4d and n-dimensional physics engine

Question

Was somebody trying to implement 4d or n-dimension physics realtime (or not) engine?

What difficulties in this implementation, compare to 3d and 2d physics engines? Of course, one of which is presentation problem. Is's an interesting to look at and to find out more about 4d hyperspheres, hypercubes, springs, joints, liquids and other objects.

I am just curious, and not have a real application using it.

Generalization of my idea is physics in lobachevskian or riemann geometries, distortion spaces (you can go through the needle's eye), looped spaces (returning to the same place), physics paradoxes and other amazing things.

Irrational

I have not tried to implement a 4+D physics engine, but I would guess you might find collision-detection more complex, and things like fluid simulation more resource-intensive. If you are interested in Riemannean geometry simulations, you might check out the work being done in numerical evaluation of general relativity. – Masters

Collision detection in 4-D space, would simulate big bang maybe? – Epiphenomenon

If you want to go into non-Euclidean space, use Langrangian mechanics, which is ideally suited to the task. In high-dimensional Euclidean spaces, Hamilton's equations work as usual. If you can write down the equations, you can simulate. If you can't write down the equations, you have a physics problem and not a programming problem. – Yerga

Answer 1

An example of a 4D physics engine is 4D Toys, created by Marc ten Bosch.

The author goes into more detail about how it works on their blog (see this post about geometric algebra, for instance).

Their technical paper, N-Dimensional Rigid Body Dynamics, was also accepted to SIGGRAPH 2020.

I also explained a bit how angular velocity works in higher dimensions here.

Pergrim

Answer 2

There are numerous research groups using relativistic codes, for all sorts of physics problems; from Relativistic Electrodynamics, Relativistic Fluid Dynamics/Magnetohydrodynamics and for gravitational based simulations etc. Astrophysical applications are the main place you would meet relativistic codes.

A 4D game engine is what you already have in games like FIFA and COD. This is just a 3 + 1 implementation, which incedently is what many relativistic codes are (they use the 3 + 1 formulation of space-time). This splitting of space-time is much easier to handle computationally for many different reasons. Of course as you go from 1D to 2D etc. you complexity increases inline with the simulated physics.

To me it makes no sense to have a physics engine in n-dimensions. We do not experience physical processes in n-diemensions, but four. To ask about hypercubes etc. is not physics but geometrical/mathematical constructs. These are separate from what you would traditionally associate with a physics engine.

Appetence

Just to explain my downvote: 1. "Astrophysical applications are the only places you would need relativistic codes." is not correct, but I do think this is just a typo. 2. Higher dimensional systems are absolutely an important part of physics, both in established models and theories of physics beyond the standard model. Although I do think your answer is much clearer than the question. – Inject

Do you have a reference for a simulation involving strings, supergravity, higher dimensional gauge theories etc? I genuinely wasn’t aware this was an active area. However, for “physics engines”, Newtonian Physics is all that is required, so I stand by the last paragraph. – Appetence

-1 because a physics engine in n-dimensions makes perfect sense. Classical mechanics works perfectly well in higher dimensions. See Marc Bosch’s 4D Toys. – Pergrim

Okay, to address these downvotes. @andrew.punnett with simulation of higher dimensional physics (string theory, higher dimensional gauge theories etc.) these are not "physics engines", they are computer codes studying certain esoteric physical theories. When I talk of a "physics engine" here, I am talking about the well accepted use of the word, that being the engine that would provide the dynamics in a 4D world as you would see in a video game. – Appetence

@Pergrim A physics engine in n-dimensional space to most people does not "make perfect sense". It might do from an abstract mathematical perspective and even then, for most mathematicians these concepts are difficult to conceptualize. I challenge you to draw a lovely 4D cube in a 5D space time - not that easy - does not make perfect sense. If you achieve this, please post the result and link it here. – Appetence

@Pergrim this is a 3D spatial rendering (on a 2D screen) of a 4D spatial environment. It also makes very little sense. – Appetence

@Appetence The points in your answer that I still disagree with are: 1. Your assertion that 4 dimensional game engines are the same thing as game engines with 3 spatial and 1 temporal dimension. If this were true then, by analogy, 2D platormer games, such as Super Mario Brothers, would be referred to as 3D games. 2. Your claim that hypercubes are not part of physics. – Inject

We would largely agree if we could have a conversation - I will leave it here. – Appetence

I think you're right! I've changed my downvote to an upvote. – Inject