Isaac Ben Jacob

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The "Double Slit Experiment", and the theory of singly-positioned particles

The present study is dedicated to the experiment of Feynman called "Double-Slit" (also mentioned as "Young's Interference Experiment"). Since the object of this article is to be accessible and to put forward general hypotheses, it will be as brief as possible. Divided into several sequences, Feynman's experiment is realised with a beam of electrons or photons projected through a plate. This plate is pierced by two slits, either one of which can be blocked at will. Behind the plate and its two openings, one places a receptor wall, which records the impacts of the electrons as they hit the surface. The experiment is divided into three sequences, depending on whether one of the plate's two openings has been opened or closed, and whether the trajectory of the electron beam is being observed through the plate, or not.


In order to illustrate our point, we have attached a video commented by Professor Al-Khalili, whose explanations are relevant to this article.

Einstein Niels Bohr, 1950

Albert Einstein

Niels Bohr

The "Pilot Wave" of De Broglie - Bohm


The other interpretation relating to the Double-Slit Experiment is the one of De Broglie - Bohm. Although a minority view, it is nonetheless interesting, and bears witness to the enduring dissatisfaction of many scientists with the hypothesis of the Copenhagen school.


The De Broglie - Bohm interpretation is based on the Pilot Wave Theory. The particle and the wave (understood, according to Max Born, as "the probability density of finding a particle"), are entirely distinct elements. This concept implies the existence of empty waves, also called "ghost waves", which can propagate in space without transporting any particle. So the wave and the particle are completely autonomous here. This contradicts the usual description of quantum mechanics, which states that particles are endowed with a wave function.


As soon as 1952, David Bohm, considering the Double-Slit Experiment through the lens of De Broglie's Pilot Wave Theory, elaborated a new concept. He supposed thusly that the particle studied in sequence no. 2 was accompanied by a pilot wave. The wave would have propagated through the slits of the plate simultaneously, but on the contrary, each emitted particle would have conserved one single trajectory, its own natural trajectory, and would have passed through the plate by crossing only one of the two slits. The interference pattern registered on the receptor wall (once the particles have passed through the plate), would be produced by the wave transporting the particles, and shaped by the wave's own constructive and destructive interferences.


Finally, in sequence no. 3, upon detection of the particle, the experiment would be understood as being influenced by observation. The wave, passing uniformly through both slits, would then be separated into two wave-beams, thereby destroying the interference pattern which was previously visible on the recording wall.



Attempt at an interpretation of the experiment, by Isaac Ben Jacob


Our interpretation does not lean in favour of the Copenhagen school, nor in favour of the De Broglie-Bohm theory. Each one of these two interpretations appears to us as containing common sense elements, which contribute to enhancing comprehension of the phenomenon. Taken individually, the two interpretations are fundamentally contradictory, but when combined only in some of their aspects, they can considered as synergistic with each other.

Path A+A- conflicts with path B-B+, and they interfere by superposition, whilst cancelling each other out. Therefore, one should not understand the photon emission experiment as having a 50 % chance of taking path A+A- or B-B+. One should not, either, consider it as a splitting of the photon into two parts, taking the two paths simultaneously, because it would mean that the same particle can have two distinct positions in space. Besides, the mere fact that only detector 1 is able to receive the photon in 100 % of occurrences, means that the paths A+A- and B-B+ have cancelled each other out, and that, by eliminating the interference just after the final half-silvered mirror, they have put the photon back on its initial trajectory.


When the photon is faced with a choice, it does not proceed with determining this choice, it does not become involved in this possibility, because to it, that would mean being capable of occupying two simultaneous positions in space. The choice which presents itself to the photon, is actually not a choice, they are two hypotheses, where paths A+A- and B-B+ are two trajectories of two different photons, one could even say of three different photons: the photon preceding this sequence, the one from the sequence, and finally, the one from the moment after. It is not a matter of a 50 % vs. 50 % probability for the photon to take one path rather than another, but it is about a 100 % probability for it to interfere and to conflict with the path of another photon. In and of themselves, paths A+A- and B-B+ are distinct positions in space and time, corresponding to different photons. Which creates the interference.


Between the points A+ and A- and B- and B+, the photon does not disappear completely: a fraction of its definition takes one path, the other path being occupied by a fraction of another photon's definition. The rest of the definition of the two photons in question, is in turn interfering with the other photons which have already passed, or will later pass, through the experiment.

Therefore, during the conflict triggered by the choice being imposed on the photon, there is a partial dematerialisation of the photon, which occurs at the moment of contact with the first half-silvered mirror. At the last half-silvered mirror, the interference stops, and repositions the photon on its original trajectory. Which explains that only detector 1 can receive it.

To summarise, we distinguish between three sequences, which are composed in the following manner:


Sequence no. 1:


Electrons are spray-fired through a plate, in which two slits have been placed. One of the slits is blocked. It is then observed, on the receptor wall located behind the plate, that the electrons which have passed through, have crashed on a single, band-shaped region on the wall. One comes to the conclusion that the electrons have behaved as a beam of particles. Crossing the plate through the only open slit available, they have projected themselves directly on the wall, following a straight line.


Sequence no. 2: (which yields abnormal results)


Electrons are still spray-fired through the plate pierced by two slits. But contrary to sequence no. 1, the two slits are both open. An "interference pattern" is then observed on the receptor wall. It is a pattern comprised of several bands in which the electrons' impacts are concentrated, alternating with empty spaces. This "interference pattern" is a typical characteristic of wave propagation, and not of particle-like behaviour, which is surprising.

One must also stress the fact that the same result can be obtained by firing the electrons one at a time, separated by regular time intervals. From this, we logically deduce that the electrons crashing one by one on the wall, even when they are being projected individually, do contribute to the wave-like behaviour of all particles as a whole.


Sequence no. 3: (which yields abnormal results)


Not knowing why a beam of particles was exhibiting  this wave-like behaviour, scientists decided to observe each particle individually. Thus, they added a detector placed immediately behind one of the plate's two slits. The goal of this apparatus, being to record the trajectory of each particle during the crossing of the slits. Even more astonishingly, two impact regions re-appear on the receptor wall. The "interference pattern" has vanished.

Conclusion: When each particle's individual trajectory is being observed, the electrons behave no longer as a wave, but as particles.


Schools of thought clash, but the experiment still remains unexplained.

In the second experiment, when an obstacle is placed on path B-B+, the photon is able, not to "feel" that an obstacle is placed on this path, but rather, not to react. Indeed, already at the first half-silvered mirror, it does not conflict with another photon having a different position in space and time. Consequently, the modification in configuration intervenes at the very beginning in the experiment, and not at the theoretical moment when the photon should be able to feel the obstacle at a distance.


How can photons interfere between themselves in their positions, and therefore, in space?


When the photon is faced with a choice in trajectory, some scientists assume that the photon splits into two, interferes with itself, and takes both paths at the same time. So, they attribute to the photon two simultaneous positions in space. There is a disturbing illogicality here.


It is more reasonable to consider that the photon is faced with two alternatives, consisting in occupying two different positions in space and time. Each position corresponding, and this is very important, to one and only one photon. One photon's position in space and time is therefore deterministic of this photon's definition. Faced with these alternatives, and being incapable of occupying two places at once, the photon collides and interferes, not with itself, but with other photons which need to occupy positions in space and time different from its own. So the interference is not of the photon with itself, but of the photon with the positions of other photons. The alternative, the choice between two paths is consequently a conflict for the photon, and causes to it a loss of definition, consecutive to the superposition of the positions in time and space of several photons.



Let us now go back to the Double-Slit Experiment:


Photon α of sequence no. 2 does not duplicate itself, in actual fact. Contrary to common opinion, it does not pass simultaneously through the two openings of the plate. Contrarily, it combines in a conflictive way with the photons participating in the same experiment, and loses in definition. A fraction of its definition is dispatched through slit A (for example), which is concretely the natural trajectory of its passage. Here, slit A is the opening of the plate which would have imposed itself as the natural trajectory in sequences no. 1 and no. 3. Another fraction of the photon's definition will again pass through slit A, but it will do so during the projection of the next photon in the experiment. Besides, a similar thing would have happened with photon α, during the projection of the previous photon β, that is to say, paradoxically, before photon α was even emitted. So it is necessary to understand here, that the superposition and confusion of photons also causes a superposition and confusion of a fraction of their definition in time and space.


To summarise, the fraction of the photon passing through slit B actually comes from another photon participating in the experiment, but not from the one (α) which was emitted at moment T, and about which the common opinion assumed that it had duplicated itself between the two openings (slits A and B) of the plate. Thus, the photon emitted in sequence no. 2 does not split into two, neither does it actually pass through both openings simultaneously. In the face of the choice imposing itself to photon α, of entering path A or B, the photon does not proceed with this choice, it collides itself with the other photons, and loses in definition. Consequently, the definition of photon α gets dispatched between opening A of the plate (which is the default path for this photon), and the other photons (γ and β) emitted before and after its passage.

The Copenhagen School


The majority interpretation is undoubtedly the one of the Copenhagen school of thought, stemming from the work of Niels Bohr and Werner Heisenberg. However, this interpretation, which was elaborated around 1927, was not accepted by Albert Einstein, who considered it incomplete and unsatisfactory.


The Copenhagen school considers it useless to try to determine the exact position of a particle in sequence no. 2 of the experiment. The particles in this sequence, being described by their wave function, would not have any locality in space. Therefore, each one of the particles participating in this sequence (no. 2) would interfere with itself, and pass through both slits of the plate simultaneously.


Any attempt to measure, or to detect the particle (sequence no. 3), would highlight one of the positions included within the wave. Here, we are referring to the wave produced by the particles when they are being projected through the plate. In other words, according to the Copenhagen school, when sequence no. 2 is not being observed, any interrogation relating to a particle's position is pointless and useless. In this way, the Copenhagen interpretation states that "reality is in the observations, not in the particle".


As a conclusion, according to Niels Bohr, reality consists in what is actually detected. The wave function of the particles studied in sequence no. 2 has no value by itself, it is not only theoretical, but also, does not correspond to any intelligible and scientific reality. Consequently, sequence no. 2 does not constitute a valid object of study. Only sequence no. 3 matches a scientific reality.


Albert Einstein's criticism regarding the Copenhagen interpretation


Faced with this opinion, the paternity of which was partly attributable to Niels Bohr, Einstein exclaimed: "Do you really think the moon isn't there if you aren't looking at it?" Einstein was deeply bothered by the Copenhagen interpretation, because he considered it incomplete, and he believed that the particle studied in sequence no. 2  had to have some kind of definition, even when it was not being observed. He expressed such an opinion in 1935 in a ground-breaking article (co-authored with two of his students, Podolsky and Rosen), entitled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"  Generally speaking, Einstein could not conceive, as he liked to put it, that "Providence plays dice with the laws of physics". Which was equivalent to saying that the opinion of Bohr and the Copenhagen school deemed it acceptable for the particle's state in sequence no. 2 to be indeterminate in scientific terms. For Einstein, there was an illogicality here, which could not account for physical reality.

Introduction :


The wave-particle ambivalence is a principle of physics, according to which all particles exhibit, more or less, wave-like and particle-like properties. This principle is one of the foundations of modern quantum mechanics.

This ambivalence of quantum objects is a middle-ground solution, accommodating both the theories of Christiaan Huygens and of Isaac Newton, who considered, respectively, that light was a wave (Huygens), or a train of particles (Newton).


But there are essential differences between waves and particles, which lead one to think that the particle is the definite state, whereas the wave is the degraded state of a particle, superposed and confused with other particles.


Generally speaking, we can say that:


A/ Particles possess a localised position in space and time, a continuous trajectory, and they are numerable.


B/ Waves have a less localised position in space and time, a multi-directional and simultaneous trajectory, similar to the motion of a water wave, and they are innumerable, i.e. impossible to count as distinct quantum objects.



"The Mach-Zehnder Interferometer"


It is on this basis that we will study, as a first step, the experiment called the "Mach-Zehnder Interferometer". Only then will we come to our own study relating to the Double-Slit Experiment. The Mach-Zehnder Interferometer was indeed considered by Albert Einstein, who made regular reference to it, as a more intelligible and more explicit version of the Double-Slit Experiment.


A semi-reflective (half-silvered) mirror is placed on the trajectory of a photon, thereby leaving two possibilities for the photon's trajectory. Nevertheless the photon, the trajectory of which could be random, choosing either one of the two proposed paths, will always be detected on one, and only one of the two photographic receptors located at the end of the route. Its trajectory will become truly particle-like again, only when an obstacle will be placed on one of the two paths.


Study of the experiment:


The Mach-Zehnder Interferometer is composed of "two  fully-silvered mirrors and of two half-silvered mirrors".

The paths are classified thusly:


1/ Half-silvered mirror, fully-silvered mirror, half-silvered mirror, noted "A+A-".


2/ Half-silvered mirror, fully-silvered mirror, half-silvered mirror, noted "B-B+".


Photons are emitted by a source noted 'V'. Inexplicably, only detector 1 records the photon exiting this apparatus. Yet, logic would dictate that detectors 1 and 2 would each have an equal probability of detecting the photon when it exits the apparatus.

The positions of photons γ, α and β are therefore partially confused in space and time, which is a causal effect of the loss in definition. This superposition leading to confusion, explains the occurrence of the interference pattern, which consists in a bundle of photons coordinated in the manner of a wave. The respective positions of the photons are then determined in function of a general pattern. This pattern implies for each photon to have interacted with all the other photons, according to a global egalitarian pattern. The destructive interference of the photons between themselves, neutralises their particle-like behaviour. From then on, the photons' wave-like behaviour substitutes itself to the particle-like behaviour, for wave-like behaviour is in conformity with the less individualistic, less identity-related, but more diffuse and egalitarian behaviour of the superposed photons.


During sequence no. 3, the interference pattern disappears because of the observation of the phenomenon. The observer, upon detection of the photon, individualises it, and gives back to it a particle-like behaviour. Through detection, he removes the choice imposed upon the photon to take path A or B. This is equivalent to saying that the action of observing a particle, increases its definition and individualises it, compared to the other photons, by detecting its position in space and time. One could add that differentiating one particle from the others, is a way of re-materialising it, and of dis-interfering it from the position conflicts which disturb its definition. Therefore, the observer and the particle are connected through quantum entanglement. The observer interacts with the particle, being an outside agent whose very own definition favours the definition of the particle. On this matter, we can suppose that the photons can interact between themselves through destructive interference when they are presented with two contradictory trajectories (the trajectories passing through openings A and B), to the same extent as the observer can influence the photon through constructive dis-interference.



Conclusion (expanded to philosophy)


Observation or consciousness (understood as a set of structured and coherent ideas), when they are the anticipation of an as-yet immaterialised reality, can modify the environment, and by gravitational effect, lead to the materialisation of that reality.

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