Dynamical suppression of topological change

This is a brief report of some work that the author carried out concerning spontaneous changes of 3-space topology. The idea that the topology of 3-space might undergo quantum fluctuations was first put forward in 1957 as follows: It one attempts to measure the average electric field in a spacetime volume L/sup 4/ in a vacuum of 00K (e.g., by observing during a time L the motion of a charged test body of volume L/sup 3/) one will not generally obtain a vanishing result. In a sequence of such measurements one will obtain a statistical distribution of values with magnitudes peaked around 1/L/sup 2/ (h-bar = c = 1). Similarly, quantization of the linearized theory of gravity suggests that if one attempts to measure the Riemann tensor averaged over a spacetime volume L/sup 4/ in a vacuum at 00K (e.g., by observing during a time L the change of strain of a gravitational attenna of volume L/sup 3/) one will probably not obtain zero but rather a value of magnitude in the neighborhood of λ/sub P//sup 2//L/sup 4/ (λp = Planck length) corresponding to a spacetime radius of curvature of order L/sup 2//λp. Wheeler noted that this radius of curvature becomes comparable to L itself when L ≅ λp. Although this is precisely the realm in which the linearized theory fails, the result suggests that the curvature at the Planck scale fluctuates so violently as practically to cause portions of space to ''pitch of'' or to become multiply connected, developing structures such as ''wormholes''