Problem of Time II
Why should space appear infinitely divisible when time does not? Of course, for the purposes of 19th century physics, the continuum is a useful construction, but now one expects this classical geometry to emerge (ie. be derived) from a collective of the large scale observations of like observers, such as ourselves. If so, where does the notion of scale originate? To begin with, we are now used to the correspondence between cosmic time and cosmic scale in an expanding cosmology, so we can ask instead: from where does our notion of cosmic time originate? We immediately observe that an estimate of cosmic time is something that, as sensible observers, we are largely in agreement upon.
What does it mean to view this kind of time on a discrete circle? We are not talking about cyclic universes, or any construction that proposes structure outside what we can possibly observe. So discrete cosmic time is a concept of quantization on cosmic scales. This sounds a bit like the old style Bohr correspondence, which after all had a good phenomenological basis. Now let us not assume that this cosmic time is universal for all observers. Then its range of values is analogous to the quantized energy levels of a hydrogen atom.