system
Given the following post, respond as if you're commenting on Reddit:
human
Is it possible to apply conventional physics to 4D space? If so, is there anything particularly interesting or different about them?
gpt
First of all, generally 4D is meant to be 3+1 dimensions, with one of them time, which is our current spacetime's dimensionality. So you'd mean 5D, or 4+1.

A lot of physical theories are susceptible to being generalized to different dimension. Most field theories readily are. 

EM can be formulated in any dimension; however the properties of magnetism can become a bit alien. In 5D for example, the electrically charged objects are still point particles, but the magnetically charged objects (which in our Universe should be monopoles, so 0-dimensional) would be 1-branes, or 1-dimensional strings. Also, EM waves have 2 polarizations in 4D, in 5D they would have 3. This is part of a class of very important generalizations of EM that appear in supergravity and string theory.

Gravity (general relativity) is funny. In higher dimension, it does essentially what you expect it to do. There is an attractive force between masses, but it falls off faster with distance; in 5D it's an r^-3 force. This makes all orbits unstable, and it's impossible to have planetary systems (actually the same is true for the Coulomb potential in EM, so also atoms are impossible!). There's black holes, but there's also a plethora of extended "black brane" things that have higher dimensionality. Gravitons (or gravitational waves) have 2 polarizations in 4D, in 5D they would have 5.

This pattern works for D>=4 but everything fails for D=3. In 3D general relativity spacetime is always flat and there is no gravitational force. Also, no gravitational waves. It's a really weird thing and has a huge theoretical relevance.

Now these were field theories. Another important class is statistical mechanics systems, where in thermal equilibrium time is not really important. Only the spatial dimensions really matter. So when a statmech person says 3D, he just mean 3 spatial dimensions. Then:

Many famous statistical systems (Ising, Landau-Ginzburg...) are hard in 3D, easy in 4D, and somewhat doable in 2D. Weird pattern.