Over the past hundred years, science has made great strides in studying the structure of our world at both the microscopic and macroscopic levels. The amazing discoveries brought to us by the special and general theories of relativity and quantum mechanics still excite the minds of the public. However, any educated person needs to understand at least the basics of modern scientific achievements. One of the most impressive and important points is wave-particle duality. This is a paradoxical discovery, the understanding of which is beyond the reach of intuitive everyday perception.

Corpuscles and waves

Dualism was first discovered in the study of light, which behaved completely differently depending on conditions. On the one hand, it turned out that light is an optical electromagnetic wave. On the other hand, there is a discrete particle (the chemical action of light). Initially, scientists believed that these two ideas were mutually exclusive. However, numerous experiments have shown that this is not the case. Gradually, the reality of such a concept as wave-particle duality became commonplace. This concept provides the basis for studying the behavior of complex quantum objects that are neither waves nor particles, but only acquire the properties of the latter or the former depending on certain conditions.

Double slit experiment

Photon diffraction is a clear demonstration of dualism. The detector of charged particles is a photographic plate or a fluorescent screen. Each individual photon was marked by illumination or a spot flash. The combination of such marks gave an interference pattern - alternation of weakly and strongly illuminated stripes, which is a characteristic of wave diffraction. This is explained by such a concept as wave-particle duality. The famous physicist and Nobel laureate Richard Feynman said that matter behaves on small scales in such a way that it is impossible to feel the “naturalness” of quantum behavior.

Universal dualism

However, this experience is valid not only for photons. It turned out that dualism is a property of all matter, and it is universal. Heisenberg argued that matter exists in both forms alternately. Today it has been absolutely proven that both properties appear completely simultaneously.

Corpuscular wave

How can we explain this behavior of matter? The wave that is inherent in corpuscles (particles) is called the de Broglie wave, named after the young aristocratic scientist who proposed a solution to this problem. It is generally accepted that de Broglie's equations describe a wave function, which, squared, determines only the probability that a particle is at different points in space at different times. Simply put, the de Broglie wave is a probability. Thus, equality was established between the mathematical concept (probability) and the real process.

Quantum field

What are corpuscles of matter? By and large, these are quanta of wave fields. A photon is a quantum of an electromagnetic field, a positron and an electron are an electron-positron field, a meson is a quantum of a meson field, and so on. The interaction between wave fields is explained by the exchange of certain intermediate particles between them, for example, during electromagnetic interaction there is an exchange of photons. From this directly follows another confirmation that the wave processes described by de Broglie are absolutely real physical phenomena. And particle-wave dualism does not act as a “mysterious hidden property” that characterizes the ability of particles to “reincarnate.” It clearly demonstrates two interrelated actions - the movement of an object and the wave process associated with it.

Tunnel effect

The wave-particle duality of light is associated with many other interesting phenomena. The direction of action of the de Broglie wave appears during the so-called tunnel effect, that is, when photons penetrate through the energy barrier. This phenomenon is caused by the particle momentum exceeding the average value at the moment of the wave antinode. Tunneling has made it possible to develop many electronic devices.

Interference of light quanta

Modern science speaks about the interference of photons in the same mysterious way as about the interference of electrons. It turns out that a photon, which is an indivisible particle, can simultaneously pass along any path open to itself and interfere with itself. If we take into account that the wave-particle duality of the properties of matter and the photon is a wave that covers many structural elements, then its divisibility is not excluded. This contradicts previous views of the particle as an elementary indivisible formation. Possessing a certain mass of movement, the photon forms a longitudinal wave associated with this movement, which precedes the particle itself, since the speed of the longitudinal wave is greater than that of the transverse electromagnetic wave. Therefore, there are two explanations for the interference of a photon with itself: the particle is split into two components, which interfere with each other; The photon wave travels along two paths and forms an interference pattern. It was experimentally discovered that an interference pattern is also created when single charged particles-photons are passed through the interferometer in turn. This confirms the thesis that each individual photon interferes with itself. This is especially clearly seen when taking into account the fact that light (neither coherent nor monochromatic) is a collection of photons that are emitted by atoms in interconnected and random processes.

What is light?

A light wave is an electromagnetic non-localized field that is distributed throughout space. The electromagnetic field of a wave has a volumetric energy density that is proportional to the square of the amplitude. This means that the energy density can change by any amount, that is, it is continuous. On the one hand, light is a stream of quanta and photons (corpuscles), which, thanks to the universality of such a phenomenon as particle-wave duality, represent the properties of an electromagnetic wave. For example, in the phenomena of interference and diffraction and scales, light clearly exhibits the characteristics of a wave. For example, a single photon, as described above, passing through a double slit creates an interference pattern. With the help of experiments, it was proven that a single photon is not an electromagnetic pulse. It cannot be divided into beams with beam splitters, as the French physicists Aspe, Roger and Grangier showed.

Light also has corpuscular properties, which manifest themselves in the Compton effect and the photoelectric effect. A photon can behave like a particle that is absorbed entirely by objects whose dimensions are much smaller than its wavelength (for example, an atomic nucleus). In some cases, photons can generally be considered point objects. It makes no difference from what position we consider the properties of light. In the field of color vision, a stream of light can act as both a wave and a particle-photon as an energy quantum. A spot focused on a retinal photoreceptor, such as the cone membrane, can allow the eye to form its own filtered value as the main spectral rays of light and sort them into wavelengths. According to the quantum energy values, in the brain the object point will be translated into a sensation of color (focused optical image).

Wave-particle duality of light means that light simultaneously has the properties of continuous electromagnetic waves and the properties of discrete photons. This fundamental conclusion was made by physicists in the 20th century and followed from previous ideas about light. Newton believed that light was a stream of corpuscles, that is, a stream of particles of matter flying in a straight line. This theory explained well the rectilinear propagation of light. But difficulties arose in explaining the laws of reflection and refraction, and the phenomena of diffraction and interference could not be explained at all by the corpuscular theory. Therefore, the wave theory of light arose. This theory explained diffraction and interference, but had difficulty explaining straight light. Only in the 19th century, J. Fresnel, using the discoveries of other physicists, was able to combine the already derived principles into one theory, according to which light is a transverse mechanical wave. Later, Maxwell discovered that light is a type of electromagnetic radiation. But at the beginning of the 20th century, thanks to Einstein’s discoveries, ideas about light changed again. Light came to be understood as a stream of photons. But certain properties of light were perfectly explained by the wave theory. Light has both corpuscular and wave properties. In this case, the following regularities exist: the shorter the wavelength, the brighter the corpuscular properties appear; the longer the wavelength, the brighter the wave properties appear.

According to de Broglie, each microobject is associated, on the one hand, with corpuscular characteristics - energy E and momentum p, and on the other hand, with wave characteristics - frequency and wavelength.

In 1924, the French physicist L. de Broglie put forward a bold hypothesis: wave-particle duality has a universal character, i.e. all particles having a finite momentum P have wave properties. This is how the famous de Broglie formula appeared in physics where m is the mass of the particle, V is its speed, h is Planck’s constant.

So, the corpuscular and wave properties of a micro-object are incompatible with respect to their simultaneous manifestation, however, they equally characterize the object, i.e. complement each other. This idea was expressed by N. Bohr and he formed the basis of the most important methodological principle of modern science, which currently covers not only the physical sciences, but also all of natural science - principle of complementarity (1927). The essence The principle of complementarity according to N. Bohr comes down to the following: no matter how far the phenomena go beyond the classical physical explanation, all experimental data must be described using classical concepts. To fully describe quantum mechanical phenomena, it is necessary to use two mutually exclusive (additional) sets of classical concepts, the combination of which provides the most complete information about these phenomena as a whole.

The principle of complementarity, as a general principle of knowledge, can be formulated as follows: every true natural phenomenon cannot be defined unambiguously using the words of our language and requires for its definition at least two mutually exclusive additional concepts. Such phenomena include, for example, quantum phenomena, life, psyche, etc. Bohr, in particular, saw the need to apply the principle of complementarity in biology, which is due to the extremely complex structure and functions of living organisms, which provide them with almost inexhaustible hidden capabilities.

Wave-particle duality– the property of any microparticle to detect signs of a particle (corpuscle) and a wave. The wave-particle duality is most clearly manifested in elementary particles. An electron, a neutron, a photon, under some conditions, behave like well-localized material objects (particles) in space, moving with certain energies and impulses along classical trajectories, and in others, like waves, which is manifested in their ability to interfere and diffraction. Thus, an electromagnetic wave, scattering on free electrons, behaves like a stream of individual particles - photons, which are quanta of the electromagnetic field (Compton effect), and the momentum of the photon is given by the formula p = h/λ, where λ is the length of the electromagnetic wave, and h is Planck’s constant . This formula in itself is evidence of dualism. In it, on the left is the momentum of an individual particle (photon), and on the right is the wavelength of the photon. The duality of electrons, which we are accustomed to consider as particles, is manifested in the fact that when reflected from the surface of a single crystal, a diffraction pattern is observed, which is a manifestation of the wave properties of electrons. The quantitative relationship between the corpuscular and wave characteristics of an electron is the same as for a photon: р = h/λ (р is the momentum of the electron, and λ is its de Broglie wavelength). Wave-particle duality is the basis of quantum physics.

Wave (fur) is a process always associated with a material environment that occupies a certain volume in space.

64. De Broglie waves. Electron diffraction Wave properties of microparticles.

The development of ideas about the corpuscular-wave properties of matter received in the hypothesis about the wave nature of the movement of microparticles. Louis de Broglie, from the idea of ​​symmetry in nature for particles of matter and light, attributed to any microparticle a certain internal periodic process (1924). Combining the formulas E = hν and E = mc 2, he obtained a relation showing that any particle has its own wavelength : λ B = h/mv = h/p, where p is the momentum of the wave-particle. For example, for an electron with an energy of 10 eV, the de Broglie wavelength is 0.388 nm. Subsequently, it was shown that the state of a microparticle in quantum mechanics can be described by a certain complex wave function coordinates Ψ(q), and the squared modulus of this function |Ψ| 2 defines the probability distribution of coordinate values. This function was first introduced into quantum mechanics by Schrödinger in 1926. Thus, the de Broglie wave does not carry energy, but only reflects the “phase distribution” of some probabilistic periodic process in space. Consequently, the description of the state of microworld objects is probabilistic nature, in contrast to objects of the macroworld, which are described by the laws of classical mechanics.

To prove de Broglie's idea about the wave nature of microparticles, the German physicist Elsasser proposed using crystals to observe electron diffraction (1925). In the USA, K. Davisson and L. Germer discovered the phenomenon of diffraction when an electron beam passes through a plate of nickel crystal (1927). Independently of them, the diffraction of electrons passing through metal foil was discovered by J.P. Thomson in England and P.S. Tartakovsky in the USSR. Thus, de Broglie’s idea about the wave properties of matter found experimental confirmation. Subsequently, diffraction, and therefore wave, properties were discovered in atomic and molecular beams. Not only photons and electrons, but also all microparticles have particle-wave properties.

The discovery of the wave properties of microparticles showed that such forms of matter as field (continuous) and matter (discrete), which from the point of view of classical physics were considered qualitatively different, under certain conditions can exhibit properties inherent in both forms. This speaks of the unity of these forms of matter. A complete description of their properties is possible only on the basis of opposing, but complementary, ideas.

In this article, based on the physical essence of Planck’s constant, it is shown that L. De Broglie’s hypothesis about the universal nature of wave-particle duality is not correct and has neither theoretical nor experimental confirmation.

“...difficulties and problems thatarise in connection with quantum phenomena, are purely physical and must be solved by deepening scientific ideas, without any deviation with the help of epistemological or mystical fabrications.”

Mythology of quantum physics. L. Regelson.

Introduction. According to modern ideas: corpuscular-wave dualism is the most important universal property of nature, which consists in the fact that all micro-objects simultaneously have corpuscular and wave characteristics. Thus, for example, an electron, a neutron, a photon, in some conditions, appear as particles moving along classical trajectories and possessing a certain energy and momentum, and in others, they reveal their wave nature, characteristic of phenomena interference And diffraction particles. As a primary principle, wave-particle duality underlies quantum mechanics and quantum field theory.

In modern scientific understanding, the opinion is firmly established that one of the main features of quantum physics is the presence of wave-particle duality in it. For example:

“The concept of wave-particle duality is one of the basic concepts of modern quantum theory.”

“An important stage in the development of a modern understanding of the structure of matter was the put forward de Broglie in 1924, the hypothesis about the universality of wave-particle duality.”

“From everything that has gone before, we conclude that microscopic objects have the extremely general property of revealing themselves in two seemingly incompatible aspects: on the one hand, as a superposition of waves, on the other, as a particle, i.e., a localized portion of energy and momentum.”

“The wave-particle duality of the properties of matter, which is both in the form of radiation and in the form of particles with a rest mass not equal to zero, is the most important characteristic of matter, underlying various fundamental laws characterizing the microworld.”

At the beginning of the twentieth century, a number of important discoveries were made (photoelectric effect, Compton effect, electron diffraction, etc.), which created the appearance that elementary particles of matter, in particular electrons, have not only corpuscular, but also wave properties. In this way, it was experimentally proven that there is no impassable boundary between matter and field: under certain conditions, elementary particles of matter exhibit wave properties, and field particles exhibit corpuscular properties. This was called wave-particle duality and was a concept that did not fit into the framework of ordinary common sense.

“The contradiction between the concepts of a spatially extended field and a spatially localized particle turned out to be so deep that an entire philosophical school arose, which generally abandoned the classical way of describing a physical object as a reality in space and time, independent of the instruments used for observation. In the search for a realistic way out of this situation, two main paths emerged: De Broglie and Bohm considered it necessary to preserve the concept of a localized particle (corpuscle) among the basic concepts of the theory, while Planck and especially Schrödinger defended the monistic wave picture.

The first path turned out to be associated with the artificiality of theoretical premises and led to great mathematical difficulties. The second way seems more constructive, since the successfully working mathematical apparatus of quantum physics corresponds precisely to the wave picture: the corpuscular aspect appears only in the process of interpretation. However, the question immediately arises: can a realistic wave picture be reconciled with the simplest experimental facts? In this work, we come to the conclusion that such agreement is possible only if we assume an experimentally observed violation of the laws of conservation of energy and charge in single interactions.”

In interpreting wave-particle duality, in deciphering the mechanism of connection between these opposing properties, quantum mechanics encountered great difficulties that have not been completely overcome to this day. When viewed mechanically, the opposite, corpuscular and wave, properties were separated from each other and became characteristics of various objects. Ultimately, this led to the understanding that this concept has now been largely rejected as incorrect.

However, all modern educational, methodological and academic literature uses wave-particle dualism as an important and significant concept for explaining various phenomena of the physics of the microworld, ignoring the absurdity and inconsistency of this concept. Appealing to the impossibility within the framework of traditional physics to provide significant evidence of the inadequacy of this concept, in turn, the resolution of this logical contradiction, which served to create the physical foundations of quantum mechanics and quantum field theory, was proposed by rejecting visual (classical) ideas about particles and waves. To explain wave phenomena on the basis of corpuscular concepts, a description of microparticles (and systems of microparticles) was introduced using state vectors that obey the principle of superposition of states, and their statistical (probabilistic) interpretation was adopted, which made it possible to avoid a formal logical contradiction with corpuscular concepts (the presence of a particle simultaneously in several various states). On the other hand, considering classical (wave) fields as a mechanical system with an infinite number of degrees of freedom and requiring that these degrees of freedom obey certain quantization conditions, quantum field theory moves from classical to quantum fields. In this approach, particles act as excited states of the system (field). In this case, the interaction of particles corresponds to the interaction of their fields.

There are other attempts to solve this problem, in particular, in the dialectical approach emphasizes the objectivity of particle-wave properties that are simultaneously inherent in a microobject, but manifest themselves differently depending on different experimental conditions; Attention is drawn to the knowledge of these opposing properties of micro-objects in their unity and interconnection. This interpretation of particle-wave dualism, developed by Langevin, V. A. Fock, S. Vavilov and other scientists, considers a microparticle not a corpuscle or a wave, but something third, a synthesis of them, for which there are no visual physical representations yet. The mathematical formulation of this unity is given in the concept of the wave function.

It is obvious that the problem of particle-wave dualism is not due to unfavorable circumstances for it, but in the minds of its creators, who made an attempt to generalize the idea of ​​particle-wave duality of the photon to all objects of the microworld and, above all, to electrons.

Based on the above, the task of interpreting this state of this problem at the present time becomes relevant, in view of the fact that it determines the path of development of physics as a whole: either the path of prosperity of myth-making, or the development of modern concepts, for example, etherodynamics, eliminating the problems of traditional physics, including and corpuscular-wave dualism.

Justification and analysis of particle-wave dualism. In 1900, M. Planck showed that to explain the law of equilibrium thermal radiation, it is necessary to accept the hypothesis of the discrete nature of radiation, believing that the radiation energy is a multiple of a certain value ε, which he called an energy quantum: ε = hν, where ν is the wave frequency, a h — Planck's constant. Subsequently, it turned out that the more convenient value is ħ = h/2π ≈ 1.05·10 -27 erg s, then ε = ħω, where ω = 2πν is the circular frequency of the wave. Since the assumption of the discrete nature of radiation contradicted the wave theory of light, according to which the energy of a light wave can take on any (continuous) values ​​proportional to the square of the amplitude of electromagnetic oscillations, Planck first associated the discreteness of radiation energy with the properties of emitters (atoms). However, in 1905, A. Einstein, based on the experimentally established Wien's law of radiation (which is a limiting case of Planck's law of radiation, valid at high frequencies: ħω >> kT, where T is the absolute temperature), showed that the entropy of radiation in the region of validity of the law The guilt coincides with the entropy of a gas consisting of particles with energy ε = ħω. This is how the idea of ​​particles of light arose - photons, carrying a quantum of energy ε = ħω and moving at the speed of light. Subsequently, based on relativistic kinematics, the photons were assigned momentum p = (ħω/c) n = ħk, where n is the unit vector along the direction of photon motion, k = (ω/c) n = (2π/λ) n is the wave vector The concept of photons was successfully used to explain the laws of the photoelectric effect and the spectra of bremsstrahlung X-ray radiation.

In 1913, N. Bohr used Planck's constant to determine stationary states in the hydrogen atom. At the same time, he managed to explain the experimentally observed spectral patterns and express through the charge of the electron, its mass and the Planck constant, the atomic radius and the Rydberg constant, which turned out to be in good agreement with experimental data. The method for finding stationary states of electrons in atoms was improved by A. Sommerfeld, who showed that for stationary orbits the classical action is an integer multiple of 2ph. The success of Bohr's theory, which attracted quantum concepts and Planck's constant to explain atomic phenomena, which previously seemed to connect only the corpuscular and wave characteristics of electromagnetic radiation, suggested the existence of particle-wave duality for electrons. In this regard, L. de Broglie in 1924 put forward a hypothesis about the universal nature of wave-particle duality. According to de Broglie's hypothesis, any moving particle with energy ε and momentum p corresponds to a wave with ω = ε/ħ and wave vector k = p/ħ, just as particles with energy ε = ħω and momentum p = ħk are associated with any wave .

The first experimental confirmation of de Broglie's hypothesis was obtained in 1927 by American physicists K. Davison and L. Germer. They discovered that a beam of electrons scattered by a nickel crystal produced a distinct diffraction pattern similar to that produced by the scattering of short-wave X-rays by the crystal. In these experiments, the crystal played the role of a natural diffraction grating. From the position of the diffraction maxima, the wavelength of the electron beam was determined, which turned out to be in full agreement with that calculated using the de Broglie formula.

The following year, 1928, the English physicist G. Thomson (son of J. Thomson, who discovered the electron 30 years earlier) received new confirmation of de Broglie's hypothesis. In his experiments, G. Thomson observed the diffraction pattern that appears when an electron beam passes through a thin polycrystalline gold foil. In subsequent years, G. Thomson's experiment was repeated many times with the same result, including under conditions when the electron flow was so weak that only one particle could pass through the device at a time (V.A. Fabrikant, 1948). Thus, it was experimentally proven that wave properties are inherent not only in a large collection of electrons, but also in each electron individually.

Subsequently, diffraction phenomena were also discovered for neutrons, protons, atomic and molecular beams. Experimental proof of the presence of wave properties of microparticles led to the conclusion that this is a universal natural phenomenon, a general property of matter.

From the above, it is obvious that the absurdity and inconsistency of wave-particle dualism should be sought primarily in the above justification. However, such a solution will not be complete if we do not consider the historical origins of this problem.

Discoveries at the end of the 19th century. - X-rays (1895), natural radioactivity (Becquerel, 1896), electron (J. Thomson, 1897), radium (Pierre and Marie Curie, 1898), the quantum nature of radiation (Planck, 1900) were the beginning of a revolution in science. The previously dominant ideas about the immutability of chemical elements, the structureless atom, the independence of movement from material masses, and the continuity of radiation were destroyed.

However, after more than a hundred years, as a result of the activities of modern physics, it turned out that the revolutionary discoveries of the late 19th century. remained theoretically unresolved, in particular, the issues of generation of X-rays are considered on the basis of the theory of bremsstrahlung electron (a version of the myth of the free electron), the theory of radioactivity is full of errors and contradictions, the quantum nature of radiation has led to the mystification of Planck’s constants (h) and fine structure ( α), and the work associated with the discovery of the electron turned all theoretical physics upside down. As was shown in the works, the discovery of the electron was not only mythologized, but also entailed a number of gross errors: about the quantization and discreteness of the electric charge; about the existence of an elementary electric charge; about giving fundamentality to the manipulated results of Millikan's experiment, in which the physical carrier of the electric charge was not even established; about the unproven and frivolous assignment to an electron of a negative electric charge equal to the elementary one. If we add to this that modern physics has no idea, with rare exceptions, about the structures of basic elementary particles (proton, electron, photon), the mechanisms of their generation, functional purpose, their parameters and properties, then the concept of wave-particle duality and its justification become yet another myth born in the annals of quantum mechanics.

As shown in the work, the particle-wave dualism of the photon is not a very successful reflection of the specific nature of the photon’s movement in space along a helical trajectory, and Planck’s constant is a proportionality coefficient that establishes the relationship between the photon’s own gyroscopic moment and the ratio of the circular frequencies of rotation (around its own and the axis of rectilinear motion ), having the character of a quasi-constant throughout the entire region of existence of the photon:

M = h ω λ / ω γλ , (1)

where M = m λ r γλ 2 ω γλ is the own gyroscopic moment, r γλ is the radius of the body, ω γλ is the circular frequency of rotation around its own axis, ω λ = ν is the circular frequency of rotation around the axis of rectilinear motion, m λ is the mass of the photon.

According to modern concepts, Planck's constant is the main constant of quantum theory, regarding which at the XXIV General Conference on Weights and Measures (GCPM) on October 17-21, 2011, a resolution was unanimously adopted, in which, in particular, it was proposed in the future revision of the International System of Units (SI) ) redefine the SI units so that Planck's constant is exactly 6.62606X 10 −34 J s, where X stands for one or more significant figures to be determined based on the best CODATA recommendations.

The work shows that the value h = 6.62606X 10 −34 J s corresponds to twice the value of the Planck constant of a photon of X-ray radiation with a wavelength of λ ≈ 225 nm, which raises the question of the adequacy of quantum theory.

Planck's constant is a parameter of the photon and only the photon. This statement is a consequence of the physical essence of Planck’s constant (1): of all known elementary particles, only the photon moves in space along a helical trajectory, i.e., it has two circular motions - around its own axis and the axis of rectilinear motion. Therefore, the use of Planck’s constant by Bohr and Sommerfeld to determine the stationary states of electrons in the hydrogen atom should be considered incorrect, due to the discrepancy with its essence. As is known, Bohr's theory was subsequently relegated to the mythology of quantum physics. In connection with the above, L. De Broglie’s hypothesis about the universal nature of wave-particle duality does not correspond to the truth. And, if we take into account that an electron in an atom does not have independent movement and its electric charge is positive and less than the electric charge of a proton, then L. De Broglie’s hypothesis can also be attributed to the mythology of quantum physics. These arguments can be repeated for other microparticles: neutrons, protons, atomic and molecular beams.

As for the experimental confirmation of particle-wave dualism, in this part the incorrectness of the interpretation lies in the following.

In all experiments, starting with the experiments of K. Davisson and L. Germer, experimental physicists proceeded from the condition of generation of an electron beam by an experimental setup, which was not proven or substantiated by anyone, but was taken on faith in the absence of an understanding of the errors made by theoretical physics, caused by the myth of discovery of the electron.

A grave mistake in physics at the beginning of the twentieth century. , began to identify the ideas of atomic electricity and atoms of matter. One of the results of this identification was the appearance in everyday life of physics of the free electron model, also known as the Sommerfeld model or the Drude-Sommerfeld model, a simple quantum model of the behavior of valence electrons in a metal atom, developed by Sommerfeld on the basis of the classical Drude model taking into account quantum mechanical Fermi statistics - Dirac. The electrons of the metal are considered in this model as a Fermi gas.

The difference between the Sommerfeld model and the Drude model is that not all valence electrons of the metal participate in kinetic processes, but only those that have an energy within kT of the Fermi energy, where k is the Boltzmann constant, T is the temperature. Despite its simplicity, the model explains many different phenomena, including: thermionic emission and field emission (i.e., the operation of an electron gun).

The Sommerfeld model is a quantum model of a gas of free and independent Fermi electrons, which uses the Fermi-Dirac distribution, i.e., it is a model in whose mathematical description the Planck constant is widely used. From the physical essence of the Planck constant discussed above, it follows that its direct use in the Sommerfeld model (as an electron parameter) is incorrect and does not correspond to the model of a gas of free and independent electrons.

The Drude model is a classic description of the movement of electrons in metals. It is believed that free electrons (electrons that have lost contact with “their” atoms) in metals obey the laws of an ideal gas. This theory was proposed by the German physicist Paul Drude in 1900, i.e., at a time when the concept of the electron corresponded to the concept of particles carrying an electrical charge, an unidentified physical entity.

Thus, the incorrect use of Planck’s constant, a photon parameter that has the character of a quasi-constant (i.e., Planck’s constant is a function of the photon wavelength) in quantum mechanics models raises the question of their applicability not only for justifying wave-particle duality, but also for the analysis of other physical phenomena in general.

The fact that electron guns do not generate electron flows can also be justified using ideas about the physical essence of electric charge. Omitting mathematical calculations, it can be shown that the binding energy of proton-electron pairs, for example, for some atoms of a substance, will have the following values: cesium— (atomic radius 2.98 10 -10 m) 3.465 10 4 eV, zinc(1.42 10 -10 m) 7.27 10 4 eV , helium(0.32 10 -10 m) 3.227 10 5 eV. These examples provide data for proton-electron pairs in which the electron is external in the atom, i.e., the binding energy for these proton-electron pairs of atoms is minimal. The cesium atom is the largest (in terms of dimension), the helium atom is the smallest of all known from D. Mendeleev’s periodic table of chemical elements.

In seminars we read “ Rice. 3.3. Thomson's experiment. ...c) Diffraction pattern obtained by scattering electrons with an energy of 600 eV" As can be seen from the above binding energies of proton-electron pairs, the lowest electron energy in the event of breaking this bond would be 34.65 KeV (>> 0. 6 KeV), if cesium were used as an activated substance in an electron gun. So Thomson could not observe the diffraction of electrons in any way, due to the impossibility of their generation with the specified energy.

It is known that soft X-ray radiation ranges from wavelengths from 10 nm to 0.1 nm and photon energies from 124 eV to 12,400 eV, respectively. It is obvious that the experiments of physicists on “electron diffraction” are more consistent with the experiments on the diffraction of X-ray photons, which is also indicated by the coincidence of interference patterns.

The phenomenon of interference can be easily explained within the framework of not only wave, but also corpuscular theory and, therefore, cannot serve as proof of the wave nature.

Conclusions. Traditional physics understands dualism as the corpuscular properties of microparticles and the wave properties of motion, and the idea of ​​a wave as a disturbance of some medium is replaced by the idea of ​​a wave of probability of detecting a microparticle at a certain point in space.

The historical roots of particle-wave dualism should be considered the specific form of photon motion in space along a helical trajectory and Planck’s constant.

Misunderstanding of the physical essence of Planck's constant and a number of gross errors in theoretical physics at the beginning of the twentieth century led to erroneous ideas, one of which was wave-particle dualism.

To date, there is no logically correct and experimental evidence of wave-particle duality in nature.

As for “quantum theory,” it is more like a mathematical abstraction that successfully approximates empirical data.

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Lyamin V.S. , Lyamin D. V. Lvov

Typical examples of objects exhibiting dual wave-particle behavior are electrons and light; The principle is also valid for larger objects, but, as a rule, the more massive the object, the less its wave properties are manifested (we are not talking here about the collective wave behavior of many particles, for example, waves on the surface of a liquid).

The idea of ​​wave-particle duality was used in the development of quantum mechanics to interpret phenomena observed in the microworld in terms of classical concepts. In reality, quantum objects are neither classical waves nor classical particles, exhibiting the properties of the former or the latter only depending on the conditions of the experiments that are carried out on them. Wave-particle duality is inexplicable within the framework of classical physics and can only be interpreted in quantum mechanics.

A further development of the concept of wave-particle duality was the concept of quantized fields in quantum field theory.

De Broglie waves

The principle of wave-particle duality receives a quantitative expression in the idea of ​​de Broglie waves. For any object that simultaneously exhibits wave and corpuscular properties, there is a connection between momentum p (\displaystyle \mathbf (p) ) and energy E (\displaystyle E), inherent in this object as a particle, and its wave parameters - the wave vector k (\displaystyle \mathbf (k) ), wavelength λ (\displaystyle \lambda), frequency ν (\displaystyle \nu ), cyclic frequency ω (\displaystyle \omega ). This connection is given by the relations:

Where ℏ (\displaystyle \hbar ) And h = 2 π ℏ (\displaystyle h=2\pi \hbar )- reduced and ordinary Planck constant, respectively. These formulas are true for relativistic energy and momentum.

The de Broglie wave is put in correspondence with any moving object of the microworld; Thus, in the form of de Broglie waves, both light and massive particles are subject to interference and diffraction. At the same time, the greater the mass of the particle, the shorter its de Broglie wavelength at the same speed, and the more difficult it is to register its wave properties. Roughly speaking, when interacting with its environment, an object behaves like a particle if the length of its de Broglie wave is much smaller than the characteristic dimensions present in its environment, and like a wave if it is much longer; the intermediate case can only be described within the framework of a full-fledged quantum theory.

The physical meaning of the de Broglie wave is as follows: the square of the amplitude of the wave at a certain point in space is equal to the probability density of detecting a particle at a given point if its position is measured. At the same time, until the measurement is carried out, the particle is not actually located in any one specific place, but is “smeared” throughout space in the form of a de Broglie wave.

History of development

Questions about the nature of light and matter have a long history, but until a certain time it was believed that the answers to them must be unambiguous: light is either a stream of particles or a wave; matter either consists of individual particles that obey classical mechanics, or is a continuous medium.

The seemingly established wave description of light turned out to be incomplete when, in 1901, Planck obtained a formula for the radiation spectrum of an absolutely black body, and then Einstein explained the photoelectric effect, based on the assumption that light with a certain wavelength is emitted and absorbed exclusively in certain portions. Such a portion - a quantum of light, later called a photon - transfers energy proportional to the frequency of the light wave with a coefficient h (\displaystyle h)- Planck's constant. Thus, it turned out that light exhibits not only wave, but also corpuscular properties.

The principle of wave-particle duality received a more specific and correct embodiment in Schrödinger’s “wave mechanics,” which then turned into modern quantum mechanics.

Wave-particle duality of light

As a classic example of the application of the principle of wave-particle duality, light can be interpreted as a stream of corpuscles (photons), which in many physical effects exhibit the properties of classical electromagnetic waves. Light exhibits wave properties in the phenomena of diffraction and interference at scales comparable to the wavelength of light. For example, even single photons passing through the double slit produce an interference pattern on the screen, determined by Maxwell's equations.

However, the experiment shows that a photon is not a short pulse of electromagnetic radiation; for example, it cannot be divided into several beams by optical beam splitters, as was clearly shown by an experiment conducted by French physicists Grangier, Roger and Aspe in 1986. The corpuscular properties of light are manifested in the patterns of equilibrium thermal radiation, in the photoelectric effect and in the Compton effect. A photon also behaves like a particle that is emitted or absorbed entirely by objects whose dimensions are much smaller than its wavelength (for example, atomic nuclei), or can generally be considered pointlike (for example, an electron).

The shorter the wavelength of electromagnetic radiation, the greater the energy and momentum of the photons and the more difficult it is to detect the wave properties of this radiation. For example, X-ray radiation diffracts only on a very “thin” diffraction grating - the crystal lattice of a solid.

Wave behavior of large objects

Wave behavior is exhibited not only by elementary particles and nucleons, but also by larger objects - molecules. In 1999, diffraction of fullerenes was observed for the first time. In 2013, diffraction of molecules weighing more than 10,000 amu was achieved. , consisting of more than 800 atoms each.

However, it is not entirely certain whether objects with a mass greater than the Planck mass can in principle exhibit wave behavior.

see also

Notes

1. The word “corpuscle” means “particle” and is practically not used outside the context of wave-particle duality.
2. Gershtein S.S. Wave-particle duality// Physical encyclopedia: [in 5 volumes] / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1990. - T. 2: Quality factor - Magneto-optics. - pp. 464-465. - 704 p. - 100,000 copies. -