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I recently watched a video where in VR someone was manipulating a 4D geometry in 3D space that was changing into all kinds of different shapes as it was moving through space. What i found strange is that typically for geometries to break apart and dissapear like this seems like it would violate 3D conservation laws, like dissapearing into nothing and then appearing in another corner, but of course the shape is probably conserved in 4D space since it is a 4D shape. Do we have an observable higher dimensional geometry on record for physics like this? Something that actually shows geometries appearing and dissapearing? It would seem it would violate the creation/annihilation of particles, at least on large scales.

We obviously have multivariate observables, where you can define many parameters that are hidden or correlated to only show movements in 3D but i'm specifically asking about an observable higher dimensional geometry which has been seen in 3D, and if not does it have anything to do with conservation laws?

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  • $\begingroup$ More on visualization of higher dimensions. $\endgroup$ – Qmechanic Apr 26 at 13:22
  • $\begingroup$ That comment was pretty useful since it had an exact answer, it would be interesting to see a proof of why we can't see 4d observable shapes in a our 3d physical universe but that may actually end up being a math question with boundary conditions that are probably not realistic $\endgroup$ – user136128 Apr 26 at 14:10
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You are using the word "geometry" in a strange way, but I think I get what you mean. Virtual Reality technology lets us explore geometrical objects of 4 dimensions (or more), like the tesseract, but that doesn't imply that such objects have physical significance, or that such objects are somehow physically real.

Mathematics can represent all sorts of interesting structures, but the mathematical structures of relevance to physics occupy only a small corner of the full mathematical "universe". If you want to learn more about the mathematics of higher geometry, the classic reference is Regular Polytopes by H. S. M. Coxeter.

However, in physics, we often do use spaces of high dimension to model physical systems. For example, in Hamiltonian mechanics the state of a system of N particles can be modeled as a single point in 6N dimensional space. For each particle, we have 3 dimensions for its position, and 3 dimensions for its momentum.

Actually, we can extend this concept to using generalised position and momentum coordinates, not just the familiar 3D cartesian coordinates. And in quantum mechanics we can use spaces with complex number coordinates, and an infinite number of dimensions! Please see Hilbert space for further information.

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