The Further Splitting Of Wave Packets Viewed Through Systemic Functional Linguistics

Penrose (2004: 514-5):

But there are other experiments that might be performed on the photon after it emerges from the beam splitter. How can our poor little photon know, when it is about to emerge, that my colleagues do not plan a different type of fate for it? Suppose that, instead of each individually trying to detect the photon, they had concocted the following plan. They would separately reflect their parts of the wavefunction to a fourth location, where the two reflected parts would, say after a further year, simultaneously encounter a second beam splitter (Fig. 21.9). 

There, each arriving wave packet part would be individually split in two, so that one half emerges from this beam splitter in one direction to encounter a detector A, and where the other half emerges in another direction to go to another detector, B. (This applies separately for each of the two wave-packet parts, coming from the separate vicinities of each of my two colleagues.) If all the path lengths are accurately fixed appropriately (say all equal), then we find, remarkably, that the emerging photon can only activate one of the detectors, say A, and not B, because of constructive interference between the two parts of the wavefunction at A and destructive interference at B. 

No purely particulate picture of a photon can achieve this. The wavefunction is definitely needed, now, to explain the wave aspect of wave/particle duality. If the photon had already made its choice as to which of my colleagues to travel towards, when it left the first beam splitter, then the other route would become irrelevant. In that case, when the photon finally reaches the second beam splitter it comes from only one direction, and it could go either way, to reach either A or B. There is now no possibility of the needed destructive interference that prevents it from reaching the detector at B. Since A is always the detector that registers, it cannot just be the case that the photon has simply made its choice when it leaves the first beam splitter. It is necessary that both of the alternative routes that the photon might take are simultaneously felt out by the photon in its passage from the first to the second beam splitter.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this again misconstrues the wavefunction as actual instead of potential. It is not the wavefunction, in the form of a wave packet, that encounters beam-splitters, but the particle as an instance of the potential specified by the wavefunction. Again, the 'splitting of the wave packet' is the superposition of quantum potentials, and it is this superposition that specifies the total potential. Again, only one detector is activated because only one photon is emitted, and only it can encounter a beam-splitter.

The metaphor of a photon knowing, choosing and 'feeling out alternative routes' is misleading. A photon is an instance of the potential specified by the wave function, and it only becomes actual when an observation is made.