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Rolling ball argument : ウィキペディア英語版
Rolling ball argument

In topology, quantum mechanics and geometrodynamics, rolling-ball arguments are used to describe how the perceived geometry and connectedness of a surface can be scale-dependent.
If a researcher probes the shape of an intricately curved surface by rolling a ball across it, then features that are continually curved but whose curvature radius is smaller than the ball radius may appear in the ball's description of the geometry as abrupt points, barriers and singularities.
==Scale-dependent topology==
If the surface being probed contains connections whose scale is a smaller than the ball diameter, then these connections may not appear in the ball's map. If the surface contains a wormhole whose throat narrows to slightly less than the ball's diameter, the ball may be able to enter and explore each wormhole mouth, but will not be able to pass through the throat, and will produce a map in which the narrowing mouth walls each terminate in a sharp geometrical spike.
The smooth and multiply connected surface will be mapped by the physics of a "large" particle as being singly connected and including geometrical singularities.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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