Are there physics laws that only apply in space(time) with 2 or 4 spatial dimensions instead of 3? What are those laws if they exist? And how does the number of space impact certain physics laws?
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2$\begingroup$ This question is too broad. Please edit the post to focus on a single question that has a single answer (rather then asking for a list of examples of various things). $\endgroup$– BioPhysicistCommented Apr 25, 2021 at 1:01
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1$\begingroup$ This is a great question. The answer is: yes! E.g., certain topological actions for gauge fields only exist in odd spacetime dimensions (i.e., even space dimensions). Hopefully someone else has the time to write an informative answer about this, but in the mean time, check out en.wikipedia.org/wiki/Chern%E2%80%93Simons_theory $\endgroup$– Ruben VerresenCommented Apr 25, 2021 at 1:05
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Its a tricky question, as laws of physics tend to be confined to "the real world," where there are 3 dimensions. However, there are some physical properties which do arise in 2d. One interesting case is the physics of vortices. In many cases, we model our vortex systems as 2 dimensional rather than 3 because one dimension is so much thinner than the other two. It turns out that the physics is different:
Even more interesting is the fact that two- and three-dimensional fluids behave in qualitatively different fashions. In three-dimensional flows energy typically flows from large-scale features to small ones until it is dissipated by the viscosity of the fluid. In two dimensions the phenomenon tends to reverse itself, and the energy concentrates itself in a few large vortex-like structures. This phenomenon, known as the "inverse cascade", manifests itself in a striking visual way through the coalescence of many small vortices into a smaller number of larger vortices.
answered Apr 25, 2021 at 1:07