I only have limited experience studying mathematics seriously, but from what I understand of continuity, I can’t help think but that there’s no reason to expect reality to actually be continuous. It’s too easy to get apparent continuity out of (even sorta) large numbers.
I think that particular continuity is an illusion, anyhow. One should count eigenstates. There are countably many eigenstates, none of which is classical. It is in trying to assert a definite position that this particular continuity issue comes up.
I only have limited experience studying mathematics seriously, but from what I understand of continuity, I can’t help think but that there’s no reason to expect reality to actually be continuous. It’s too easy to get apparent continuity out of (even sorta) large numbers.
I think that particular continuity is an illusion, anyhow. One should count eigenstates. There are countably many eigenstates, none of which is classical. It is in trying to assert a definite position that this particular continuity issue comes up.