“The point is that we really have no conception of how to consider linear superpositions of states when the states themselves involve different space-time geometries. A fundamental difficulty with 'standard theory' is that when the geometries become significantly different from each other, we have no absolute means of identifying a point in one geometry with any particular point in the other-the two geometries are strictly separate spaces-so the very idea that one could form a superposition of the matter states within these two separate spaces becomes profoundly obscure.

Now, we should ask when are two geometries to be considered as actually 'significantly different' from one another? It is here, in effect, that the Planck scale of 10^-33 cm comes in. The argument would roughly be that the scale of the difference between these geometries has to be, in an appropriate sense, something like 10^-33 cm or more for reduction to take place. We might, for example, attempt to imagine (Fig. 6.5) that these two geometries are trying to be forced into coincidence, but when the measure of the difference becomes too large, on this kind of scale, reduction R takes place-so, rather than the superposition involved in U being maintained, Nature must choose one geometry or the other.

What kind of scale of mass or of distance moved would such a tiny change in geometry correspond to? In fact, owing to the smallness of gravitational effects, this turns out to be quite large, and not at all unreasonable as a demarcation line between the quantum and classical levels. In order to get a feeling for such matters, it will be useful to say something about absolute (or Planckian) units.”