TOPOLOGY CHANGE AND QUANTUM PHYSICS

The role of topology in elementary quantum physics is discussed in det ail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the qu antum Hamiltonian, this domain being often specified by boundary condi tions in elementary quantum physics. Examples are presented where clas sical topology is changed by smoothly altering the boundary conditions . When the parameters labelling the latter are treated as quantum vari ables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies, An existing argument of Sorkin based on the spin-statistics connection an d indicating the necessity of topology change in quantum gravity is re called. It is suggested therefrom and our results here that Einstein g ravity and its minor variants are effective theories of a deeper descr iption with additional novel degrees of freedom. Other reasons for sus pecting such a microstructure are also summarized.