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Frequently Asked Questions:

Q: Does this gravity bend light?
A: No, because space remains flat, and this is Newtonian gravity.

Q: The 4th axiom isn't an axiom.
A: Yes, I agree. I'm still struggling with how to properly name these things. Someone proposed calling it a "conjecture" or an "assumption."

Q: The behavior for the 4th axiom is expected, and in the limit, portals would still create such a gravitational effect, even if they are 0D points. This happens because there is a height difference between them.
A: Nope, my intuition was right. Someone calculated it, check you my next video: https://youtu.be/Q36ULjrK6Po?t=1519

Q: 9:10 isn't planet should have zero gravity inside? Because of the shell theorem?
A: It's a filled disk, not a shell, therefore no.

Q: You should have simulated gravitons as waves, rather than particles.
A: I don't know how to do that :(

Q: You should rotate one portal.
A: You can do it right now in my program, if you are interested. But I will definitely do that in the next video.

Q: How fast your simulation runs?
A: Depending on the triangle size. You can see a 40:57 that it runs in roughly 30fps with this kind of triangle size and not much precision of the total picture. If you make triangles large and linear and disable outer layer, it would be even 144fps. If you use small triangles and make them cubic (for more precision), it can take seconds or even a minute (in worst cases when you have like million triangles).

Q: Where did you calculate all of this? And where you made all the animations?
A: I wrote my own FEM solver from scratch in Rust. For visualization and streamlines I also did it all from scratch. I used egui for the interface and glow (OpenGL-like library) for visualization.

Q: What about one-sided portals?
A: It's impossible to introduce such thing into the calculations, because you must have other side of a portal to point into nowhere. And one-sidedness also breaks the surface irrelevance axiom.

Notable comments:

Also, I do not agree that the difference is not fundamental. The free Poisson equation has conformal invariance, which means in 2D you can make all sorts of wilds things with your solutions without breaking them, any conformal map conserves solutions. But in 3D the conformal group is not infinite-dimensional anymore, and solutions of the Poisson equation in arbitrary topology is quite difficult. (https://www.youtube.com/watch?v=DydIhwLrbMk&lc=UgyET5pTH9pTrbKsXSB4AaABAg)

Air resistance wouldn't slow down the cube in the naive portal situation because the air would also be falling through the portals (https://www.youtube.com/watch?v=DydIhwLrbMk&lc=UgzQNXZwPx_pXr9Yh794AaABAg)

Re: dependence of potential in 2D is slightly different than in 3D? It's much worse. In 2D there is no such thing as absolute potential. The Apoapsis never reaches infinity and or it's never go hyperbolic. The potential is the area under a curve of 1/X truncated at the distance which means the potential difference between anywhere and infinity is just infinity. The concept of escape velocity loses all meaning, and the velocity needed for circular orbit is simply constant with distance. Everything has an infinitely large event horizon surrounding it. (https://www.youtube.com/watch?v=DydIhwLrbMk&lc=UgzDNq1-YSlYov35o5N4AaABAg)

Now you do understand why Aperture kept testing the portal gun over and over again, they were trying to understand this mess with empirical observations

Now you're actually thinking with portals

imagine how cooked the gravity must be in the monsters inc factory

bro is developing an entire field of theoretical physics because of a funny puzzle game

Leading expert in fictional portal physics airs again

Bro is planing to snipe the Nobel Price the moment real life portals are discovered, having all his papers pre-made.

Space = Goes through portal
Gravity = Goes through portal
Time = ???

It's cool that portals create Lagrange points.

Appreciate you embracing your voice and accent instead of using a text to speech voice.

I need to write a mod for portal to see how many of the test chambers can be beaten with mathematically accurate portals! Love the great work, keep it up!

I'm kind of curious how a pair of portals would work in relativistic physics. It's probably a nightmare to calculate.

PLEASE write a scientific paper about this stuff and publish it. This is genuinely fascinating, and you'd be surprised how many mathematical fields turn out to be way more useful than you'd think.

The concept of portal edges being infinitely sharp knives is amazing

20:33 "The effect portals have on gravity depends on the height difference between them"

The final boss battle in Portal 2 would've been cataclysmic

On the question of the high potential observed on the edges of the portals, I would recommend performing a mesh study (plotting the max potential vs mesh size). It should become very apparent if you’re dealing with a singularity or not as the potential should increase as mesh size decreases if it is a singularity. This phenomenon is very common in structural finite element analysis where you observe singularities (infinite stress) in parts with sharp corners as the stress concentration is essentially infinite. I suspect something similar is happening with the edges of your portals.

I always thought it was weird that light could pass through portals, and by extension, the electromagnetic field, but the gravitational field couldn’t. So I imagined that in a real scenario, the cube would actually reach an equilibrium point between the two portals instead of falling infinitely. I’m glad you made a visual simulation of that.

hell yeah, more incomprehensible horrors becoming comprehensible!

Bro would've been a famous scientist back then. Can't believe we're just sitting with a random underrated physicist developing a theory in the internet now and calling it normal.

It never ceases to astound me that there continue to be logically consistent solutions to these kind questions