Well, the nature of time is still a mystery of physics. Relativity killed forever the idea of a global time, nad QM damaged the one of a continuous time. Hypothesis like Julian Barbour's timeless physics (which has significant support here), or Stephen Hawking's imaginary (complex number) time could change it even more.
Maybe once we have a quantum gravity theory and an agrement over the QM interpretation we could tell more... but for now, we've to admit we don't know much about the "true nature" of change or movement. We can only tell how it appears, and since any time smaller than Planck time could never be detected, we can't tell apart from that if it's continuous or discreet.
Well, I'm not so much asking about the true nature of change or movement but rather just what we mean to say when we say that something is changing or has changed. I take it that if I told any layperson that a block of wood changed from dark to pale when left out in the sun, they would understand what I mean by 'changed'. If interrogated as to the meaning of change they might say something like "well, it's when something is in one condition at one time, and the same thing is in another condition at another time. That's a change."
But obviously tha... (read more)