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The double-slit (gedanken-) experiment is the most famous experiment in quantum theory (QT). The explanation of the strange behavior of the electron in this experiment is used as a key example in QT in general. The description of the experiment includes a rationalization of when in quantum mechanics interference occurs and (most importantly) when it “collapses”. The aforementioned rule, here called the “interference collapse rule”, is contained in almost all textbooks of QT with only slight variations. However, this rule makes sense only with additional assumptions which apparently are not generally agreed upon among physicists. The paper proposes an improved interference collapse rule that connects the interference collapse to the QT measurement and a functional interpretation of QT measurement.

When the author began the development of his computer model of quantum theory (QT) (see [

When the author discussed the problem with physicists, his problem was not properly acknowledged. He instead was presented with interpretations and rephrasings of the standard textbook formulations which did not substantially help to solve the issue (from the author’s perspective). Typically, the attempts to generate an improved formulation included assumptions that were pretended implied by the original standard formulation. Indeed, the addition of further assumptions (which may be claimed to be implied by the original standard formulation) results in the generation of an improved formulation. From the abovementioned discussions there were only two problems remaining, namely 1) the proposed additional clarifying assumptions were divergent, and 2) the attempts at clarification led to the subject of QT which in itself does not have a generally agreed-upon solution (i.e., the QT measurement problem). Nevertheless, the author believes that these obstacles should not prevent attempts to improve the interpretation of the double-slit experiment by the explicit addition of the current implied assumptions.

In Section 2, a very brief description of the double-slit experiment is presented. Section 3 contains the standard explanation for when in QT interference occurs and when it does not occur. Section 4 lists the problems, questions and possible answers associated with the standard formulation. Sections 5 to 7 contain a proposal for an adaptation of the standard formulation to a “functional interpretation”. A functional interpretation (or functional description) specifies the dynamic evolution of the system in terms of state transitions and explicit actions and events.

Under the assumption that the reader is already familiar with the double-slit experiment, only a very short description is given:

The double-slit experiment demonstrates one of the most important features of QT, the relationship between the wave-like and the particle-like characteristics. In technical terms, the experiment shows the superposition of wave functions. To also show the destruction of the superposition, two variants of the double-slit experiment are typically discussed: 1) an experiment with photon source near the slits, and 2) an experiment without the photon source.

The electron starts at the source with a spatial distribution such that the wave function propagates the electron through both slits.

The two paths partly reunite again behind the splits, producing the interference pattern at the electron detector.

In addition to the process description given above, the electron wave passing the photon source may interact with a photon emitted by the photon source in such a way that the electrons wave function “collapses” and interference ceases.

In textbooks of QT, the double-slit experiment is often used to explain one of the key principles of QT which in this paper is called the “interference rule”. Here, we refer to the formulation of R. Feynman. The interference rule,in the context of explaining the double-slit experiment,is explained by Feynman in [

“When an event can occur in several alternative ways, the probability amplitude for the event is the sum of the probability amplitudes for each way considered separately”. There is interference:

If an experiment is performed which is capable of determining whether one or another alternative is taken, the probability of the event is the sum of the probabilities for each alternative. The interference is lost.

This interference (collapse) rule or slight variations of it, is contained in all textbooks on basic QT, either as an explanation of the double slit experiment. Or vice versa the double slit experiment is used to illustrate the rule. Without the photon sources near the slits, interference occurs. The inclusion of the photon source aborts the interference.

Currently, when one attempts to map the interference rule to a computer program that has the objective of simulating the double-slit experiment it turns out that this simulation is not possible. The problem is that a condition such as that of an experiment capable of determining whether one or another alternative is taken can neither reasonably be mapped to any mathematical constructs, nor to a physical facts-driven decision algorithm because it does not refer to elements of a physical state, but to some “capability of determining”. With a closer examination of the situation, it becomes clear that this is not a problem of writing a specific computer program; rather, the lack of comprehension is more general in nature.

The lack of comprehension can be expressed in the following list of question that can be asked with respect to the interference collapse rule:

1) Why is it said “capable of determining” as opposed to “is determined”?

2) What are the precise rules that allow me (or a computer program) to decide whether my experiment is capable of determining?

3) Does the condition “capable of determining” always refer to an observation or event (e.g. measurement) during the movement of the waves during the waves towards the observation of the interference pattern? Or are other capabilities of determining imaginable?

4) In QT it is often the case that the capability to decide between A and B is a matter of probability. Does the interference rule apply also to probabilistic decisions? Or does the rule assume decisions with certainty?

5) Does the rule state a logical implication (i.e., IF a THEN b) or a logical identity (i.e., IF a THEN b AND IF b THEN a)? In other words, if interference ceases, does this also imply that it should be in principle possible to determine which alternative was taken?

Attempts to defend and explain the standard QT interference rule typically focus on an answer to question 3 above (“Does the condition ‘capable of determining’ always refer to an observation or event (e.g. measurement)... ?”). Therefore let us attempt a modification of the standard QT interference rule which clarifies which types of events may occur that are capable of causing a collapse of the interference in regard to the electron wave on its way to the screen.

The proposed modification is the following:

“Interference is lost (i.e., the probabilities must be added) if through a measurement it is possible to determine that a particular path is taken”.

This phrasing still requires that the term “measurement” be more precisely defined. However, when a situation may be considered to exactly represent a measurement is one of the open questions of the unresolved measurement problem. At minimum, it is controversial whether the addition of the photon source in the double-slit experiment represents a measurement.

In [

1. A measurement always implies interactions between the measured quantum object and the measurement environment. Measurements of QT observables can be performed using a variety of measurement devices, apparatuses, and processes. All such measurement processes must include at least one interaction in which the measured object exchanges information with some other entity belonging to the measurement apparatus.

2. The model of measurement is based on “QFT interactions”. QFT interactions are “normal” interactions between the measured QT object and the measurement apparatus that adhere to the laws of quantum field theory (QFT) and must be treated using methods of QFT.

3. In general, the interacting particles/waves consist of multiple “paths” with different associated probability amplitudes. The interaction always occurs at a definite position. Only the paths that cover the interaction position determine the result of the (measurement) interaction.

4. The measurement process includes a collapse of the wave function. After the interacting paths are determined and used to generate the interaction result (i.e., measurement result), all of the remaining paths are discarded. This process may be considered to be the “collapse of the wave function”.

5. Interactions support only a non-bijective mapping of the “in” state to the “out” state and thus only the limited exchange of information. This limited exchange of information is the cause of some of the limitations and peculiarities of QT measurements.^{1}

With the above described functional interpretation of the QT measurement process, it is possible to unify the collapse of the interference (as it may, for example, occur in the double-slit experiment) with the collapse of the wave function associated with QT measurement and to reformulate the interference collapse rule as follows:

Interference is lost (i.e., the probabilities must be added) if the particle/wave becomes involved in a QFT interaction on its way to the observation target.

The above proposed improved interference collapse rule is based on a functional model of QT measurement as described in [

The same holds true for alternative collapse theories, such as, for example, the GRW theory (see [

The proposed interference collapse rule associates the collapse of the interference (as well as the collapse of the wave function) with the occurrence of a “QFT interaction”. In [

The traditional interference collapse rule in quantum theory appears to be simple, albeit mysterious. Upon closer examination, as necessitated by the attempt to map the rule to a computer program, it turns out that the traditional interference collapse rule does not provide satisfactory answers to a number of questions regarding its precise meaning.

An alternative to, or at least modification of the traditional interference collapse rule is proposed by the author unifying of the collapse of interference as it occurs in the double-slit experiment and the collapse of the wave function associated with QT measurements. Unfortunately this alternative leads to the QT measurement problem for which there exists apparently no generally agreed upon theory. Nevertheless, the proposed “interference collapse rule” is considered by the author to be an improvement, because (a) it refers to criteria that have well-defined meanings within QT, and (b) it is compatible with a variety of interpretations of QT measurement, including the authors functional model of the QT measurement process described in [

Hans H. Diel, (2015) An Improved “Interference Collapse Rule” of Quantum Mechanics. Open Access Library Journal,02,1-5. doi: 10.4236/oalib.1101838