Preamble

The continuum viewpoint is consistent with our physical prejudices, engendered by sensory evidence. However such a perspective gives rise to some fundamental conceptual and physical difficulties which involve questions of scale, interpretation, and reproducibility of phenomena. Here we outline several of these difficulties and indicate how one is forced to take account of the fundamentally discrete nature of matter and the spatial scales at which physical systems are monitored.

The Natural Continuum Prejudice

We unconsciously adopt a continuum viewpoint when observing and interacting with the world about us. For example, we regard the air we breathe as tangible (when feeling the wind on our faces or filling our lungs) and as permeating the space about us. If we pour some water into a glass, then this water appears to take up a definite shape, determined by the sides and base of the glass and by the free water surface. The water seems to fill this shape, apart from possible visible bubbles of trapped air or immersed foreign particles. The glass itself appears to occupy a definite region, delineated by its bounding surfaces, with the possible exception of visible imperfections. However, while we can see ‘inside’ water and glass, this is not the case for opaque objects, for which only the external boundary is amenable to direct observation. Nevertheless, we often regard opaque objects to be full of matter in the sense of occupying all space within their perceived external boundaries.