'Null Measurement' Viewed Through Systemic Functional Linguistics

Penrose (2004: 545):

Let us consider a situation … where a single photon is aimed at a beam splitter, and its state is partially reflected and partially transmitted. After the encounter, the state is thus a sum of these two orthogonal parts, the transmitted part |τ⟩ and the reflected part |ρ⟩:

|ψ⟩ = |τ⟩ + |ρ⟩

(see Fig. 22.5). 

Suppose that a detector is placed in the transmitted beam where, for the purposes of argument, we assume that the detector has 100% detection efficiency. Moreover, the photon source is to be such that each photon emission event is recorded (at the source) with 100% efficiency. … If we find that, on some occasions, the source has emitted a photon but the detector has not received it, then we can be sure that on these occasions the photon has ‘gone the other way’, and its state is therefore the reflected one: |ρ⟩. The remarkable thing is that the measurement of non-detection of the photon has caused the photon’s state to undergo a quantum jump (from the superposition |ψ⟩ to the reflected state |ρ⟩), despite the fact that the photon has not interacted with the measuring apparatus at all! This is an example of a null measurement.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a single photon aimed at a beam splitter is not 'partially reflected and partially transmitted'. It is either reflected or transmitted, and only observation will resolve which alternative is the case. The 'sum of these two orthogonal parts' represents the potential of the quantum system, not any actual instance (photon) of that potential.

The reason why the observed absence (null measurement) of a photon at one detector guarantees its presence at the other is that the experimental set-up provides only two possibilities. If the probability of finding a proton at one detector is 0%, then the probability of finding a proton at the other detector is 100%.