Is Heisenberg's Uncertiantly principle in conflict with modern
physics where calculus is used, which demands continuity?
I am afraid calculus was around long before Heisenberg,
and in fact calculus is associated more with the quaint
old physics of Newton etc. than with modern physics (though
there is plenty of room for calculus still). But no, there
is no conflict. You may be thinking that perhaps Heisenberg's
principle suggests that space is discontinuous, but that is not true.
It merely claims that for particles in space you cannot localize
them to within a certain distance or else there momentum will become
random and very large. This is quite different from discontinous
space (which may actually be true at some very small length-scale).
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Update: June 2012