We live in a a universe with 3 spatial dimensions and 1 time dimension. However, if we lived in a universe with 4 or more spatial dimensions, under the right conditions (such as a general lack of momentum in the 4th dimension for particles in our world), life on Earth could look entirely the same, with humanity's perceived existence merely limited to 3 spatial dimensions.
What experimental techniques (if any) could be used to search for evidence of higher spatial dimensions? Are any techniques in current use? Has there ever been any serious discussion about this in the scientific community?
I am aware of the implications of string theory and various other theories of quantum gravity, that extra dimensions can exist in various ways that are concealed from the macroscopic universe, but I specifically ask about higher dimensions occurring on a macroscopic level.