Quanta or the programmed death of the continuum in physics

Quanta or the programmed death of the continuum in physics

The notion of molecule has already represented the end of the continuity of matter, as the chemist August Kékulé noted : "In chemical reactions there is a quantity which enters and leaves in a smaller proportion and never in a fraction of this proportion. These quantities are the molecules defined chemically."

The notion of quanta put forward by Planck and Einstein gave a completely different meaning to the discontinuity of matter. It is not mass (or energy) that contains an integer number of elementary quantities. It is a product of energy and time that is in an integer number of grains. This quantity is called action. That action is quantified means that it is not only the mass of matter that is discontinuous but also the interactions. At that time, it was not far from being considered that light (the grains called photons) but also space, time and the void (virtual photons) were also quantified, a new qualitative leap that quantum physics would have to make, completely abandoning the old ideal of continuity...
"Contrary to what we often hear, the discontinuity that Planck discovers here (with quanta) affects not matter, but interactions. (...) Planck’s calculations show that the exchanges of electromagnetic energy are carried by grains, whereas they were believed to be continuous. (...) What Planck discovered was that in every interaction there is an exchange and, moreover, that there is a minimum exchange below which there is no more interaction. (...) It is to Planck that the credit goes for having carried out the first "one-two" against continuity. In 1905, Einstein concluded Planck’s "one-two" with a decisive uppercut : he attributes to radiation itself, and not only to energy exchanges, a corpuscular structure. Radiation, essentially discontinuous, is, according to him, formed of a set of corpuscles each carrying a quantum of energy. (...) Radiation is not emitted in a continuous manner." writes Etienne Klein in "Regards sur la matière"

Etienne Klein and Bernard D’Espagnat added in "Regards sur la matière" : "The quantum, as we will see, has a minuscule value, but the idea of ​​the quantum has become as unavoidable as a mastodon. It is indeed proof that one can be both ghostly and essential. Truth of paradoxes, Zeno of Elea already argued."

Gilles Cohen-Tannoudji explains in "Time and its Arrow" (collective work directed by Etienne Klein and Michel Spiro) :

"Heisenberg’s inequality marks the irruption of the discontinuous where it was not expected, in interactions. While the discontinuous was accepted in matter, since it is essentially the foundation of the atomic hypothesis, it was thought that interactions were completely continuous. It is indeed the thought of the continuous which constitutes the foundation of Newton’s theory of universal gravitation, and Maxwell’s theory of electromagnetism is a wave theory, and what is more continuous than a wave or a field ? Neither special relativity nor general relativity changes anything : in classical physics, interactions are entirely continuous. Now the quantum of action is fundamentally a quantum of interaction : there is no interaction unless an action at least equal to the quantum of action is brought into play. We must therefore admit the idea that, just as there are elementary particles of matter, the fermions, there must be elementary particles of interaction. And, In fact, it is proven that the fundamental interactions are indeed carried, conveyed, transmitted, by authentic elementary particles, the bosons. The photon is the boson of the electromagnetic interaction, the W+, W- and Z° bosons are the bosons of the weak interaction and the gluons are the bosons of quantum chromodynamics (the strong interaction at the quark level)."

Henri Poincaré in “Last Thoughts” :

"We are no longer only asking ourselves whether the differential equations
of Dynamics should be modified, but whether the laws of motion can still be expressed by differential equations. And this would be the most profound revolution that Natural Philosophy has undergone since
Newton. The clear genius of Newton had clearly seen (or thought he saw, we are beginning to wonder) that the state of a moving system, or more generally that of the universe, could only depend on its immediately preceding state, that all variations in nature must occur in a continuous manner.
Certainly, it was not he who had invented this idea : it was found in the
thought of the ancients and the scholastics, who proclaimed the adage : Natura non
facit saltus ; but it was stifled there by a host of weeds which
prevented it from developing and which the great philosophers of the 17th century ended up pruning.
Well, it is this fundamental idea which is in question today ; we
wonder if we should not introduce into natural laws discontinuities, not apparent, but essential (…)

CONCLUSIONS

We see what the state of the question is ; the old theories, which
until now seemed to account for all known phenomena, have come up against an
unexpected obstacle. It seemed that a modification was necessary. A hypothesis
first presented itself to Mr. Planck’s mind, but so strange that one was
tempted to seek all means of freeing oneself from it ; these means, one has
sought them in vain until now. And this does not prevent the new theory
from raising a host of difficulties, many of which are real and are not
simple illusions due to the laziness of our mind which is reluctant to change its
habits.
It is impossible for the moment to predict what the final outcome will be ;
will another, entirely different explanation be found ? Or, on the
contrary, will the partisans of the new theory succeed in removing the obstacles preventing its unreserved adoption ? Will discontinuity reign over the physical universe and is its triumph definitive ?

Louis de Broglie , in “New Physics and Quanta” :

"Without quanta, there would be neither light nor matter, and, if we may paraphrase a Gospel text, we can say that nothing that has been made has been made in them."

Physicist Leon Lederman :

"If the electron is a point, where is the mass, where is the charge ? How do we know the electron is a point ? Can I get my money back ?"

The electron does not have a fixed position : its charge quivers, its mass jumps from one point to another, its polarization cloud interacts with its neighbors... This defines various "dimensions" of the electron. If it is captured, it is point-like. Its mass is point-like. Its charge is point-like. If it interacts, it is considered by the other object as a non-zero dimension zone. The various dimensions have a ratio between them equal to the fine structure constant alpha. These are the results of quantum physics on the "elementary particle".

What is the atom, the elementary, the "unbreakable" ? A cloud of points at many scales ! These points are the electrified particles, called virtual, which make up the void. The mass property of the electron jumps from one virtual particle in the cloud to another.

Light is made up of two (or an even number) opposing virtual particles of electricity.

The void, with its various hierarchical levels, is therefore the basic constituent of the matter/light universe.

The probabilistic nature of the electron comes from the fact that it is not a single object but a set of nested levels based on the agitation of the vacuum.

The duality property of the elementary particle (behaving both as a corpuscle and as a wave) has been one of the most difficult questions in quantum physics. The wave and the corpuscle are two very opposite descriptions of reality, and yet matter, like light, have been shown to be both corpuscular and wave-like. Both does not mean that one can carry out an experiment that gives both results at the same time. On the other hand, as soon as one carries out an experiment giving a wave-like result, one obtains a wave. And, each time one carries out a corpuscle-like experiment, one obtains a corpuscle. From this arose an interpretation according to which it was human observation that decided the nature of reality…
In fact, duality comes from the fractal nature of the particle. It exists at several scales. If one measures at one scale, one obtains a result at that scale. One therefore loses the result found at another scale.
If the experiment performs a measurement on the polarization cloud, we obtain a wave-like result. If we interact with the material point, we obtain a corpuscular result which proves that the electron is indeed a point and is indeed a single being. But this being exists simultaneously at different levels. On the other hand, as soon as the corpuscle is captured, in an extremely short time, the cloud disappears. Indeed, at the level where the virtual particles are located, the speed limit of light no longer applies. It is the "reduction of the wave packet" which has so complicated the lives of quantum physicists.
We can interpret in this way all the properties, often apparently strange, of the so-called elementary particle, the electron.
Physicists had long noticed that there was a problem in understanding its nature. As Abraham Pais points out in "Subtle is the Lord," probably the best biography of Einstein, "All that remains of this (the work of Abraham, Lorentz, Poincaré, Einstein, ... on the self-energy of the electron) is that we still do not understand this problem." Some physicists even theorize the impossibility of representing it Margenau (1961) : "Electrons are neither particles nor waves (...) An electron is an abstraction, which can no longer be described by an intuitive image corresponding to our everyday expectation but determined through mathematical formulas." But, as Einstein said to Wheeler : "If I cannot imagine it, I cannot understand it." And Einstein affirmed : "You know, it would be enough to really understand the electron. "In 1991, the International Electron Conference in Antigonish wrote : "We are gathered here to discuss our current knowledge of the electron. (…) It is strange to see what an enormous amount of technology is based on the electron without us being able to understand this particle."

These remarks stemmed from numerous theoretical difficulties in interpreting the observed phenomena. The interpretation given here is that of the fractal character of the electron. It explains in particular the quantum jumps of the particle and the atom. There is a jump at each interaction between levels of reality of the particle. The jump in scale explains the jump of the phenomenon. For example, the electron does not follow a trajectory, but jumps from one position to another. This discontinuity comes from the fact that the electron does not move in a continuous space, but interacts with the virtual particles of the vacuum. The "simple" displacement is already the product of this fractal character. The same is true for the interactions between particles of matter, between matter and light, and, more generally, between matter and vacuum.
As for the probabilistic character of the particle, so strange that its discoverer Einstein could not accept it, it would not exist if we were able to study reality simultaneously at all scales.
Much has been said about the "uncertainty" inherent in quantum physics, the supposed limit of human capacity to understand the world or even, some say, proof that materialist realism should be abandoned. In fact, it is the fractal nature of reality that causes this indeterminacy when measuring at a scale.
What physicists have noticed is that when measuring or reasoning at a scale, we must not seek to exceed a certain precision. Otherwise, we do not improve our image, we deteriorate it, but they wondered why. It has often been said that this is contrary to our daily experience and common sense. I do not believe so. When we read a text, we get a little closer to read correctly, but if we get too close, we see less well. There is a favorable scale for reading and we cannot read at all scales at the same time. Similarly, you can’t have a map at a scale that can simultaneously show several distant cities and the streets within those cities. You have to choose. Does this mean the map chooses what reality will be ? No, it just means that reality exists at several scales that are different enough that they can’t be examined simultaneously.
The polarization cloud surrounding the electron is made up of elements from a lower world, the world of virtual particles characterized by two interrelated properties : no mass and no space-time as we know it at our macroscopic scale nor as it exists (locally) in the environment of a mass. These particles are electrified positively or negatively and dynamically arrange themselves around the electron in alternating positive and negative layers, thus screening the field of the electric charge near the electron. This explains why no electric charge can approach to the point of touching the electron. There are always layers of virtual particles between two "real" particles. Let us recall once again that the so-called virtual particles are just as real as those called real but are located at another level of reality. They are not the only ones since they exist at an even lower level, the "virtual of virtual". Thus, two virtual particles are themselves surrounded, at a lower hierarchical level, by electrified particles. These worlds are not only nested. The levels are interactive. And even more so, since each level emerges from the lower level. The "real" particles are structures carried by virtual particles that receive a Higgs boson. When the virtual particle becomes a mass carrier, it builds a space-time field around itself ; it structures the disordered space-time of the virtual level.
The polarization cloud rotates due to magnetism through the action of the electron’s movement. This is called the electron’s spin. But the positive and negative layers do not rotate in the same way because the electron is negatively charged. This explains why it takes a turn to return to the initial situation, which is called spin ½.
The electron’s charge is point-like. Its mass is point-like. Yet experiments also show that they are never exactly in the same place, hence the internal rotational properties of the electron structure. This difference arises from the fact that the electron’s jump does not produce the same reaction at the various space-time scales. Mass moves more slowly than bosons. It takes longer to move. It therefore travels less far. This produces several different motions. The cloud of charge positions is much larger than that of mass : the ratio called the "fine structure constant" is the scaling ratio of the different nested hierarchical worlds and is therefore also the ratio between times or distances. It is therefore also the ratio between the different "electron radii". While mass wobbles around its position (a property called "zitterbezegung"), charge spreads over an entire area.

Henri Poincaré writes in "Lectures on Thermal Radiation" :
"The hypothesis of quanta of action consists of assuming that these domains, all equal to each other, are no longer infinitely small, but finite and equal to h, h being a constant."

Joseph Liouville’s theorem, reported by Jean-Paul Auffray in "L’atome" :
"The density of points in the neighborhood of a given point in the phase extension is constant over time."

Poincaré’s statement in "The Quantum Hypothesis" :

“Energy is equal to the product of frequency and the element of action. (...) The quantum of action is a universal constant, a true atom. (...) A physical system is capable of only a finite number of distinct states ; and it jumps from one of these states to another without passing through a continuous series of intermediate states. (...) the set of points representative of the state of the system is a region (...) in which the points are so tightly packed that they give us the illusion of continuity. (...) these isolated representative points must not be distributed in space in any way (...) but in such a way that the volume of any portion of matter remains constant. (...) The state of ponderable matter could vary in a discontinuous manner, with only a finite number of possible states. (...) The universe would therefore jump abruptly from one state to another ; but in the meantime it would remain motionless, the various instants during which it remained in the same state could no longer be distinguished from one another : we would thus arrive at the discontinuous variation of time, at the atom of time. (...) If several representative points constitute an indivisible elementary domain in the phase extension, then the states of the system that these points represent necessarily also constitute one and the same state.

Jean-Paul Auffray in "The Atom" :
"Richard Feynman asked his son : ’When an atom makes a transition from one state to another, it emits a photon. Where does the photon come from ?’ (...) In Feynman’s terminology, the quantum is a virtual photon."

Lochak, Diner and Fargue in “The Quantum Object” :

"Quantum theory developed simultaneously in two different ways. The first consists of highlighting the existence of discontinuous states in the microphysical world and of transitions between these states. The second consists rather in highlighting the fact that corpuscular and wave properties (…) are mixed with each other in all domains. The two ways are therefore closely intertwined. (…) Planck introduced into physics an element of discontinuity, where continuity seemed to reign. According to him, an atom could not absorb light energy little by little, continuously : it could only do so in packets, in quanta, whose extremely small, but still finite, value was determined by a constant that he designated h : Planck’s famous constant. (…) The quantum hypothesis meant the strange thing that the motion of atoms does not evolve continuously but by discontinuous leaps : as if a rocket could not rise gradually above the earth to any orbit and could only reach certain particular orbits by jumping abruptly from one to another.

Louis de Broglie , in “New Physics and Quanta” :

"Without quanta, there would be neither light nor matter, and, if we may paraphrase a Gospel text, we can say that nothing that has been done has been done in them. We can therefore understand what an essential inflection the course of the development of our human science underwent the day when quanta surreptitiously entered it. On that day, the vast and grandiose edifice of classical physics was shaken to its very foundations, without anyone really realizing it at first. (…) Faithful to the Cartesian ideal, classical physics showed us the universe as analogous to an immense mechanism capable of being described with complete precision by the location of its parts in space and their modification over time, a mechanism whose evolution could in principle be predicted with rigorous exactitude when we possessed a certain amount of data on its initial state. But such a conception rested on certain implicit assumptions that were accepted almost without realizing it. One of these assumptions was that the framework of space and time in which we almost instinctively seek to localize all our sensations is a perfectly rigid and determinate framework in which every physical event can, in principle, be rigorously localized independently of all the dynamic processes taking place within it. From then on, all developments in the physical world are necessarily represented by changes in the local states of space over time, and this is why in classical science dynamic quantities, such as energy and momentum, appear as derived quantities constructed with the help of the concept of velocity, kinematics thus serving as the basis for dynamics. The point of view of quantum physics is quite different. The existence of the quantum of action, to which we shall have to return so often in the course of this work, in fact implies a sort of incompatibility between the point of view of localization in space and time and the point of view of dynamic evolution ; each of these points of view is capable of being used for the description of the real world, but it is not possible to adopt them simultaneously in all their rigor. Exact localization in space and time is a sort of static idealization which excludes all evolution and all dynamism ; the idea of ​​a state of motion taken in all its purity is, on the other hand, a dynamic idealization which is in principle contradictory with the concepts of position and instant. The description of the physical world in quantum theories can only be done by using more or less one or the other of these two contradictory images.(…) It is nevertheless perfectly legitimate to use kinematics when studying large-scale phenomena ; but for phenomena at the atomic scale where quanta play a predominant role, we can say that kinematics, defined as the study of movement made independently of any dynamic consideration, completely loses its meaning. (…) Classical mechanics and physics were built to account for phenomena that occur at our scale and they are also valid for higher scales, astronomical scales. But, if we go down to the atomic scale, the existence of quanta limits their validity. Why is this so ? Because the value of the quantum of action measured by the famous Planck constant is extraordinarily small compared to our usual units, that is to say, compared to the quantities that intervene at our scale. (…)

The equations of classical dynamics of the material point express that the product of the mass of the material point by any of the rectangular components of its acceleration is equal to the corresponding component of the force. (…) This result expresses that the classical dynamics of the material point is entirely in agreement with the postulate of physical determinism, postulate according to which the future state of the material world must be entirely predictable when we have a certain number of data on its present state.
Another interesting remark is to be made here. Since the material point is assumed to be punctual, its trajectory is a line which explores only a one-dimensional continuum in three-dimensional space. (…) It explores the force field only along its trajectory. (…) In classical mechanics, the topological accidents which may exist in space at finite distances from the trajectory of a material point cannot in any way influence its movement. Let us place, for example, on the trajectory of a material point, a screen pierced with a hole. If the trajectory passes towards the center of the hole, it will not be disturbed in any way by the topological accident constituted by the presence of the screen. (…) It is inconceivable, in classical mechanics, that the movement of the material point crossing the hole in question depends on whether or not there are other holes in the screen. We immediately understand the importance of these remarks for a corpuscular interpretation of Young’s hole experiment and we sense that wave mechanics must contribute something new on this point. (…) Since light waves pass through empty spaces without difficulty, it is not matter that transmits them. What then is the support of these waves, what is the medium whose vibration constitutes the light vibration ? This is the question posed to the protagonists of the theory of waves. (…) The ether considered as an elastic medium must be an infinitely more rigid medium than steel because it can only transmit transverse vibrations and yet this very rigid medium exerts no friction on the bodies that pass through it and in no way slows down the movement of the planets. (…) After having shown that the rotational force of the magnetic field is equal to the density of the electric current, thus giving rise to electromagnetism, (…) Maxwell, after having written the general laws of electrical phenomena, realized the possibility of considering light as an electromagnetic disturbance. By this, he brought the entire science of optics within the framework of electromagnetism, thus uniting two fields that seemed entirely distinct. (…) Maxwell’s electromagnetic theory provided equations representing exactly on our scale the connection between measurable electromagnetic fields on the one hand, and electric charges and currents on the other. Obtained by uniting the results of macroscopic experiments into a single formal system, their value was incontestable in this field. But to describe the details of electrical phenomena within matter and within atoms, to predict the radiation emitted or absorbed by the ultimate material particles, it was necessary to extrapolate Maxwell’s equations and give them a form applicable to the study of phenomena on the atomic and corpuscular scale. This is what was done,with more boldness than it might appear at first glance, one of the great pioneers of modern theoretical physics, HA Lorentz.

Lorentz took as his starting point the idea of ​​introducing the discontinuous structure of electricity into the equations of electromagnetism. (…) By operating averages on elementary microscopic phenomena, we can return from Lorentz’s equations to Maxwell’s equations. (…) The theory of electrons, built on the bases that we have just outlined, has led to important successes in the prediction of a large number of phenomena. First, it made it possible to rediscover the interpretation of the laws of dispersion. Then, and this was undoubtedly its most important success, it made it possible to predict in an exact manner the normal Zeeman effect, that is to say the way in which the spectral lines emitted by an atom are affected in the simplest case by the presence of a uniform magnetic field. (…) The theory of electrons also seemed to provide the solution to a crucial problem : the origin of the emission of radiation by matter. According to the Lorentz equations, an electron moving in a rectilinear and uniform motion carries its electromagnetic field with it globally and, consequently, in this case there is no emission of energy into the surrounding space. But if the movement of an electron involves acceleration, it can be demonstrated that there is emission of an electromagnetic wave and the energy thus lost at each instant by the electron is proportional to the square of its acceleration. (…) If we want to interpret the radiation of atoms by the movement of intra-atomic electrons, we must assume that in the normal state the electrons inside the atom are immobile ; otherwise, forced to move within the very small domain of the atom, they would necessarily be animated by very accelerated movements and would constantly emit energy in the form of radiation, which would be contrary to the very idea of ​​stability of the atom. (…)

The origin of quantum theory lies in the research carried out around 1900 by Mr. Planck on the theory of dark radiation. (…) If we consider an enclosure maintained at a uniform temperature, the bodies kept in this enclosure emit and absorb radiation and a state of equilibrium is eventually established (…) Kirchoff showed that this state of equilibrium is unique and corresponds to a perfectly determined spectral composition of the radiation enclosed in the enclosure. Moreover, the composition of this radiation depends solely on the temperature of the enclosure. (…) It is often called by the rather incorrect name of “dark radiation” corresponding to this temperature. (…) Mr. Planck had begun by resuming the study of the question by imagining that matter is formed of electronic oscillators, that is to say of electrons capable of oscillating around an equilibrium position under the action of a force proportional to the elongation. (…) Mr. Planck was able to see that the inaccuracy of Rayleigh’s law stems from the excessive role played by high-frequency oscillators in the classical image of energy exchanges between oscillators and radiation. (…) Mr. Planck then had the brilliant idea that it was necessary to introduce into the theory a new element, entirely foreign to classical conceptions, which would restrict the role of high-frequency oscillators, and he posed the following famous postulate : "Matter can only emit radiant energy in finite quantities proportional to the frequency." The proportionality factor is a universal constant, having the dimensions of a mechanical action. It is Planck’s famous constant h. Bringing into play this paradoxical hypothesis, Planck took up the theory of thermal equilibrium and found a new law of spectral distribution of black radiation to which his name remained attached. (…)

Gradually, the fundamental importance of Planck’s idea became apparent. Theorists realized that the discontinuity expressed by the quantum hypothesis was incompatible with the general ideas that had until then served as the basis of physics and required a complete revision of these ideas. (…) To find a general form for his theory, Planck had to abandon the primitive hypothesis of energy quanta and substitute it with the hypothesis of action quanta (product of energy by time or of a quantity of movement by a length).

(...) But Planck’s quantization method only applied to movements for the description of which a single variable is sufficient. (...) On the other hand, if the electromagnetic theory in the Lorentz form were really applicable to the elementary particles of electricity, it would allow the calculation without any ambiguity of the radiation emitted by an atom of the Rutherford-Bohr planetary model. (...) the atom constantly losing energy in the form of radiation, its electrons would all very quickly fall on the nucleus and the frequency of the emitted radiation would constantly vary in a continuous way. The atom would be unstable and there could not exist spectral lines with well-defined frequencies, absurd conclusions. To avoid this essential difficulty, Mr. Bohr admitted that the atom in its stationary states does not radiate, which amounts to denying the possibility of applying the electromagnetic theory of radiation to the orbital movement of electrons on their stable trajectories. (..) Bohr resolved the question of the frequencies of spectral lines by assuming that each transition between quantized states is accompanied by the emission of a quantum of radiant energy. (...) In other words, according to quantum theory, the emission of spectral lines from a simple body is discontinuous and proceeds by isolated individual acts.

Louis de Broglie, in “New Perspectives in Microphysics”

"In 1927, I considered it (the pilot wave, called the "de Broglie wave") as a solution with singularity of the linear equations admitted by wave mechanics for the Phi wave (the wave called "probability of presence" by quantum physics). Various considerations, and in particular the connection with the theory of general relativity, made me think that the true equation of propagation of the de Broglie wave could be non-linear like those encountered in Einstein’s theory of gravitation, a non-linear equation which would admit as an approximate form the linear equation of wave mechanics when the values ​​of the de Broglie wave were quite low. (...) Unfortunately, this change of point of view does not facilitate the resolution of the mathematical problems which arise because, if the study of solutions with singularities of linear equations is often difficult, that of the solutions of non-linear equations is even more difficult. (…) Einstein placed great emphasis on an important property of nonlinear equations. If the equations of a certain field are linear, one can always find a singularity solution to these equations such that the singularity has a predetermined motion. One can also add a continuous solution to the singularity solution and this addition will have no influence on the motion of the singularity. This is no longer the case if the field equations are nonlinear because one can no longer obtain a solution by adding several solutions : the nonlinearity creates a sort of solidarity between solutions that would have been independent if the linear approximation had been valid everywhere. This nonlinearity explains why the singularity and the de Broglie wave are not independent as they would be if there were linearity and why they remain in phase. (…) Moreover, the non-linearity, not very noticeable in the body of the wave train, can reappear on their edges where the derivative groups of the de Broglie wave could take large values ; there is also a circumstance which can oppose the spreading of the wave trains. It therefore appears that a non-linear theory of de Broglie waves could make it possible to obtain “wave groups without spreading” representing for example a corpuscle which would move in a rectilinear and uniform motion without losing its wave (…) We have seen that in the theory of de Broglie waves, as in the relativistic interpretation of gravitation, the non-linearity of the basic equations must play an essential role and alone can explain the solidarity of the wave and the corpuscle. We have now arrived at the following image. A de Broglie wave train, constituting a corpuscle in the broad sense of the word, would be a sort of extended and organized unit, somewhat analogous to a "cell" in the biological sense of the term.It would in fact essentially comprise the following three parts : 1° a sort of nucleus, the singular region, the corpuscle in the narrow sense of the word, the seat of essentially non-linear phenomena ; 2° an extended surrounding region, the seat of a substantially linear phenomenon ; 3° an envelope constituting the edges of the wave trains where non-linearity would perhaps once again play an important role. Now, it seems to me to be the intervention of non-linear phenomena which would give this "cell" its unity, its solidarity and its permanence.
If it is true that non-linearity is the true key to corpuscular Microphysics, it is easy to understand why current quantum physics has not managed to write the wave-corpuscle dualism and has had to be content with a purely statistical and probabilistic description of phenomena on the atomic scale. Taking a priori linear equations as its basis and not leaving the domain of linear analysis, the current theory makes local accidents due to non-linearity disappear (such as singular regions and possibly abrupt edges of wave trains), it thus erases corpuscular structures and, incapable of grasping the true relationship between wave and corpuscle, it can only lead to continuous images of a statistical nature. (…) The continuous wave (…) not comprising any singular region (…) does not really describe physical reality.

Ten reasons why quanta, real and virtual particles, atomic nuclei, atoms and molecules are not objects in the sense of those in the world of our daily life.

The reasons for clearly distinguishing between, on the one hand, rocks, carpets, furniture, books, living beings, bottles and, on the other, molecules, atoms, atomic nuclei, particles, quanta, is that….

1°) The first are all different, they are individuals and there are no two that cannot be distinguished, even if they are very similar. The identical does not exist among the objects that surround us, whether they are inert or living. There are no more two absolutely identical marbles than two identical human beings or two identical wires or identical stars. On the other hand, two quanta of the same type in the same state are identical. If they come closer, they can no longer be distinguished. The same is true of two electrons or two protons, two nuclei, two atoms or two molecules of the same type in the same state. They cannot be distinguished not only by observation but also by theory. This means that nature itself does not distinguish the two quanta. It is therefore exactly the opposite of the situation of two objects on our scale which are never absolutely identical.

2°) Objects on our scale, non-quantum if we can say so because we will see that in fact all reality has a quantum foundation, have another particularity which distinguishes them from quantum objects : the former follow trajectories, the latter do not. The former seem to pass continuously from one point to another without break while the latter always jump from one position to another, without continuity. The jump does not apparently exist in reality on our scale and it is the rule for quanta. We can follow the trajectory of a cannonball or an airplane as if they followed continuous paths without any jump, in a way completely opposed to the movement of quanta. Even worse, when we follow the path of a quanta, we cannot even be sure that it is always the same ! Here too, it is not our observation which does not allow us to be sure, the theory also does not allow it which means that nature cannot discriminate between one particle and another passing nearby. They can be exchanged without changing the dynamics...

3°) In fact, quanta cannot move from one position to another continuously because they do not have a position but a probability of presence concentrated in a zone which is determined and they jump from a probability of presence in one zone to another… probability of presence (and not a position) ! This is absolutely not the case for matter at our scale. Quanta are marked in an obligatory and permanent manner by Heisenberg inequalities which cannot be violated while they absolutely do not exist for matter at our scale. These inequalities connect parameters describing the object, parameters whose precisions are connected in the following way : the more one is precise, the more the other… is not ! For example, the position of a quanta and its speed cannot be precise at the same time. This property absolutely does not exist for matter at our scale. Details of parameters of the same object that decrease while others increase are not found for cannonballs, airplanes, vehicles, planets, or any other object in our everyday world.

4) At our scale, objects can be measured, illuminated, captured, or observed without modifying or interrupting the dynamics and this is not at all the case at the quanta scale (from particle to molecule). Even worse, for quanta, it is enough to measure or capture one element of the quanta for the others to disappear !

5°) Quanta are both waves and corpuscles, whereas the objects in our world are either one or the other exclusively. Therefore, capturing the quantum corpuscle immediately suppresses the wave ! As if we were suppressing a duck or a boat by suppressing the wave it produces on a water surface !

6°) Rotation is still a source of discord between quantum and classical (as we call the macroscopic level where quantum effects do not manifest themselves). Indeed, a quantum object is brought back to its initial state by a rotation of two turns while a classical object is brought back by a rotation of only one turn. And there is no classical object that needs two turns to return to its initial state !

7) Another disagreement : when we count the number of objects. On our scale, we find a fixed number that cannot change unless we bring an object from outside. Those who claim the opposite are magicians, mystics, sorcerers and other nonsense talkers. On the quantum scale, the number of objects is not fixed. Quantum objects can perfectly well appear and disappear without there being anything mysterious or magical about it. We understand how it works perfectly : it is enough for a vacuum particle, called virtual, to receive enough energy (for example by receiving a Higgs boson) for it to suddenly become real (it has doubled its internal energy).

8°) The law of conservation of the total energy of an isolated system, always verified at our scale, cannot work at the quantum level for the simple reason that there is no isolated system there and that the vacuum energy can constantly provide it to the quanta.

9°) Causality following the arrow of time is a rule on our scale and not at all on the quantum scale. It is very possible that actions take place in quantum terms in the opposite direction of the arrow of time. Quanta do not follow a single sequence of punctual events but they obey the passage from one set of possibilities with various probabilities to another set of possibilities with various probabilities.

10°) Multiple notions, such as spin, orbitals, wave packet reduction, presence probability wave, tunnel effect, virtual cloud, virtual particles and antiparticles and their formation in clouds allowing in particular the screening of the particle and the phenomenon of Young’s slits, creation-annihilations, quantum numbers, quantum transitions and many others do not have any currency at our scale (classical physics) and are unavoidable at the quantum level.

What should we conclude from this ? That classical physics is completely wrong and that we are misled by our everyday worldviews ? Not really ! That quantum physics is talking nonsense ? Not at all ! It underpins all of reality, both quantum and classical, and explains both, as well as the transition from one to the other (called "decoherence").

In fact, it is quantum reality that is at the base of the world, and at the foundations of this quantum reality, there are the different levels of the quantum vacuum, called the virtual. This physics is the quantum physics of discrete fields in the sense that it is based on virtual quanta (particles and antiparticles with an energy half that of so-called real particles). And in this regard, let us recall an eleventh opposition between the quantum and classical worlds : in the former, the vacuum is not diametrically opposed to matter, whereas in the latter, matter is vacuum !