Corpuscular properties of light. Wave and corpuscular theories. Corpuscular properties of light What parameters determine the corpuscular properties of light

According to the concepts of classical physics, light is electromagnetic waves in a certain frequency range. However, the interaction of light with matter occurs as if light were a stream of particles.

In Newton's time, there were two hypotheses about the nature of light - corpuscular, which Newton adhered to, and wave. Further development of experimental technique and theory made a choice in favor of wave theory .

But at the beginning of the XX century. new problems arose: the interaction of light with matter could not be explained within the framework of wave theory.

When a piece of metal is illuminated with light, electrons fly out of it ( photoelectric effect). It was to be expected that the speed of the emitted electrons (their kinetic energy) would be the greater, the greater the energy of the incident wave (the intensity of light), but it turned out that the speed of electrons generally does not depend on the intensity of light, but is determined by its frequency (color) .

Photography is based on the fact that some materials darken after illumination with light and subsequent chemical treatment, and the degree of their blackening is proportional to the illumination and illumination time. If a layer of such material (photographic plate) is illuminated with light at a certain frequency, then after development, the homogeneous surface will turn black. With a decrease in light intensity, we will get homogeneous surfaces with less and less blackening (different shades of gray). And it all ends with the fact that at very low illumination we get not a very small degree of blackening of the surface, but black dots randomly scattered over the surface! As if the light hit only these places.

Features of the interaction of light with matter forced physicists to return to corpuscular theory.

The interaction of light with matter occurs as if light were a stream of particles, energy and pulse which are related to the frequency of light by the relations

E=hv;p=E /c=hv /c,

where h is Planck's constant. These particles are called photons.

photoelectric effect could be understood if one took the point of view corpuscular theory and consider light as a stream of particles. But then the problem arises, what to do with other properties of light, which were dealt with by a vast branch of physics - optics based on the fact that light is an electromagnetic wave.

The situation in which individual phenomena are explained using special assumptions that are inconsistent with each other or even contradict one another is considered unacceptable, since physics claims to create a unified picture of the world. And the confirmation of the validity of this claim was just the fact that shortly before the difficulties that arose in connection with the photoelectric effect, optics was reduced to electrodynamics. Phenomena interference and diffraction definitely did not agree with ideas about particles, but some properties of light are equally well explained from both points of view. electromagnetic wave has energy and momentum, and the momentum is proportional to the energy. When light is absorbed, it transfers its momentum, i.e., a pressure force proportional to the light intensity acts on the barrier. The flow of particles also exerts pressure on the barrier, and with a suitable relationship between the energy and momentum of the particle, the pressure will be proportional to the intensity of the flow. An important achievement of the theory was the explanation of the scattering of light in the air, as a result of which it became clear, in particular, why the sky is blue. It followed from the theory that the frequency of light does not change during scattering.

However, if you take the point of view corpuscular theory and consider that the characteristic of light, which in the wave theory is associated with frequency (color), in the corpuscular theory is associated with the energy of the particle, it turns out that during scattering (collision of a photon with a scattering particle), the energy of the scattered photon should decrease . Specially carried out experiments on the scattering of X-rays, which correspond to particles with an energy three orders of magnitude higher than for visible light, showed that corpuscular theory true. Light should be considered a stream of particles, and the phenomena of interference and diffraction were explained within the framework of quantum theory. But at the same time, the very concept of a particle as an object of vanishingly small size, moving along a certain trajectory and having a certain speed at each point, has also changed.

The new theory does not cancel the correct results of the old one, but it can change their interpretation. So, if in wave theory Color is associated with wavelength corpuscular it is related to the energy of the corresponding particle: the photons that cause the sensation of red in our eye have less energy than those of blue. material from the site

For light, an experiment was carried out with electrons (Yung-ha's experience). The illumination of the screen behind the slits had the same form as for electrons, and this picture light interference, falling on the screen from two slits, served as proof of the wave nature of light.

Problem related to wave and corpuscular properties of particles, actually has long history. Newton believed that light is a stream of particles. But at the same time, the hypothesis about the wave nature of light, associated, in particular, with the name of Huygens, was in circulation. The data on the behavior of light that existed at that time (rectilinear propagation, reflection, refraction and dispersion) were equally well explained from both points of view. In this case, of course, nothing definite could be said about the nature of light waves or particles.

Later, however, after the discovery of phenomena interference and diffraction Sveta ( early XIX c.) the Newtonian hypothesis was abandoned. The "wave or particle" dilemma for light was experimentally resolved in favor of a wave, although the nature of light waves remained unclear. Further, their nature became clear. Light waves turned out to be electromagnetic waves of certain frequencies, i.e., the propagation of disturbance electromagnetic field. The wave theory seemed to have finally triumphed.

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In the 1920s, it was established that any particle has a corpuscular-wave nature. According to the theory of L. de Broglie (1924), each particle with a momentum corresponds to a wave process with a wavelength λ, i.e. λ = h / p. The smaller the particle mass, the longer the wavelength. For elementary particles W. Heisenberg formulated the uncertainty principle, according to which it is impossible to simultaneously determine the position of a particle in space and its momentum. Therefore, it is impossible to calculate the trajectory of the electron in the field of the nucleus; one can only estimate the probability of its being in the atom using wave functionψ, which replaces the classical notion of a trajectory. The wave function ψ characterizes the wave amplitude depending on the electron coordinates, and its square ψ 2 determines spatial distribution an electron in an atom. In the simplest version, the wave function depends on three spatial coordinates and makes it possible to determine the probability of finding an electron in atomic space or its orbital. Thus, atomic orbital(AO) is a region of atomic space in which the probability of finding an electron is greatest. Wave functions are obtained by solving the fundamental relation of wave mechanics - the Schrödinger equation. (The exact solution is obtained for a hydrogen atom or hydrogen-like ions; different approximations are used for many-electron systems). The surface that limits 90-95% of the probability of finding an electron or electron density is called the boundary. The atomic orbital and the electron cloud density have the same boundary surface (shape) and the same spatial orientation. The atomic orbitals of an electron, their energy and direction in space depend on four parameters - quantum numbers.

The program represents a computer experiment on the passage of an electron beam through one or two slits. It allows you to get acquainted with the manifestation of the dual nature of micro-objects, that is, the presence of their wave and corpuscular properties. The Heisenberg uncertainty principle is illustrated.

It is known that light has both wave and particle properties. Wave properties appear at light propagation(interference, diffraction). Corpuscular properties appear when interaction of light with matter (photoelectric effect, emission and absorption of light by atoms).

Properties of a photon as a particle (energy E and momentum p) are related to its wave properties (frequency ν and wavelength λ) by the relations

where h= 6.63 10 -34 J∙s - Planck's constant.

The French physicist Louis de Broglie in 1924 suggested that the combination of wave and particle properties is inherent not only in light, but also in any material body. According to de Broglie, each body of mass m moving at a speed v, corresponds to a wave process with a wavelength

Wave properties are most clearly manifested in elementary particles. This is because, due to the small mass of particles, the wavelength is comparable to the distance between atoms in crystal lattices. In this case, when the particle beam interacts with the crystal lattice, diffraction. For example, electrons with an energy of 150 eV correspond to a wavelength λ ≈ 10–10 m. Interatomic distances in crystals are of the same order. Therefore, the electron beam will scatter on the crystal as a wave, i.e., according to the laws of diffraction.

For illustration wave properties particles often use a thought experiment - the passage of an electron beam (or other particles) through a slit of width Δ x. From the point of view of wave theory, after diffraction by the slit, the beam will broaden with an angular divergence θ ≈ λ / Δ x. From the corpuscular point of view, the broadening of the beam after passing through the slit is explained by the appearance of a certain transverse momentum in the particles. The spread in the values of this transverse momentum (“uncertainty”) is

Ratio

Δ pxΔ x ≈ h

is called uncertainty relations. This ratio in corpuscular language expresses the presence of wave properties in particles.

An experiment on the passage of an electron beam through two closely spaced slits can serve as an even clearer illustration of the wave properties of particles. This experiment is analogous to the optical Young's interference experience.

WAVE AND CORPUSCULAR PROPERTIES OF LIGHT

Kostroma State University
1 May Street, 14, Kostroma, Russia
Email: *****@; *****@***

It logically deduces the possibility of considering light as a periodic sequence of excitations of the physical vacuum. As a consequence of this approach, the physical nature of the wave and corpuscular properties of light is explained.

A logical conclusion of the possibility to regard light as a period sequence of physical vacuum excitements is given in the article. As a consequence of such an approach the physical nature of wave and corpuscular characteristics of light are explained here.

Introduction

Centuries-old attempts to understand the physical nature of light phenomena were interrupted at the beginning of the 20th century by the introduction of the dual properties of matter into the axiomatics of the theory. Light began to be considered both a wave and a particle at the same time. However, the radiation quantum model was built formally, and there is still no unambiguous understanding of the physical nature of the radiation quantum.

This work is devoted to the formation of new theoretical concepts about the physical nature of light, which should explain qualitatively the wave and corpuscular properties Sveta. Earlier, the main provisions of the developed model and the results obtained within the framework of this model were published:

1. A photon is a set of elementary excitations of vacuum propagating in space in the form of a chain of excitations with a constant relative to vacuum speed, independent of the speed . For an observer, the photon's speed depends on the observer's speed relative to vacuum, modeled logically as absolute space.

2. Elementary vacuum excitation is a pair of photons, a dipole formed by two (+) and (-) charged particles. The dipoles rotate and have an angular momentum, collectively making up the photon's spin. The radius of rotation of photons and the angular velocity are related by the dependence Rω = const .

3. Photons can be thought of as thin long cylindrical needles. Imaginary surfaces of cylinders-needles are formed by spiral trajectories of photons. The higher the rotation frequency, the thinner the photon needle. One complete revolution of a pair of photons determines the wavelength in space along the direction of motion.

4. The energy of a photon is determined by the number of photon pairs n in one photon: ε = nhE, where hE is a value equal to Planck's constant in units of energy .

5. The quantitative value of the photon spin ћ is obtained. An analysis of the relationship between the energy and kinematic parameters of a photon has been carried out. As an example, the kinematic parameters of a photon produced by the 3d2p transition in the hydrogen atom are calculated. The length of a photon in the visible part of the spectrum is meters.

6. The mass of a pair of photons was calculated m0 = 1.474 10–53 g, which coincides in order of magnitude with the upper estimate of the photon mass mg< 10–51 г . Простые вычисления показывают, что частица с массой mg не может быть массой фотона, отождествляемого с квантом энергии излучения. Возможно, пары фотов – это “виртуальные фотоны”, ответственные за электромагнитное взаимодействие в modern theory.

7. A conclusion was made about the change in the constants C and h when a photon moves in a gravitational field.

From the periodic structure of the photon, the reason for the wave properties of light is intuitively clear: the mathematics of the wave as a process mechanical oscillation the physical environment, and the mathematics of a periodic process of any qualitative nature, coincide. The papers give a qualitative explanation of the wave and corpuscular properties of light. This article continues the development of ideas about the physical nature of light.

Wave properties of light

As noted earlier, the elements of periodicity associated with the physical nature of light cause the manifestation of wave properties. The manifestation of the wave properties of light has been established by numerous observations and experiments, and therefore cannot be in doubt. A mathematical wave theory of the Doppler effect, interference, diffraction, polarization, dispersion, absorption and scattering of light has been developed. The wave theory of light is organically connected with geometric optics: in the limit, as l → 0, the laws of optics can be formulated in the language of geometry.

Our model does not cancel the mathematical apparatus of the wave model. The main goal and the main result of our work is the introduction of such changes in the axiomatics of the theory that deepen the understanding of the physical essence of the phenomenon and eliminate paradoxes.

The main paradox of modern concepts of light is wave-particle duality (CWD). In accordance with the laws of formal logic, light cannot be both a wave and a particle in the traditional sense of these terms. The concept of a wave implies a continuum, a homogeneous medium in which periodic perturbations of the elements of the continuum arise. The concept of a particle implies the isolation and autonomy of individual elements. The physical interpretation of HPC is not so simple.

The combination of corpuscular and wave models according to the principle “a wave is a perturbation of a set of particles” raises an objection, since it is considered firmly established that a single, single particle of light has wave properties. The interference of rarely flying photons was discovered by Janoshi, but the quantitative results, details and detailed analysis of the experiment in training course no. Information about such important, fundamental results is absent both in reference books and in the course on the history of physics. Apparently, the question of the physical nature of light is already a deep rear of science.

Let us try to reconstruct the quantitative parameters of Yanoshi's experiment, which are logically essential for interpreting the results, using a stingy description of similar experiments by Biberman, Sushkin, and Fabrikant with electrons. Obviously, in Yanoshi's experiment, the interference pattern obtained from a short light pulse of high intensity JB was compared with the pattern obtained over a long time from a weak photon flux JM. The essential difference between the two situations under consideration is that in the case of the JM flux, the interaction of photons within the limits of the diffraction device must be excluded.

Since Yanoshi did not find a difference in the interference patterns, let's see what conditions are necessary for this within the framework of our model.

A photon with a length Lf = 4.5 m passes given point space during the time τ = Lf / C = 4.5 /3ּ108 ≈ 1.5ּ10–8 s. If the diffraction system (instrument) has a size of about 1 m, then the time of passage of the device by a photon of length Lf will be longer: τ’ = (Lf + 1) / C ≈ 1.8ּ10–8 s.

An outside observer cannot see single photons. An attempt to fix a photon destroys it - there is no other option to “see” an electrically neutral particle of light. The experiment uses time-averaged properties of light, in particular, intensity (energy per unit time). So that photons do not intersect within the diffraction device, it is necessary to separate them in space along the trajectory of movement so that the time of passage of the device τ' is less than the time t separating the arrival of successive photons to the installation, i.e. τ'< t, или t >1.8ּ10–8 s.

In experiments with electrons, the average time interval between two particles successively passing through the diffraction system was approximately 3-104 times longer than the time spent by one electron to pass through the entire device. For point particles, this relation is convincing.

The experiment with light has a significant difference from the experiment with electrons. If the uniqueness of electrons can be controlled due to a slight distortion of their energy, then this is impossible with photons. In the experiment with photons, the belief in the isolation of photons in space cannot be complete; it is statistically possible for two photons to arrive almost simultaneously. This can give a weak interference pattern over a long observation time.

The results of Yanoshi's experiments are indisputable, however, such a conclusion cannot be made about the theory of experience. In theory, it is actually postulated that the interference pattern arises solely as a result of the interaction of particles with each other on the surface of the screen. In the case of strong light fluxes and the presence of many particles, this is the intuitively most probable cause of interference, but for weak light fluxes, another reason for the appearance of periodicity in screen illumination can also become significant. Light changes direction when it interacts with a solid body. Slit edges, strokes grating and other obstacles that cause diffraction - this is a surface that is far from ideal, not only in terms of surface finish. Atoms of the surface layer are a periodic structure with a period comparable to the size of an atom, i.e., the periodicity is of the angstrom order. The distance between photon pairs inside a photon is L0 ≈ 10–12 cm, which is four orders of magnitude less. The reflection of photo pairs from the periodic structure of the surface should cause a repetition of illuminated and unilluminated places on the screen.

Inequality in the directions of propagation of the reflected light should always be, when reflected from any surface, but with strong light fluxes, only average characteristics are significant, and this effect does not appear. For weak light fluxes, this can lead to screen illumination that resembles interference.

Since the dimensions of an electron are also much smaller than the dimensions of the periodic structure of the surface of the body, for electrons there should also be an inequality in the directions of diffracting particles, and for weak electron fluxes this may be the only reason for the manifestation of wave properties.

Thus, the presence of wave properties in particles, whether photons or electrons, can be explained by the presence of wave properties of the reflective or refractive surface of a diffractive instrument.

For a possible experimental confirmation (or refutation) of this hypothesis, some effects can be predicted.

For strong light fluxes, the main reason for the interference properties of light is the periodic structure of the light itself, an extended photon. Pairs of photons from different photons either reinforce each other on the screen when the phase coincides (vectors r between the centers of the photons of the interacting pairs coincide in direction), or weaken in the case of a phase mismatch (vectors r between the centers of the photos do not coincide in direction). In the latter case, pairs of photos from different photons do not cause a joint simultaneous action, but they fall into those parts of the screen where a decrease in illumination is observed.

If the screen is a transparent plate, then the following effect can be observed: a minimum in reflected light corresponds to a maximum in transmitted light. In places where a minimum of illumination is observed in reflected light, light also enters, but it is not reflected in these places, but passes inside the plate.

Mutual complementarity of the light reflected and transmitted through the plate in the phenomenon of interference - known fact, which is described in theory by a well-developed formal-mathematical apparatus of the wave model of light. In particular, the theory introduces a loss of a half-wave during reflection, and this “explains” the phase difference between the transmitted and reflected components.

What is new in our model is the explanation of the physical nature of this phenomenon. We argue that for weak light fluxes, when the interaction of photons within the diffraction device is excluded, the essential reason for the formation of an interference pattern will not be the periodic structure of the light itself, but the periodic structure of the surface of the device that causes diffraction. In this case, there will no longer be interaction of pairs of photons from different photons on the surface of the screen, and interference should manifest itself in the fact that in those places where the light hits, there will be a maximum of illumination, in other places it will not be. In places with a minimum of illumination, the light will not get at all, and this can be checked the absence of mutual complementarity of the interference pattern for reflected and transmitted light.

Another possibility of testing the prediction under consideration and our hypothesis as a whole is that for weak light fluxes, a diffraction device made of another material, which differs by a different surface density of atoms, should give a different interference pattern for the same light output. This prediction is also verifiable in principle.

The atoms of the surface of the reflecting body are involved in thermal motion, the nodes crystal lattice commit harmonic vibrations. An increase in the crystal temperature should lead to blurring of the interference pattern in the case of weak light fluxes, since in this case the interference depends only on the periodic structure of the reflecting surface. For strong light fluxes, the effect of the temperature of the diffraction device on the interference pattern should be weaker, although it is not excluded, since thermal vibrations of the crystal lattice sites should violate the coherence condition for the reflected pairs of photons from different photons. This prediction is also verifiable in principle.

Corpuscular properties of light

In our publications, we have proposed the term “structural model of a photon”. Analyzing today a combination of words enclosed in quotation marks, it is necessary to recognize it as extremely unsuccessful. The point is that in our model the photon as a localized particle does not exist. A quantum of radiant energy, identified in modern theory with a photon, in our model is a set of vacuum excitations, called pairs of photons. Excitations are distributed in space along the direction of motion. Despite the enormous extent for the scale of the microworld, due to the smallness of the time interval during which such a set of pairs flies past any microobject or collides with it, and also due to the relative inertia of the objects of the microworld, quanta can be completely absorbed by these microobjects. A quantum photon is perceived as a separate particle only in the process of such interaction with micro-objects, when the effect from the interaction of a micro-object with each pair of photons can be accumulated, for example, in the form of excitation electron shell atom or molecule. Light exhibits corpuscular properties in the course of such an interaction, when an essential, model-conscious, theoretically taken into account factor is the emission or absorption of a certain discrete amount of light energy.

Even a formal idea of energy quanta allowed Planck to explain the features of black body radiation, and Einstein to understand the essence of the photoelectric effect. The concept of discrete portions of energy helped to describe such physical phenomena, as light pressure, light reflection, dispersion - what has already been described in the language of the wave model. The idea of energy discreteness, and not the idea of point particles-photons, is what is really essential in the modern corpuscular model of light. The discreteness of the energy quantum makes it possible to explain the spectra of atoms and molecules, but the localization of the energy of the quantum in one isolated particle conflicts with the experimental fact that the time of emission and the time of absorption of the energy quantum by an atom is quite long on the scale of the microworld - about 10–8 s. If a quantum is a localized point particle, then what happens to this particle in a time of 10–8 s? The introduction of an extended quantum-photon into the physical model of light makes it possible to qualitatively understand not only the processes of emission and absorption, but also the corpuscular properties of radiation in general.

Quantitative parameters of photos

In our model, the main object of consideration is a couple of photos. Compared to the dimensions of a photon (longitudinal dimensions for visible light are meters), vacuum excitation in the form of a pair of photons can be considered as a point (longitudinal dimension is about 10–14 m) . Let us quantify some photo parameters. It is known that γ-quanta are produced during the annihilation of an electron and a positron. Let two γ-quanta be born. Let us estimate the upper limit of their quantitative parameters, assuming the energy of the electron and positron to be equal to the rest energy of these particles:

The number of photo pairs that appear is:

. (2)

The total charge of all (–) photons is –e, where e is the electron charge. The total charge of all (+) photons is +e. Let us calculate the modulus of the charge carried by one photo:

Cl. (3)

Approximately, not taking into account the dynamic interaction of moving charges, we can assume that the centripetal force of a rotating pair of photons is the force of their electrostatic interaction. Since the linear speed of rotating charges is equal to C, we get (in the SI system):

where m0 / 2 = hЭ / C2 is the mass of one photo. From (4) we obtain an expression for the radius of rotation of photon charge centers:

m. (5)

Considering the “electrical” cross section of a photon as the area of a circle S of radius REl, we obtain:

The paper provides a formula for calculating the cross section of a photon in the framework of QED:

where σ is measured in cm2. Assuming ω = 2πν, and ν = n (without taking into account the dimension), we obtain an estimate of the cross section using the QED method:

. (8)

The difference with our estimate of the photon cross section is 6 orders of magnitude, or about 9%. In this case, it should be noted that our result for the photon cross section of ~10–65 cm2 was obtained as an upper estimate for the annihilation of immobile particles, while the real electron and positron have the energy of motion. Taking into account the kinetic energy, the cross section should be smaller, since in formula (1) the energy of particles passing into radiation will be greater, and, consequently, the number of pairs of photons will be greater. The calculated value of the charge of one photo will turn out to be less (formula 3), therefore, REl (formula 5) and the cross section S (formula 6) will be less. Taking this into account, our estimate of the photon cross section should be recognized as approximately coinciding with the QED estimate.

Note that the specific charge of phot coincides with the specific charge of an electron (positron):

. (9)

If a phot (like an electron) has a hypothetical “core”, in which its charge is concentrated, and a “fur coat” from a perturbed physical vacuum, then the “electrical” cross section of a pair of photons should not coincide with the “mechanical” cross section. Let the centers of mass of photons rotate around a circle of radius RMex with a speed C. Since C = ωRMex, we obtain:

. (10)

Thus, the length of the circle along which the photo centers of mass rotate is equal to the wavelength, which is quite natural when the translational and rotational velocities are equal in our interpretation of the concept of “wavelength”. But in this case, it turns out that for photons obtained as a result of the annihilation considered above, RMex ≈ 3.8∙10–13 m ≈ 1022∙REl. The coat of perturbed vacuum, surrounding the cores of photons, has gigantic dimensions compared to the core itself.

Of course, these are all rather rough estimates. Any new model cannot compete in accuracy with an already existing model that has reached its dawn. For example, when the heliocentric model of Copernicus appeared, for about 70 years practical astronomical calculations were carried out in accordance with the geocentric model of Ptolemy, since this led to a more accurate result.

The introduction of models on a fundamentally new basis into science is not only a collision with subjective opposition, but also an objective loss of the accuracy of calculations and predictions. Paradoxical results are also possible. The resulting ratio of orders of ~1022 between the electrical and mechanical radii of rotation of photons is not only unexpected, but also physically incomprehensible. The only way to somehow understand the ratio obtained is to consider that the rotation of a pair of photons has a vortex character, because in this case, with equality linear speeds components at different distances from the center of rotation, their angular velocities must be different.

Intuitively, the vortex nature of the rotation of a three-dimensional structure from a thin medium - physical vacuum, is even more understandable than the idea of the rotation of a pair of photons, reminiscent of the rotation of a solid body. An analysis of the vortex motion should further lead to a new qualitative understanding of the process under consideration.

Results and conclusions

The work continues the development of ideas about the physical nature of light. The physical nature of corpuscular-wave dualism is analyzed. Fundamentally verifiable effects are predicted in experiments on the interference and diffraction of weak light fluxes. Quantitative calculations of mechanical and electrical parameters of photons have been performed. The cross section of a pair of photons is calculated and a conclusion is made about the vortex structure of the pair.

Literature

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2. Moiseev and energy in the structural model of the photon. - Dep. in VINITI 01.04.98, No. 000 - B98.

3. On the total energy and mass of the body in motion. - Dep. in VINITI 12.05.98, No. 000 - B98.

4. Moiseev in a gravitational field. - Dep. in VINITI 10.27.99, No. 000 - B99.

5. Moiseev photon structures. - Kostroma: Publishing House of the KSU im. , 2001.

5. Moiseev photon // Proceedings of the Congress-2002 “Fundamental problems of natural science and technology”, part III, pp. 229–251. - St. Petersburg, Publishing House of St. Petersburg State University, 2003.

7 Phys. Rev. Lett.3). http://prl. aps. org

8. Sivukhin and nuclear physics. In 2 hours. Part 1. Atomic physics. – M.: Nauka, 1986.

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12. Akhiezer electrodynamics /, - M .: Nauka, 1981.

Wave and corpuscular properties of elementary particles

Wave properties of light

The fact that light has wave properties has long been known. Robert Hooke in his Micrographia (1665) compares light to the propagation of waves. Christian Huygens in 1690 published a "Treatise on Light", in which he develops the wave theory of light. Interestingly, Newton, who was familiar with these works, in his treatise on optics convinces himself and others that light consists of particles - corpuscles. Newton's authority for some time even prevented the recognition of the wave theory of light. This is all the more surprising because Newton not only heard about the work of Hooke and Huygens, but also designed and manufactured a device on which he observed the phenomenon of interference, known today to every schoolchild under the name "Newton's Rings". The phenomena of diffraction and interference are simply and naturally explained in the wave theory. He, Newton, had to change himself and resort to "inventing hypotheses" of a very vague content in order to make the corpuscles move properly.

Newton, as a scientist, achieved the greatest success in explaining the motion of the planets using the laws of mechanics he discovered. Naturally, he tried to use the same laws to explain the movement of light, but in order for this to become possible, light must necessarily consist of corpuscles. If light consists of particles, then the laws of mechanics apply to them, and in order to find the laws of their motion, it remains only to find out what forces act between them and matter. To explain such diverse phenomena as the motion of the planets and the propagation of light on the same principles is a daunting task, and Newton could not deny himself the pleasure of looking for its solution. modern science does not recognize Newton's corpuscular theory, however, since the publication of Einstein's work on the photoelectric effect, light has been considered to be composed of photon particles. Newton was not mistaken in the fact that the movement of the planets and the propagation of light are governed by some general principles that were unknown to him.

Let us recall the most well-known experiments, devices and devices in which the wave nature of light is most clearly manifested.

1. "Newton's Rings".

2. The interference of light as it passes through two holes.

3. Interference of light upon reflection from thin films.

4. Various instruments and devices: Fresnel biprism, Fresnel mirrors, Lloyd's mirror; interferometers: Michelson, Mach-Zander, Fabry-Perot.

5. Diffraction of light by a narrow slit.

6. Diffraction grating.

7. Poisson's spot.

All these experiments, devices, devices or phenomena are well known, so we will not dwell on them. I would like to recall only one curious detail related to the name "Poisson's spots". Poisson was an opponent of the wave theory. Considering Fresnel's method, he came to the conclusion that if light is a wave, then there should be a bright spot in the center of the geometric shadow from an opaque disk. Considering that this conclusion is absurd, he advanced it as a convincing objection to the wave theory. However, this absurd prediction was experimentally confirmed by Aragon.

Corpuscular properties of light

Since 1905, science has known that light is not only a wave, but also a stream of particles - photons. It all started with the discovery of the photoelectric effect.

The photoelectric effect was discovered by Hertz in 1887.

1888 - 1889 the phenomenon was experimentally studied by Stoletov.

1898 Lenard and Thompson established that particles emitted by light are electrons.

The main problem that the photoelectric effect posed to scientists was that the energy of electrons torn out of matter by light does not depend on the intensity of light incident on matter. It depends only on its frequency. Classical wave theory could not explain this effect.

1905 Einstein gave a theoretical explanation of the photoelectric effect, for which he received the Nobel Prize in 1921.

According to Einstein's assumption, light consists of photons, the energy of which depends only on frequency and is calculated using Planck's formula: . Light can pull an electron out of matter if the photon has enough energy to do so. It does not matter the number of photons that fall on the illuminated surface. Therefore, the intensity of the light is irrelevant for the onset of the photoelectric effect.

When explaining the photoelectric effect, Einstein used Planck's well-known hypothesis. Planck at one time suggested that light is emitted in portions - quanta. Now Einstein suggested that light, moreover, is absorbed in portions. This assumption was sufficient to explain the photoelectric effect. Einstein, however, goes further. It assumes that light is distributed in portions or photons. There were no experimental grounds for such a statement at that time.

The most direct confirmation of Einstein's hypothesis came from Bothe's experiment.

In Bothe's experiment, a thin metal foil F was placed between two gas-discharge counters Cch. The foil was illuminated with a weak beam of X-rays, under the influence of which it itself became a source of X-rays. Secondary photons were captured by Geiger counters. When the counter was triggered, the signal was transmitted to the mechanisms M, which made a mark on the moving tape L. If the secondary radiation were emitted in the form spherical waves, then both counters would have to operate simultaneously. However, experience has shown that the marks on the moving tape were located completely independently of each other. This could be explained in only one way: the secondary radiation occurs in the form of individual particles that can fly either in one direction or in the opposite direction. Therefore, both counters cannot work at the same time.

Compton experience

In 1923, Arthur Holly Compton, an American physicist, investigating the scattering of X-rays by various substances, discovered that in the rays scattered by matter, along with the initial radiation, there are rays with a longer wavelength. This behavior of X-rays is only possible from a quantum mechanical standpoint. If X-rays consist of quanta - particles, then these particles must lose energy in collisions with electrons at rest, just like a fast-flying ball loses energy when it collides with a resting one. A flying ball, having lost energy, slows down. A photon cannot slow down, its speed is always equal to the speed of light, in fact, he himself is light. But since the energy of the photon is , the photon reacts to the collision by reducing the frequency.

Let the energy and momentum of the photon before the collision be:

;

Energy and momentum of a photon after scattering by an electron:

;

Energy of an electron before collision with a photon:

Its momentum before the collision is zero - the electron is at rest before the collision.

After the collision, the electron acquires momentum , and its energy increases accordingly: . The last relation is obtained from the equality: .

Let us equate the energy of the system before the collision of the photon with the electron to the energy after the collision.

The second equation is obtained from the momentum conservation law. In this case, of course, we should not forget that momentum is a vector quantity.

;

Let's transform the energy conservation equation

and square the right and left sides

We equate the obtained expressions for the square of the electron momentum

, from where we get: . Normally,

we introduce the notation .

The quantity is called the Compton wavelength of the electron and is denoted by . With this notation, we can write an expression that represents the theoretical derivation of Compton's experimental result: .

De Broglie's hypothesis and the wave properties of other particles

In 1924, de Broglie hypothesized that photons are no exception. Other particles also, according to de Broglie, must have wave properties. Moreover, the relationship between energy and momentum, on the one hand, and wavelength and frequency, on the other hand, must be exactly the same as for electromagnetic photons.

For photons , . According to de Broglie's assumption, a particle must be associated with a wave of matter with a frequency and wavelength .

What is this wave and what is it physical meaning, de Broglie could not say. Today, it is generally accepted that the de Broglie wave has a probabilistic meaning and characterizes the probability of finding a particle at various points in space.

The most interesting thing about this is that the wave properties of the particles were discovered experimentally.

In 1927, Davisson and Jammer discovered the diffraction of electron beams upon reflection from a nickel crystal.

In 1927, the son of J.J. Thomson and, independently of him, Tartakovsky obtained a diffraction pattern when an electron beam passed through a metal foil.

Subsequently, they received diffraction patterns and for molecular beams.

Wave and corpuscular properties of light - page №1/1

WAVE AND CORPUSCULAR PROPERTIES OF LIGHT

Kostroma State University
1 Maya Street, 14, Kostroma, 156001, Russia
Email: [email protected] ; [email protected]

The possibility of considering light as a periodic sequence of excitations of the physical vacuum is logically deduced. As a consequence of this approach, the physical nature of the wave and corpuscular properties of light is explained.

Introduction

This work is devoted to the formation of new theoretical ideas about the physical nature of light, which should explain qualitatively the wave and corpuscular properties of light. Earlier, the main provisions of the developed model and the results obtained within the framework of this model were published:

1. A photon is a set of elementary excitations of vacuum propagating in space in the form of a chain of excitations with a constant relative to vacuum speed, independent of the speed of the light source. For an observer, the photon's speed depends on the observer's speed relative to vacuum, modeled logically as absolute space.

4. The energy of a photon is determined by the number of pairs of photons n in one photon: ε = nh E, where h E is a value equal to Planck's constant in units of energy .

5. The quantitative value of the photon spin ћ is obtained. An analysis of the relationship between the energy and kinematic parameters of a photon has been carried out. As an example, the kinematic parameters of a photon produced by the 3d2p transition in a hydrogen atom are calculated. The length of a photon in the visible part of the spectrum is meters.

6. The mass of a pair of photons was calculated m 0 = 1.474 10 -53 g, which coincides in order of magnitude with the upper estimate of the photon mass m 

7. A conclusion was made about the change in the constants C and h when a photon moves in a gravitational field.

From the periodic structure of a photon, the reason for the wave properties of light is intuitively clear: the mathematics of a wave, as a process of mechanical vibration of a physical medium, and the mathematics of a periodic process of any qualitative nature, coincide. The papers give a qualitative explanation of the wave and corpuscular properties of light. This article continues the development of ideas about the physical nature of light.

Wave properties of light

As noted earlier, the elements of periodicity associated with the physical nature of light cause the manifestation of wave properties. The manifestation of the wave properties of light has been established by numerous observations and experiments, and therefore cannot be in doubt. A mathematical wave theory of the Doppler effect, interference, diffraction, polarization, dispersion, absorption and scattering of light has been developed. The wave theory of light is organically connected with geometric optics: in the limit, as  → 0, the laws of optics can be formulated in the language of geometry.

The combination of corpuscular and wave models according to the principle “a wave is a perturbation of a set of particles” raises an objection, because the presence of wave properties in a single, single particle of light is considered to be firmly established. The interference of rarely flying photons was discovered by Janoshi, but there are no quantitative results, details and detailed analysis of the experiment in the training course. Information about such important, fundamental results is absent both in reference books and in the course on the history of physics. Apparently, the question of the physical nature of light is already a deep rear of science.

Let us try to reconstruct the quantitative parameters of Yanoshi's experiment, which are logically essential for interpreting the results, using a stingy description of similar experiments by Biberman, Sushkin, and Fabrikant with electrons. Obviously, in Yanoshi's experiment, the interference pattern obtained from a short light pulse of high intensity J B was compared with the pattern obtained over a long time from a weak photon flux J M. The essential difference between the two situations under consideration is that in the case of a flux J M, the interaction of photons within diffractive instrument should be excluded.

Since Yanoshi did not find a difference in the interference patterns, let's see what conditions are necessary for this within the framework of our model.

A photon of length L f = 4.5 m passes a given point in space in time τ = L f / C = 4.5 /3ּ10 8 ≈ 1.5ּ10 –8 s. If the diffraction system (device) has a size of about 1 m, then the time it takes for a photon to pass through the device of length L f will be longer: τ’ = (L f + 1) / C ≈ 1.8ּ10 –8 s.

An outside observer cannot see single photons. An attempt to fix a photon destroys it - there is no other option to “see” an electrically neutral particle of light. The experiment uses time-averaged properties of light, in particular, intensity (energy per unit time). So that photons do not intersect within the diffraction device, it is necessary to separate them in space along the trajectory of movement so that the time of passage of the device τ' is less than the time t dividing the arrival of successive photons to the installation, i.e. τ' 1.8ּ10 –8 s.

In experiments with electrons, the average time interval between two particles successively passing through the diffraction system was approximately 3-10 4 times longer than the time spent by one electron to pass through the entire device. For point particles, this relation is convincing.

The results of Yanoshi's experiments are indisputable, however, such a conclusion cannot be made about the theory of experience. In theory, it is actually postulated that the interference pattern arises solely as a result of the interaction of particles with each other on the surface of the screen. In the case of strong light fluxes and the presence of many particles, this is the intuitively most probable cause of interference, but for weak light fluxes, another reason for the appearance of periodicity in screen illumination can also become significant. Light changes direction when it interacts with a solid body. Slit edges, diffraction grating strokes and other obstacles that cause diffraction - this is a surface that is far from ideal, not only in terms of surface finish. Atoms of the surface layer are a periodic structure with a period comparable to the size of an atom, i.e., the periodicity is of the angstrom order. The distance between photon pairs inside a photon is L 0 ≈ 10 –12 cm, which is 4 orders of magnitude smaller. The reflection of photo pairs from the periodic structure of the surface should cause a repetition of illuminated and unilluminated places on the screen.

For a possible experimental confirmation (or refutation) of this hypothesis, some effects can be predicted.

Effect 1

The mutual complementarity of the light reflected and transmitted through the plate in the phenomenon of interference is a well-known fact, described in theory by a well-developed formal mathematical apparatus of the wave model of light. In particular, the theory introduces a loss of a half-wave during reflection, and this “explains” the phase difference between the transmitted and reflected components.

Effect 2

Effect 3

The atoms of the surface of the reflecting body participate in thermal motion, the nodes of the crystal lattice perform harmonic vibrations. An increase in the crystal temperature should lead to blurring of the interference pattern in the case of weak light fluxes, since in this case the interference depends only on the periodic structure of the reflecting surface. For strong light fluxes, the effect of the temperature of the diffraction device on the interference pattern should be weaker, although it is not excluded, since thermal vibrations of the crystal lattice sites should violate the coherence condition for the reflected pairs of photons from different photons. This prediction is also verifiable in principle.

Corpuscular properties of light

In our publications, we have proposed the term “structural model of a photon”. Analyzing today a combination of words enclosed in quotation marks, it is necessary to recognize it as extremely unsuccessful. The point is that in our model the photon as a localized particle does not exist. A quantum of radiant energy, identified in modern theory with a photon, in our model is a set of vacuum excitations, called pairs of photons. Excitations are distributed in space along the direction of motion. Despite the enormous extent for the scale of the microworld, due to the smallness of the time interval during which such a set of pairs flies past any microobject or collides with it, and also due to the relative inertia of the objects of the microworld, quanta can be completely absorbed by these microobjects. A quantum photon is perceived as a separate particle only in the process of such interaction with micro-objects, when the effect from the interaction of a micro-object with each pair of photons can be accumulated, for example, in the form of excitation of the electron shell of an atom or molecule. Light exhibits corpuscular properties in the course of such an interaction, when an essential, model-conscious, theoretically taken into account factor is the emission or absorption of a certain discrete amount of light energy.

Even a formal idea of energy quanta allowed Planck to explain the features of black body radiation, and Einstein to understand the essence of the photoelectric effect. The concept of discrete portions of energy helped to describe in a new way such physical phenomena as light pressure, light reflection, dispersion - what has already been described in the language of the wave model. The idea of energy discreteness, and not the idea of point particles-photons, is what is really essential in the modern corpuscular model of light. The discreteness of the energy quantum makes it possible to explain the spectra of atoms and molecules, but the localization of the energy of the quantum in one isolated particle conflicts with the experimental fact that the time of emission and the time of absorption of the energy quantum by an atom is quite large on the scale of the microworld - about 10–8 s. If a quantum is a localized point particle, then what happens to this particle in a time of 10–8 s? The introduction of an extended quantum-photon into the physical model of light makes it possible to qualitatively understand not only the processes of emission and absorption, but also the corpuscular properties of radiation in general.

Quantitative parameters of photos

In our model, the main object of consideration is a couple of photos. Compared to the dimensions of a photon (longitudinal dimensions for visible light are meters), the excitation of vacuum in the form of a pair of photons can be considered pointlike (the longitudinal dimension is about 10–14 m) . Let us quantify some photo parameters. It is known that γ-quanta are produced during the annihilation of an electron and a positron. Let two γ-quanta be born. Let us estimate the upper limit of their quantitative parameters, assuming the energy of the electron and positron to be equal to the rest energy of these particles:

. (1)

The number of photo pairs that appear is:

. (2)

The total charge of all (–) photons is –e, where e is the electron charge. The total charge of all (+) photons is +e. Let us calculate the modulus of the charge carried by one photo:

Cl. (3)

, (4)

where m 0 / 2 \u003d h E / C 2 - the mass of one photo. From (4) we obtain an expression for the radius of rotation of photon charge centers:

m. (5)

Considering the “electrical” cross section of a photon as the area of a circle S of radius R El, we obtain:

The paper provides a formula for calculating the cross section of a photon in the framework of QED:

, (7)

where σ is measured in cm 2. Assuming ω = 2πν, and ν = n (without taking into account the dimension), we obtain an estimate of the cross section using the QED method:

. (8)

The difference with our estimate of the photon cross section is 6 orders of magnitude, or about 9%. At the same time, it should be noted that our result for the photon cross section of ~10 –65 cm 2 was obtained as an upper estimate for the annihilation of immobile particles, while the real electron and positron have the energy of motion. Taking into account the kinetic energy, the cross section should be smaller, since in formula (1) the energy of particles passing into radiation will be greater, and, consequently, the number of pairs of photons will be greater. The calculated value of the charge of one photo will be less (formula 3), therefore, R El (formula 5) and the cross section S (formula 6) will be less. Taking this into account, our estimate of the photon cross section should be recognized as approximately coinciding with the QED estimate.

Note that the specific charge of phot coincides with the specific charge of an electron (positron):

. (9)

. (10)

Thus, the length of the circle along which the photo centers of mass rotate is equal to the wavelength, which is quite natural when the translational and rotational velocities are equal in our interpretation of the concept of “wavelength”. But in this case, it turns out that for photons obtained as a result of the annihilation considered above, R Mex ≈ 3.8∙10 –13 m ≈ 10 22 ∙R El. The coat of perturbed vacuum, surrounding the cores of photons, has gigantic dimensions compared to the core itself.

The introduction of models on a fundamentally new basis into science is not only a collision with subjective opposition, but also an objective loss of the accuracy of calculations and predictions. Paradoxical results are also possible. The resulting ratio of orders of ~10 22 between the electrical and mechanical radii of rotation of photons is not only unexpected, but also physically incomprehensible. The only way to somehow understand the ratio obtained is to assume that the rotation of a pair of photons has a vortex character, since in this case, if the linear velocities of components at different distances from the center of rotation are equal, their angular velocities should be different.

Results and conclusions

Literature

1. Moiseev B.M. Photon structure. - Dep. in VINITI 12.02.98, No. 445 - B98.

2. Moiseev B.M. Mass and energy in the structural model of the photon. - Dep. in VINITI 01.04.98, No. 964 - B98.

3. Moiseev B.M. On the total energy and mass of a body in a state of motion. - Dep. in VINITI 12.05.98, No. 1436 - B98.

4. Moiseev B.M. Photon in a gravitational field. - Dep. in VINITI 27.10.99, No. 3171 - B99.

5. Moiseev B.M. Modeling the structure of a photon. - Kostroma: Publishing House of the KSU im. ON THE. Nekrasova, 2001.

5. Moiseev B.M. Photon microstructure // Proceedings of the Congress-2002 “Fundamental problems of natural science and technology”, part III, pp. 229–251. - St. Petersburg, Publishing House of St. Petersburg State University, 2003.

7 Phys. Rev. Lett. 90 081 801 (2003). http://prl.aps.org

8. Sivukhin D.V. Atomic and nuclear physics. In 2 hours. Part 1. Atomic physics. – M.: Nauka, 1986.

9. Physical Encyclopedic Dictionary. In 5 volumes - M .: Soviet Encyclopedia, 1960-66.

10. Physics. Big encyclopedic dictionary. - M .: Great Russian Encyclopedia, 1999.

11. Kudryavtsev P.S. Course in the history of physics. - M .: Education, 1974.

12. Akhiezer A.I. Quantum electrodynamics / A.I. Akhiezer, V.V. Berestetsky - M .: Nauka, 1981.

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