Caustic I by Eric J. Heller. "We often think of focal points as where light gathers after passing through a lens, but more generally for “random” lenses there are much more interesting patterns to examine. In Caustic I, rays of light from a point source have passed through two imaginary, successive layers of water, each with a wavy surface... The bright patches, or “caustics”, are similar to those produced when sunlight shines on a swimming pool, giving the familiar ribbed pattern... The swimming pool provides only one refracting surface, but what if there are more? We were led to this question by recent work on the motion of electrons in random landscapes where they are deflected by hills and valleys."

Regions of space, we said, do not exist by themselves, as intrinsic parts of a self-existent continuum. A region R exists for a given object O at a given time t if and only if the proposition "O is in R at t" has a truth value, which is the case if and only if a truth value is indicated ("measured"). A region that does not exist for any material object, does not exist at all.

A possible objection: Suppose that W is a region disjoint from R, and suppose that O's presence in R (at a time t) has been established. Isn't O's absence from W thereby implied? Are we not entitled to infer that the proposition "O is in W at the time t'' has a truth value (namely, "false")?

Response: Because the distinction we make between "inside W" and "outside W" has no reality per se, the answer is negative. Unless W is the sensitive region of an actually existing detector, this distinction cannot correspond to anything in the real world. If neither W nor its spatial complement (the region outside W) is the sensitive region of a detector, neither "inside W" nor "outside W" is available for attribution to O. All we can infer from O's presence in R is the truth of a counterfactual: if W were the sensitive region of a detector, O would not be detected by it.

An array of detectors (monitoring a set of disjoint regions R_i) therefore performs two necessary functions:

This conclusion bears generalization, not least because every measurement outcome is ultimately indicated by a "pointer" position. The measurement apparatus that is presupposed by every quantum-mechanical probability assignment is needed not only for the purpose of indicating the possession, by a material object, of a particular property (or the possession, by an observable, of a particular value) but also for the purpose of realizing a set of properties or values, of making them available for attribution.

This amply justifies Bohr's insistence that, out of relation to experimental arrangements, the properties of quantum systems are undefined.

At last we are in a position to see why this is so: if space (qua expanse) is intrinsically undifferentiated, it falls to its material "content" to realize spatial distinctions, along with those properties that (like positions) are defined in terms of spatial distinctions.