Chapter XVIII


Wave-particle duality




"The pessimist complains about the wind, the optimist expects it

to change and the realist adjusts the sails. "

- William Ward -


       Let us imagine an electromagnetic wave, a beam of light, focusing on a screen where there are two fissures. When the wave passes through these holes, each one of them will be a new source of a wave motion, such as a material wave, like water, for example.

      A key feature of this undulatory movement is the phenomenon of interference, which reflects the fact that the oscillations from each source of material wave can be added or subtracted from one another.

      If we put a second screen, after the first one, so that we can detect the intensity of the electromagnetic wave that hits it, we will see an image of interference, resulting of a composition of alternating maximum and minimum, corresponding to a pattern of lighter and darker lines which are called as interference fringes. This phenomenon matches with the wave interpretation of Young’s experiment and has proved the wavy nature of light.

      If you repeat the same experience with material particulate, shooting bullets, for example, we can very intuitively deduce what will be the pattern formed on the last screen. There will be bullets that pass through one fissure and bullets that pass through the other fissure, so that the ending result is the concentration of particles/ bullets in two specific and distinct directions. In this case, there is no phenomenon of interference. This is, therefore, the result expected by classical physics, corresponding to Newton's corpuscular interpretation.

     So far, so good, but only until now ...

     Because if we try to do this experience with other kind of particles, like electrons, for example, being thrown against the screen, with both slits open, it will be formed at the last screen an interference image!

      Supposedly, we would think that the electrons will pass through one or other fissure, and it will be expected for them to form on the last screen a standard corpuscular concentration of particles, like the same case of the shooting bullets experiment, but, in fact, that is not what happens. Surprisingly, what is seen is the same phenomenon of interference, which is a property of waves and as such we must assume that the electrons also have wave characteristics. But how is this possible?! …

      This experience becomes even stranger when we try to conduct the same experiment but only with one particle, starting by fire up a single electron against the screen. First, we can see that there is a single particle that hits and reaches the last screen in only one point, in a very specific direction.

      But when try to repeat this experiment several times in succession, releasing one electron at a time, one after another, each electron reaches the screen in a different point, however, when we overlap all the results together it is obtained, amazingly, the same figure of previous interference!! Magnificent!

      How come individual electrons passing through a slit or other randomly, can conspire together to form an image of interference?

     This is one experience that can turn our neurons in to ashes … how is this possible? Is there a logical way for this to happen and be so?!

      Now, let us perform the same experience with photons, imagining that we can reduce the intensity of the beam of light until we can throw individual photons against the screen, with both slits open. Initially it appears that each photon reaches the screen in just a final point, and always in different points, in a very specific localization, just like if they were corpuscular particles. So we can deducted that the photon passed through one slit or the other, but it did not pass through by both fissures simultaneous and at the same time, which shows the corpuscular characteristic of light. But if you wait long enough, the photons will pass through one slit or another, but at the end of many passages it will also be form a picture of interference!

     But if we close one of the holes and begin to shoot the photons, one by one you, we will get back the standard corpuscular and located concentration of particles, just like if we were shooting bullets with one hole open.

      The fundamental issue of these experiences is that they allow us to characterize both particle of radiation and particles of matter as having both corpuscular and wave characteristics and therefore we can establish this feature of wave-particle duality.

     To get a clearer idea of this experiment, we will carefully view the following images which constitute evidence about this phenomenon:


- Experience of Double Fissure -

- Behavior of any wave and corpuscular particle: photons, electrons, etc. -


      The wave particle duality can become even more exotic. If we try to determine from witch fissure did the electron or photon passed, we change the final result of the experience!! The figure of interference is destroyed leading to only a concentration of particles very well located!

      This phenomenon, as a whole, is truly amazing, and gives us a lot of thinking! Is it possible to deduct that when we try to perform an experiment that shows the corpuscular nature of matter, that is, that locates from which fissure did the particle went and pass through, we completely destroy its wavy characteristic?!

      The Quantum Mechanics states that we interfere with the alternative that the system chooses! Supposing that, in the microscopic world we have to ignore our intuition and all the classical physics concepts. So there is a well-known statement of Richard Feynman: "No one understands Quantum Mechanics.".

      Compared with the clear and logical construction of Newton's laws of motion, or the electromagnetic theory of Maxwell, we can say that quantum theory is in a chaotic state, almost impossible to understand.

      The Quantum Mechanics does not give us a very efficient description of these experiences. Despite the success of this theory in other fields, for example, the Schrödinger equation, which describes the physical states of a particle and its temporal evolution, later updated with the Dirac equation. It is this equation that replaces the Newton's equations in classical mechanics for a mechanics applied to particles such as photons and electrons, accurately defining all their characteristics and properties. However, for this case in particular, Quantum Mechanics does not feel very comfortable with the strangeness of their own experiences.

     But is Quantum Mechanics so different from Classical Physics?

     Many will say, without a doubt, that the answer to this question is a round and absolutely yes.

     Allow me to say that I completely disagree!

     The Quantum Mechanics presents us with very different concepts. Between probabilities, uncertainties, wave functions, and the wave-particle duality, all of that are quite radical new ideas that transform our vision of reality, capable to lead any classical and traditional physicist in to dizziness, hard to convince and to convert. These principles capture the essence of Quantum Mechanics. Properties that normally are above any suspicion, for example, the definition of the position, speed, time and energy of a quantum object, is now seen as mere fluctuations, uncertain, undefined probabilities.

      The quantum physicist advise us to accept Nature just like the way it is. However, we must not fail to fall in to this current of mystical connotation and indetermination concepts of the quantum world, judging, from the beginning, these experiences as instantly illogical and impossible to understand.  Some also give quantum science other descriptions, more dramatic, such as bizarre, absurd and irrational.

     We should not let ourselves be seduced and surrender completely by these new concepts, without even trying to fit them into a coherent relationship.

      The compromise between the concept of wave and corpuscle becomes a relationship almost impossible to assimilate and overcome, a concept incompatible with the human spirit.

      My own conviction is based on a profound belief in the cause-effect relationship. I admit that I may be wrong, but personally I do not believe in the uncertainty and undefined concepts of Quantum Mechanics.

      It seems to me that, and to quote the physicist Ernest Rutherford: "While we are not able to explain something in simple terms and not technical, it means that we did not completely understand the phenomenon.". I think that we still understand very little about Quantum Mechanics. As it still is necessary to explain physical processes in terms of technical and mathematical calculations rather than words and concepts, it can only show how far we are to properly assimilate the whole phenomenon.

      The advantage of quantum mechanics is relying on statistical methods, without this tool, quantum mechanics is uncapable to explain a process or a phenomenon. The treatment of a phenomenon is seen when comparing to a large number of particles, and their statistical analysis allows a probabilistic forecast quite correct. A bit like the thermodynamic analysis of particles of gas in the atmosphere. It is impossible for a meteorologist predicts accurately the movement of all single particles in the air, but it is possible to obtain an analysis of the global movement of all particles, through a statistical and probabilistically treatment.

      Thus, Quantum Mechanics works when applied to a large number of particles, but, unfortunately, it cannot be apply to treatment of a single particle. Because, for these individual cases, Nature has not yet revealed its greatest mystery!

      The experience of the double-fissure exposes this mystery into the light, making it very clearly and absolutely intrigued the physicists. The fact is that no one can make an objectively analysis and enlightening explanation about this phenomenon, and this leaves all physicists absolutely and completely unarmed, without any chance of explanation, the only thing that it can be said is that we simply know this is how it happens.

      The orthodox interpretation of Quantum Mechanics states that before the operation of any measure we cannot talk about realities because all that it exists is potentialities.

     Before we continue let us see, in general terms, which solutions were presented for these phenomena.

      Quantum Physics does not succumb to the tradition of Classical Physics saying that a particle passes through one slit or through another. It says that the particle passes through both!

      Nor does it refer to the tradition physical concepts saying that a photon travels through one path or through another path. Quantum Theory says that the photon travels through all infinite paths simultaneously!

      They wish to convince a layperson that one single particle passes through different paths simultaneously, and nothing less than an infinite number of them!?

     And still that the relationship between the observer and the experience changes the final result of the experience. If the observer tries to intervene in order to understand and confirm from which slit the particle passed through, the system realizes it, it cheats, and chooses a slit defined!

      I would personally ask for the Claims Book. This is absolutely insane!

     The quantum interpretation rejects the concept of physical waves and only considers waves of probability. This means that, necessarily, to explain this experience we must abandon the concept of causality.

      In my point of view if we reject this causal relationship, that involves giving up our ability to think about things and physical processes.

      If we cannot establish a rationale thought based on the cause-effect relationship, in which way do we intend to make progress in science and consolidate new knowledge?

      Personally, I think, both Strings Theory and the Uncertainty Principle have weakened the foundations of Science, in different and distinct ways.

     If the Strings Theory questions the relationship between theory and experiment, the Physics itself as an experimental science; on the other hand, the Uncertainty Principle leads us to a destination without direction, because while it opens the doors to these new concepts of uncertainty, it closes the concept of certainty.

     From here now it becomes almost impossible to make new science. If science loses consistency of theory with experimental verification, if science abdicates the cause-effect relationship, in which level is Science placed?

      The major issue here is, again, the fundamental concept of Science!

      The science of the old traditional scientists, worked with classical physical concepts, has always been a good guide, and has always given its fruits for those who were patient t and for those who truly believed ...

      Back to the duality:

      Quantum mechanics claims and argues for the probability intervention, ensuring that the particle did not quite split into smaller pieces, it only indicates the existence of regions where the particle can be found with higher probability.

     What in practice does not explain very much about the physical process, the fundamental part of the experience that we all would like to know ... the 'how'!?

      Physicists are already very familiar with these experiences but, in my view, they are still waiting for an explanation.

      Let us focus and concentrate ourselves only on the description of the facts. And it’s worth to pay much attention on the details. If indeed this experience happens, then, it’s because it is possible. We just have to know how!

      I have a suggestion, not very accurate but it can raise another hypothesis ... more classical!

      I would like to have the opportunity to emphasize, once again, that Modern Physics should not forget and exclude all the principles taught by the modest Classical Physics. This old science accumulates immense wisdom and has not yet revealed all its knowledge.

      There is a law in the Universe in which I still cannot quit believing that is the cause-effect relationship, and this is the fundamental pillar of the whole construction of Classical Physics.

      How someone would once say "God does not play dice." - Einstein - therefore it is obvious that Nature have found a way to manage the duality in a logical process.

      If you take an overview and look at the complete picture, we can notice that we have three major problems in modern physics which are waiting for a resolution: The experience of wave-particle duality; Intervention in the double fissure; and the electron quantum jump. Looking closely we can see that all of these problems are waiting for a common explanation, because they deeply are all effects of the same phenomenon!

      First, let us go to the enigmatic quantum leap of the electron:

      In a first approach, apparently magical, we can say that, when photons collide with the electrical atmosphere of an atom they materialize the electron at that point, making it in a corpuscular particle.  The action of the photon at the periphery of the atom establishes the concentration of the electrical charge density of the electron in to a specific area and location, according to its corresponding energy level.

      The principal quantum number that sets the radius of the orbit where the electrons can remain have a specific definition with discontinuous ranges, because they define the distances in which the emission and absorption of energy can take place, thus means  the energy levels of  the atom. Only in those specific orbital and only in such moments is when the electron takes its corpuscular behavior. With the absorption of energy from the photon occurs the collapse of the wave of the electron. In this process the distribution of the electrical density is transformed into a concentrated point of electrical charge, thus, the electron becomes a corpuscular particle.

      On the other side, we have the opposite process: with the emission of the energy from the electron occurs the collapse of its corpuscular behavior and the electron spreads apart into a cloud of electrical density, spreading into a wave of electrical charge, being no longer a concentrated corpuscular particle.

      However, initially, the electron has got its density of electrical charge more or less evenly distributed surrounding the atom, according to the shape of the orbit around the nucleus. In the presence of the photon the distribution of this density is changed and it is then when it seems to occur the quantum leap, which in reality is not exactly a jump but rather a linear change of the distribution of the electron density charge, which becomes concentrated into a single point, with a radius distance from the nucleus very well defined, corresponding to the energy level. And then we say that the electron described a quantum leap, but in fact what happened was that the electron assumed its material appearance.

     When this happens it is because the photon has got the power to act upon the charge of the electron, concentrating it into a single point, transforming it into a corpuscular particle, so that we can consider the photon as a particle carrying out its own field which will have action on the attraction of minimum amount of electrical charges, in this case, the negative charge of the electron.

      We could assume an analogy,  just like the Strong Force that attracts the positively protons charged in the nucleus, keeping them together, the photon would have the feature to attract, unite and concentrate low densities of minimum charges, joining and keeping together the electrical charge of a single electron, the elementary charge.

      In this first stage, let us keep only the major idea of this concept, which is that particles in their natural state of balance always assume their wave status but if they are disturbed by a photon they will change their form and assume their corpuscular appearance. The intervention of the photon is crucial.

      Now, let's see what is happening in the double fissure experiment ...

      The conditions of the experiment are very important. The experiment is performed as follows: isolating the system from outside light, that is, placing the emitter of particles, the bulkhead with two fissures and a final light-sensitive screen in a closed system, isolated from the intervention of external photons, since what we want to check is the pattern of light and contrast that is formed in the last screen, just like a photographers film.

     When photons are project, the photographic plate records the light that passed through the slits showing clear points of light. When particles such as electrons use projected it is used a phosphorus screen, this substance is sensitive to any external action, and is basically the same principle that is present in old televisions with cathode ray tubes, and he shock caused by these particles will also cause bright points.

      Having this clear, we can move on to the first phase of the experiment: the projection of an electron beam with two fissures open:

     When the electrons are projected against the material target, against the screen, they gain speed and as such they assume their wave nature. Since during this journey there is no interference with photons, the electrons do not suffer any disruption and once they have not been disturb by any photon they continue their path in its wave aspect. The wave nature of the particle is then preserved.

      As we have two slits open, the wave nature of electrons gives rise to the phenomenon of interference. The result in the final screen is the projection of waves.

      Second phase of the experiment: the projection of a light beam with both slits open. This experience is virtually identical to the above:

      The light is an electromagnetic wave, consisting of a huge number of photons, just like the waves of water are formed by a huge current of H2O molecules. The wave nature of light is maintained from the beginning until the end and, as expected, it is formed the phenomenon of interference in the final screen. The result is the projection of waves.

      Now, in an attempt to keep this line of thought, we will move forward into the part of the experience where we want to know in which fissure did the electron passed through.

      Of course, if we wish to know which fissure is that the electron passed through, we must point some light on it in order to see it. When we project light on the electron this one reflects its presence and position, as any other object. But, this intervention by itself causes the necessary interference to change the aspect of the initial wave appearance of the electron. The contact of the electron with the photon transforms it automatically and necessarily in its corpuscular aspect, for the reason that has been explained in the quantum leap.

     There is no direct relationship with the observer, there is a relation of cause and effect! The intervention of the photon is fundamental.

      Now, the trick of the magician is at the end of the experiment, at the corpuscular property of the electron and the photon!

      The light shell still contain many properties that we don’t know and certainly many secrets to reveal.

     However, in the double-fissure experiment we have been paying attention only to the first part of the experience, thus we have been only focus on the part of the action and we are forgetting of the 3rd law of Newton about the principle of action-reaction!

      The final screen provides a reaction, reaction which modifies the final destination of the experiment. Let's see how: We know that when a material wave is spread towards an obstacle, for example, we can consider a sound or water wave, we know that there will be a reaction, the wave can be reflected in whole or in part, because the barrier offers a reaction.

      Could it be that in the case of the projection of one individual particle, whether it is a corpuscular or a radiation particle, our obstacle also offers a reaction? And if it does, what kind of reaction could that be?

      We must first clarify what we mean by 'particles' of radiation or by ‘corpuscular particles’. I can already say that the corpuscular concept is the one which impairs our reasoning.

     Let us move first to the experiment with only one electron.

     For the specific case of one electron, I must confess that, I was initially thinking about the phosphorescence property of the material and on the reemission of light and, therefore, on the action of photons. But this would only make the problem even more complex and reduce the chances of achieving the exact same standard image in the final screen. Then it came out another option, much more simple!

     After we have in our hands the solution of a process, it is only then that we realize how simple it is ...

      It is good to think that things and processes are simple, this is always a good guide. But sometimes they can even be annoyingly simple!

      Again, the photons always have its primary role, they decide the final outcome of the experiment.

      As should be recalled, the electrons do not only emit photons when they are transitating energy levels. There is another way to produce the emission of photons. And what is that other way?

     I leave you to think for a moment ...

      The solution to this experience comes from the following relationship:

- Feynman diagrams! -


     With this concept in mind, we can proceed with some more information:

     When two electrons are on a route of collision they communicate with each other repulsive, informing and warning the other electron of their presence and proximity. Since the nature of these particles is naturally repulsive it starts up a 'fight' between them with the transmission of photons against each other.

      In a way, the photons act as a messenger that carries out the information from one electron to another, communicating the following message: 'do not get near me, our charges are repulsive. "

      With this concept in mind we can proceed with some more explanation.

      Recall, first, that the initial movement of the electron is always a wave. Whenever the electron starts in motion or is moving with velocity it assumes its natural facet which is undulatory.

     Only at the time when there is the collapse or spreading of the wave, which corresponds respectively to the moments of absorption and emission of photons, and only in those cases, the exact moment of collision or the collapse, is that the speed of electron is changed and, therefore, the particle assumes its dual nature permutating into a corpuscular or undulatory form.

      In this experience of the projection of an electron at a time, with both fissures open, the final result, initially, stars by being corpuscular but at the end we will have an undulatory composition. Let's see how can we paint this picture.

      First part:

       What happens in the passage through the fissures of the first screen? The electron passes through them like a wave or as a particle?

      We have seen before that quantum mechanics considers that the particle passes through both simultaneously, as if the electron had the gift of ubiquity.

     One step at a time, and once again it is necessary to gain some degree of abstraction: First we must assume that the electron travels in its wave aspect, since that is that their natural state and, therefore, it approaches the first screen, consisting of two fissures ,in the form of a wave.

      And what happens when the electron reaches the shield of the two fissures?

      Although the electron initially travels toward the first screen in the form of a wave, it does not pass through both holes like a wave, that is, simultaneously. Once the wave front approaches the screen and confronts the shield, and whether if the electron is not immediately absorbed in the first screen, there still is a slightly chance that the front wave of the electron that is moving is slightly closer to one fissure or another.

      Remember that when a wave is spread it has always got a circular design with a constant radius around a central point, therefore we can consider the advance of a front wave.

      Once this front wave is sufficiently closer to one of the fissures it stars the recognition of the possible collision with the electrons of the plate closer to the fissures and, as such, the electronic wave of the electron collapses and it is transformed in its corpuscular aspect. It is on this stage that the traveler electron exchange photons with the electrons of the plate surrounding the fissures.

     Summarizing, being the fissures of a small size, the wave front of which is closer to get through one of the slots should be close enough to recognize the electrons of the slot itself. As such, there is an exchange of photons between the electrons around the fissure and the traveling electron. The electron takes its corpuscular performance, and this fight avoids the route of collision between the electrons of the plate and the electron traveler, so that the electron can 'turn aside' and overcome the hole of the slot with safety, the dispersion of the electron avoids the frontal shock with the first screen.

      As soon as it gets through the fissure, our traveler electron is now far away from the first plate and, thus, the traveler electron can quietly continue its journey assuming, again, a wave facet. With the particularity that the exchange of energy with photons has changed its momentum and direction. For that reason, when new front wave advance they always get spread in different directions, moving towards the final screen with distinct courses of collision, shocking the final screen always in completely different points. And, again, before colliding with the final plate, the fight with photons stars over again and undulatory and corpuscular permutation repeats.

      Second Part:

      Let us now focus only on the final plate.

      When it is near to the final shield, the new front wave that comes, which carries another momentum and direction, begin to detect electrons nearby and the possible collision with the electrons of the final plate.

      When both electrons are close enough to recognize each other start up the combat with photons. And where there are photons in the proximities, what happens? The collapse of the wave of the traveling electron and therefore it reaches the final screen in its corpuscular aspect! Since there are no fissures where our traveler electron can escape, the collision is inevitable.

      In the case of emission of several electrons simultaneously, as I mentioned at the beginning, the end result is the image of interference, however, the situation is the same as the emission of a single electron. There are always waves on the way but they always crash on the screen in a corpuscular form. What is happening is that, given the speed of displacement of these particles, whose values are on the order and magnitude of the speed of light, around 107 m/s, the process of corpuscular overlap is so fast and it happens so quickly, that induces our eyes the feeling of having arrived a single wave simultaneously. But that is not quite what happens.

     Let us see this process closer and in slow motion …

     The first front wave moves with speed, the electrons of the final shield begin to feel the threat and start preparing their defense. The Soldiers of the Command of the front wave that is approaching make their first assessment of the impact territory and detect the enemy, the Elite's Soldiers of the final shield. When the front wave is sufficiently close enough, it begins the attack without mercy with shots of photons. The electrons take their position and assume their corpuscular form, continuing the fight. Meanwhile, more Soldiers of the Command come on the way, new front waves advance and move quickly, taking the opportunity because they know that the Elite’s Soldiers of the final shield are still busy with the first soldiers of the command. The Soldiers of the Command are in majority and the Elite's Soldiers of the final shield are powerless for so many invaders, that is when other fronts begin to arrive, to distribute, and take possession of the territory in other areas, away from the center, reaching the target in other fronts.

     A plan of attack that not even Napoleon would remember!

     And that is why the interference figure is slightly brighter in the center and softer on the edges!



- Graphic of distribution of the spatial intensity on target. -


        For the experiment with a single photon, the phenomenon is identical to that of a single electron.

       The subtlety of the reasoning is the following: Everything starts as waves but everything ends as particles!

      As you can see, the wave-particle dualism does not carry the uncertainty of position and velocity, what it does carry is a complete unknown of a process or a phenomenon.

      When speaking about electrons, photons, protons, etc., we must say that these quantum entities propagate themselves as waves but exchange energy as particles! And we can consider that this exchange occurs in the form of packets of energy, quanta, or as discrete quantities of energy fields.