Speaking of the discrete orbits of electrons, Bertrand Russell asks the following:
"Do we know that, between one orbit and the next, other orbits are geometrically possible? Einstein has led us to think that the neighbourhood of matter makes space non-Euclidean; might it not also make it discontinuous?" (Bertrand Russell, The Analysis of Matter)
It seems to me that there might be two possibilities here:
- The property of discontinuity might be attributed to space itself, determining the path of electrons presumably by not providing possible positions where it does not exist. The curvature of space could also be seen a property determining the path of light.
- The discreteness and curvature are determined by some (possibly unknown) factor independent from space.
Consider the following: Russell speaks of a region between one orbit and another. The idea of discontinuous space also assumes a region between where space exists and where it doesn't. Usually, we would also designate such an empty area as being "space" as well, so this idea suggests space within space; i.e. one space that has the property of being discontinuous within another that lacks such a property. In the same way, we could think of curved space as having a recognizable curvature in virtue of it existing within space which lacks any curvature. We recognize such things by means of contrast.
(Please note that these observations are only some things to consider. I'm not offering any opinion.)
My question: Is there any reason to prefer the first possibility to the second? Or, is there any reason not to identify the two possibilities and say that the "space within space" is the unknown factor independent from the space within which it's contained?