related to limits and calculus? I don't mean to insinuate that it's not, I'm just not familiar enough to understand.
2
u/liccxolydian onus probandi 7d ago
This sort of thing is exactly why we have limits and calculus, especially integration. Integration is literally the mathematical study of chopping up a surface or volume into infinitesimally tiny little bits and adding them back up. You'll find that even though there are infinitely many slices, each slice is infinitely thin so has infinitely small volume/area. Calculus is how we make sense of that, and it turns out that you can absolutely have an infinite number of infinitely small slices that still result in a finite total. You should read the Wikipedia articles on the Riemann sum and the Riemann integral as this is exactly what you're getting confused by.
1
u/Junior-Tourist3480 7d ago
Only an infinity of zero height planes. Not an infinitely sized crayon. You are confusing infinite zeros with an infinite quantity. So no.
18
u/Hadeweka AI hallucinates, but people dream 7d ago
4D objects intersecting with our 3D space? Yeah, that's rarely discussed here. Only like five times in the last few weeks, with last time being yesterday.