The key puzzle is that somehow a photon (or other quantum particle) seems to have to ‘know’ what kind of experiment is going to be performed upon it well in advance of the actual performing of that experiment. How can it have the foresight to know whether to put itself into ‘particle mode’ or ‘wave mode’ as it leaves the (first) beam splitter?
The way that quantum theory works is not to give the particle any such ‘foresight’ but simply to accept the non-local holistic character of a wavefunction. In both of the above experiments, we take the wavefunction to be split into two parts at the initial beam splitter, and the particle-like aspect of the wave/particle only shows up at the detector, when the measurement is finally performed. The measurement makes the holistic character of the wavefunction manifest, in the sense that the particle always shows up in just one place, its appearance at one location forbidding its simultaneous appearance anywhere else.
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From the perspective of Systemic Functional Linguistic Theory, the 'non-local holistic character of a wavefunction' derives from the fact that it construes the probabilistic range of potential locations of the particle, rather than the actual location ('the one place') of the particle.
The wavefunction is not 'split into two parts' at the beam splitter because the wavefunction is not actual. Instead, the wavefunction construes the probability of a particle going one way or the other at the beam splitter. The reason that the particle is detected, rather than the wave, is that only the particle is actual.
The measurement 'makes the holistic character of the wavefunction manifest' in the sense that an observation construes one instance — one particle at one location — of the overall quantum potential.
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