The Two-Slit Experiment Viewed Through Systemic Functional Linguistics

Penrose (2004: 504-5):

One of the most convincing (and best known) reasons for our having to face up to the fact that particles can behave as waves and waves as particles is the two-slit experiment. Here we have a source of particles and a detector screen, where there is a barrier with a pair of narrowly separated parallel slits in it, situated between source and screen; see Fig. 21.4a. 

We suppose that one particle at a time is emitted, aimed at the screen. If we start with one slit open and the other closed, then a haphazard pattern of dots will appear at the screen, forming one at a time as individual particles from the source hit it. The intensity of the pattern (in the sense of the greatest density of dots) is most extreme in a central strip close to the plane connecting source to slit, as is to be expected, and it falls off uniformly in both directions from this central strip (Fig. 21.4b). This pattern is effectively the same if the experiment is repeated with the other slit being the open one (Fig. 21.4c). No puzzle here. But if the experiment is run once more when both slits are now open, then something extraordinary happens; see Fig. 21.4d.  

The particles still make dots on the screen one at a time, but now there is a wavy interference pattern of parallel bands of intensity, where we even find that there are regions on the screen that are never reached by particles from the source, despite the fact that when just one or the other of the slits was open, then particles could reach those regions perfectly happily! Although the spots reach the screen one at a time at localised positions, and although each occurrence of a particle meeting the screen can be identified with a particular particle emission event at the source, the behaviour of the particle between source and screen, including its ambiguous encounter with the two slits in the barrier, is like a wave, where the wave/particle feels out both slits during this encounter.  Moreover … the spacing of the bands on the screen tells us what the wavelength of our wave/particle must be… 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, wave-particle duality is the complementarity of potential and instance. In this experiment, it is particles that are emitted at the source and detected on the screen, and so it is particles that are actual. The fact that waves are neither emitted at the source nor detected on the screen demonstrates that the wave aspect is not actual.

The wave, as quantum potential, measures the probability of a particle's location, and the actual locations of particles on the detector screen are instances of that probability, with the most frequent locations (highest densities) being instances of the highest probability.

When only one slit is open, quantum potential is measured by one wave of probability, so the pattern of particle detections reflects this. But when two slits are open, quantum potential is measured by two waves of probability, such that the actual locations of particles on the detector screen are in line with the constructive and destructive interference patterns of the two waves of probability.

In this view, then, the spacing of the bands on the detector screen manifests a wavelength of equiprobability, and to say that the behaviour of the particle between the source and the screen is like a wave is to mistake potential for actual. Moreover, as Richard Feynman explained to his BBC TV audience in 1965:

To conclude that it goes either through one hole or the other when you are not looking is to produce an error.