Rolling Ball Argument - Topology Change Without Topology Change

Topology Change Without Topology Change

If the surface being explored is flexible or elastic, the way the ball is used may affect the reported topology. If the ball is forced into a wormhole mouth that is slightly too small, and the ball and/or throat distorts to allow the ball through, then in the ball's description of the surface, a "new" wormhole connection has suddenly appeared and disappeared again, and the connectivity of the surface has fluctuated unexpectedly.

In this case, no real geometry-change occurs in the deduced shape of the underlying metric – the process identified and "caught" a wormhole candidate (getting the ball wedged in the throat), then modified the curvature of the metric over time, forcing the throat to inflate to dimensions that allowed it to be traversed.