I’ve posed the following inquiry on Philosophy Stack Exchange:
Can the idea of continuity make sense in the real world?
A summary of it is presented here:
Continuity in mathematics means no jumps or gaps in functions, akin to the real numbers' property where there's no smallest number after any given number. The question ponders if this applies to the universe, using time as an example. It discusses the paradox of infinite moments within any time interval, suggesting that if time were truly continuous, it might imply that time doesn't actually pass, questioning the existence of continuity in the universe. If time were continuous, an infinite number of moments would precede any given moment, making the passage of time impossible. So doesn’t this suggest that time cannot be continuous?
This is a portion of the answer provided by the user @TKoL:
This is actually an open question in physics - it's currently unclear if physics requires any kind of spatial infinite continuum, or if all of spacetime may be discrete. Physicists take both possibilities seriously, and some prefer the idea of discrete for various reasons, and others prefer to think that it is a genuine continuum, and many are just uncertain and undecided and comfortable saying "I don't know".
But then, I wonder: if this is an open question, what exactly do the Planck time and Planck length imply? Don’t they necessarily suggest that both time and spatial distances are discontinuous? If not, why not?
