The specific example of an electron orbiting in the field of a charged
sphere and a superimposed uniform magnetic field is used to illustrat
e that in classically chaotic systems, irreducible uncertainties requi
red by the Heisenberg principle are amplified exponentially to the mac
roscopic level in short times. According to the Copenhagen interpretat
ion of quantum theory irreducible quantum uncertainties have led to qu
antum indeterminacy on a macroscopic scale in interesting times.