Abstract:
This is an old question, considered already by Plato, Aristotle, and others. More precisely, we ask to which extent is the number 3 decisive for the physical space, that is, to which extent the validity of physical laws depends on 3D. In this way, the question was probably posed for the first time by Kant. In modern physics, the justification of precisely 3D has evolved. I will, however, tackle the time honored Newtonian space-time, where time and space are separated. Our local space, of the extent, say, of the Solar System, looks like that. Dimensions other than three can be visualized in various manners. For example, our space could be immersed into a space of a higher dimension, to which we are not allowed to enter (in contradistinction to angels, for example). Or there could be additional folded dimensions, like they appear for strings. I will consider a specific question: what would happen, if the Newtonian space had a dimension different from 3. Either lower, 2 or 1, or, on the opposite, a higher one. It would remain Euclidean, however. Some principles of physics depend on the spatial dimension, some other do not. How would then come out their interplay? Specific questions:

• gravity law
• planetary movements
• Coulomb law of electrostatics
• Bohr-Sommerfeld quantization and the n-dimensional hydrogen
• Schrödinger equation for hydrogen in R_n
• [if time permits: wave equation and the Huyghens principle in R_n ]