A Semiotic Analysis of the Double Slit Experiment

by Swinton Roof

Sept 5, 2001

"Symbolic Knowledge is forever and always, partial and incomplete, yet has an optimum expression which involves both the knower and the known in a significant way" ... Rasputin11

This paper assumes one is somewhat familiar with the famous double slit experiment which establishes the quantum wave-particle paradox using either photons or electrons. The slits are reduced in size until interference effects show up on a screen and then the light source is reduced in intensity until only one photon or particle is emitted at a time. The particle elicits interference as if going through both slits at the same time. Simple knowledge of which path (without interfering with the path) it took, however, destroys the interference effect. Observer knowledge conditions the result! The experiment is paradoxical and not explainable in classical or logical terms.

Now suppose we take a semiotic viewpoint. Is it possible to gain any new insights? This is what we will attempt to do here. To do so, we first have to determine what aspects of signification can be identified. Recall that a sign is a triple relation between the principle sign itself(the representative form), the interpretant (observer or semantic response), and the object referent (the thing it points to). In other words, something has to signify, something has to be signified, and the relation has to be significant.

There are a few things that will help us make these assignments. The sign itself is typified by some selection , demarcation, or boundary and is digital in the sense of being a space-time modulation or pattern. Referents are typically mass-energy analog events. The interpretant makes the selection and evaluates the significance of the sign-referent relation.

Let's isolate the sign first. Imagine a hunter out looking for signs of game. He spots some tracks in the mud. The hunter interprets the tracks to mean that some animal was previously standing there. The hunter (interpretant) selects the sign (tracks) and connects it to a referent (animal). The sign (digital selected space-time pattern) represents an analog mass-energy event (referent animal) and is significant in the context of looking for game. The sign thus is an effect of the original cause or referent. Now in advanced human semiotic situations involving language it is a condition that the sign-referent relation can be entirely arbitrary. If we are going to have a semiotic view of events without an actual sentient observer, however, we must demand that the interpretant actually have a logical consistent law-abiding relation between the sign and referent. There is nothing in semiotics that demands the contrary. We can thus identify cause-effect as referent-sign in such situations. The interpretant then is the physical laws that produce the relation. The effect is a sign for the cause and physical law is the significance.

Using the above ideas, it now becomes apparent that the sign in our experiment is the pattern on the screen. The referent cause is the electron. The interpretant is the experimental setup itself. Quantum physics implies an observer but actually the experiment can be set up to run automatically and the results will be the same. The observer in the context of the experiment is the registering equipment and physical setup. In other words, it is the system itself in which sign-referent relations are embedded. This distinction holds in sentient signing also, wherein the interpretant system is simply the semantic subject himself.

Now it was said that the interpretant makes a selection or demarcation in the context of the sign. That selection is simply the double slits. The slits select out of many possible electrons only a certain few (even one at a time) going along a precise path. The digital space-time modulation effect or sign is a sequence of bright and dark stripes (on/off pattern) on the screen. The screen can in fact be replaced by an array or grid of photomultiplier tubes each of which detect a single photon or electron. The final whole grid pattern then becomes essentially a grid of zeros and ones, where ones represent a hit and zeros dont. When performed this way, it is found that only one and one detector at a time will display a one. The spatio-temporal pattern of interference lines emerges only after some time has elapsed and the results are added up. This is logically consistent. No paradox there. The apparent paradox is that the final pattern has holes or empty spaces where no particles end up. The catch is that the exact path is indeterminate. The interpretant system does not know through which slit the particle passed for each hit of the detector. We must come up with a significant law abiding relation for the interpretant to explain the time averaged pattern.

Consider the experiment with just one slit. As the slit is reduced the resultant sign starts as a broad spot which shrinks in size as the slit becomes more narrower. The time averaged sign relects the law-abiding situation wherein the interpretant system gradually becomes more selective. The final time-averaged spot or sign represents the time-averaged analog particle events in a law abiding way. At some point when the slit becomes very narrow, the spot spreads out and eventually the pattern is one completely random spread of on/off. The classical physicist explains this as diffraction if using a wave viewpoint and scattering if using a particle description. The quantum physicists explains it as the complex quantum wave equation having all possible paths equivalent. The semiotician must say that the selection has been made so precise that all the relevant law-abiding information has been excluded and the interpretant can only represent this sign as an uncertain smear. With semiotics and signing we are talking about making sense of distinctions. Distinctions exclude relevant information. When all the relevant information has been excluded, the result is nonsense i.e. random dots. While this interpretation may not appeal to the materialist, it non-the-less appears to satisfy the semiotic requirements.

Now set up the experiment again with two slits but include detectors that can sense which slit the particle goes through. The interference pattern should reappear but it doesn't, hence the paradox in the eyes of physics. The normal interpretation is that knowledge of the path influences the result but this appears absurd. From the semiotic view recall that the interpretant is the system of slits,detectors, and screen. The interpretant in this case is thus actually making a selection when the particle takes a particular path. The experiment is totally equivalent semiotically to the single-slit version! And indeed, the resulting sign is exactly the same. From the semiotic view there is no paradox here at all. The resultant effect (sign) has the same semantic significance as the single slit experiment!

Now all that remains to explain is the original condition of having two slits and an interference pattern (time averaged remember). The interpretant in this case is still making a selection but of a different sort since two slits or paths are now available. In fact, the interpretant is faced with coming up with a law-abiding digital sign for a 50/50 proposition. The interpretant itself cannot know at all which path is taken, only that one must be taken. Taking two paths at the same time would be a logical inconsistency from the interpretive viewpoint of particle detection as singular events. The interpretant would produce a total random spread from either slit alone so the combination must be 50/50 spread separate from and distinct from the single spread situation. To produce the same result would elicit a sign independant of the selection process and thus insignificant! Semantically it makes sense for the result to be an alternating pattern that repeats and spreads over the whole screen but with a diminishing effect the further removed one is from center. Adding slits would complexify the resulting sign but the overall tendency would be for the resulting sign to merge with a wide slit as more slits are added. Semantically an interference pattern is an acceptable lawabiding sign for the analog referent events, and still we have no paradox. Semiotically speaking, we have no paradox!

There is one other aspect that needs attention. The pattern itself as derived from classical and quantum physics is mathematically very simply a sine wave function of two variables, the path difference and the frequency of the photon (or electron). From this we see that the digital space-time modulated sign witnesses that the interpretant pulls spatial information from the slit to screen spatial relations and time information from the analog event itself. The selection process culls out information partially from the referent and partially from the interpretant itself. The semantics of perception involves the interpretant himself (itself) in its own perceptions. The perception is thus colored by the perceiver. This appears to be a principle of semiotics necessary to establish relations of signification. If this is universal, the implication is that the referent conditions the sign with time modulation and the interpretant conditions the sign with space information. This seems consistent with an observer or awareness projecting space but experiencing time.

The only real difficulty from a semiotic perspective, as I see it, is that we have stated in a round about way that the selective process leading up to a signification has a limit which is determined by the referent. As the selective process narrows toward this limit, the sign becomes less representative of the nature of the referent and becomes more arbitrary (the spot from a single slit spreads out). Might we thus consider that the nature of signification itself has a degree of arbitrariness built in that is equivalent to the uncertainty principle of physics? In other words, can the referent of any signification be entirely known? To do so would imply that the sign has become the referent would it not? At which point, what digital semantic knowledge can the interpretant claim to have? The process of signification has been short circuited in a sense. Now imagine the two extremes - slit narrowing to zero and slit widening to infinity. Both have the same sign as resultant - significant knowledge equal to zero (random spread). The selective slit narrowing process within the interpretant produces a valving effect, which seems to have some maximum significance at some intermediary point. The resultant sign thus has a best representational effect at a certain degree of selectivity. Might this same phenomenon apply to high level semiotics also?

Is there a lesson here for man and his abstract language representations? When we attempt to be extremely precise with our language definitons, the sense is lost because the extra contextual information within the interpretant has been excluded. The same result can acrue when we are too vague (less selective) and have too much context, too many possible meanings. There seems to be an optimum degree of selectivity when communicating. People seeking absolutes are destined to end up in confusion. Semantic Inquistions are doomed to fail!

The experiment even has a semiotic analog with the eye and perception. The eye with it's lens and retina performs a selective valving that seems to produce a best effect (most significant sign, best image, most knowledge about the referent object) when the pupil size is adjusted to just the right amount. Is this a semiotic principle? Can it be formalized in the language of math? Time will tell.

It is apparent to the author, that the field of semiotics is still in it's infancy but has potential for solving a great many mysteries. The physical and biological sciences might benefit immensely from such a viewpoint even now. Eventually, this methodology might be formalized into a true mathematical theory with quantitative theorems.