I would like to return to the earlier consideration of Planck's time, about which I have a thought.
Peter Lynds, “Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity” (Obtainable from the CERN document server). Makes the point that there can be no static instant of time, during which change could be considered as having paused. He reasons that if there were such an instant, then all change, all motion, would come to a permanent standstill at that point. Presumably, if we consider time as being static, in its entirety, then we have to regard any motion through time as being a smooth, continuous motion that cannot be frozen at any particular instant.
If Planck’s time is defined as the smallest interval of time that has any meaning, beyond which it is not possible to further sub-divide time, then, surely, we must regard this as the quantum of time.
Planck’s time has a duration, albeit unthinkably small. That being the case, it must be possible to attribute a degree of change, during that period, to any object in relative motion; otherwise, as Lynds points out, that object would be stationary.
There is something more than a little familiar about this line of reasoning. In the same way that light has to be regarded as a wave for some purposes, and as a particle in other situations, could something similar be true of time?
The discussion about whether time is continuous or quantised is ongoing, but it may be no more meaningful than trying to resurrect the argument about whether light is a wave or a particle. Time could be particulate or continuous depending on what question you are asking about it.
