An investigation of Hawking's proposal that the inclusion to topologically non-trivial manifolds in the functional integral of quantum gravity leads to the loss of quantum coherence is carried out. We discuss some of the problems associated with Hawking's $-matrix theory, including the breakdown of the connection between symmetry principles and conservation laws. It is proposed to use Kaluza-Klein theories to study this issue, since these theories contain well-defined euclidean instantons. These can be used to perform explicit semiclassical calculations of the effects of space-time foam. A general method is presented for constructing Kaluza-Klein instantons based on solutions of ordinary Yang-Mills theory. It is argued that none of these will lead to a breakdown of quantum mechanics. The physical effects of space-time foam are discussed in some detail using explicit instantons of a four-dimensional Kaluza-Klein theory. © 1984.
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