Clarification The principles and measurement

The three principles of this chapter are those stated in the introduction — there in the particular form of a particle moving in space, here in general form; the fourth, agreement with Newton’s mechanics, comes into play in chapter four, where there is motion in space to compare with classical mechanics. One thing, however, none of the principles states: the state in which a measurement leaves the system.

This is not an oversight. To derive the Schrödinger equation there is no need to know it: that equation describes how the state evolves between one measurement and the next, and a derivation uses only the hypotheses it needs. Here, instead, it is needed, because the machines are cascaded: to predict what the second will do we must know the state the first one left it in. There is no need, however, to make it a principle: it is what Experiment 1 shows directly.

A remark. That repeating a measurement at once returns the same value holds for measurements that do not consume what they measure: a photon absorbed by the detector cannot be measured a second time. In the literature the former are called of the first kind, the latter of the second kind (the distinction goes back to Pauli). The machines in this chapter are of the first kind — the atoms pass through and carry on — and this is precisely what allows them to be cascaded.

A note on the third principle. Conservation of the total is, among the possible formulations, the most economical one: from it and from linear superposition follows the conservation of scalar products, as we show in Note 02.