We are accustomed to thinking of space and time as particulars or individuals—even if we should hesitate to describe them as things or objects or substances. We say ‘space has three dimensions’, ‘material things occupy space’, ‘the debris has disappeared into space’ and we talk in a comparable fashion about time. Not only do we think of space and time as individuals but, in many connections at any rate, we think of them as unique individuals. When we talk about spaces (...) and times in the plural, when we say ‘fill up the spaces on the form’, ‘it could go in the space between the lamp and the door’, ‘there were peaceful times in the early years of their marriage’ we think of these multiple spaces and times as parts of the unique allencompassing space and the unique all-encompassing time. Kant believed that we could not help thinking of them in this way. We do, at any rate, in fact think like this and it is this conviction that I want to examine. (shrink)

Evidence is presented that the singularities induced in causal Lorentzian spacetimes by changes in 3-space topology give rise to infinite particle and energy production under reasonable laws of quantum field propagation. In the case of the gravitational field, if 3-space is compact the total energy must vanish. A topological transition therefore induces a violent collapse that effectively aborts the transition, since the collapse mode is the only mode carrying the negative energy needed to compensate the associated infinite energy production. The (...) existence of the Hamiltonian constraint of general relativity suggests that topological stability is a local property of the quantum theory that is maintained even when 3-space is noncompact. (shrink)