10. Thus the electrons in the atom do not constantly “wind” circles in the field of the central forces of the nucleus, but perform oscillations in this field, in the course of which there occurs a continuous transition of the kinetic energy of the electron into ponderomotive energy of the field and back.
From the standpoint of classical physics such an assertion is entirely devoid of “common sense”. In a system consisting of two oppositely charged particles – the electron and the nucleus of the atom, oscillations of the electron are not possible, just as, incidentally, no forces other than those of electrostatic and gravitational interaction are possible. And yet the idea of the existence of a ponderomotive field in the atom is not a supposition requiring proof or refutation. This idea is an inference of certainty, whose truth is grounded in the fact of the being of the atom: since the atom exists over the duration of eternity, there exists in the atom also a ponderomotive field, as a necessary condition of its being.
After Schrödinger's equation, behind which stands the whole experience of modern quantum mechanics, the question now is whether this new form of matter reveals itself not indirectly but directly, in a specially designed experiment?
11. If white-hot solids give, as is known, a continuous spectrum of radiation, then “blazing” rarefied gases, heated or excited by an electric discharge, give an entirely different spectrum. Analysis of their radiation, essentially of the emission spectra of individual atoms, shows that light of most colours is absent from the spectrum, and there are only very narrow and very bright strips of definite colours, i.e. the spectrum consists of bright “lines”, each of which corresponds in practice to one wavelength. Each gas has its own characteristic set of lines. The wavelengths of the bright spectral lines have a quite definite magnitude for the atoms of each element. The lines of each element are grouped along the spectrum in regular series with a varying step, so that in the arrangement of each series some system is plainly observed.
Studying the line spectrum of the hydrogen atom, the Swiss scientist J. Balmer established (1885) a rule reflecting such a system. Balmer established [2] that the wavelengths λ of the nine lines of the hydrogen atom spectrum known by that time satisfy a formula he selected empirically
From the standpoint of classical physics such an assertion is entirely devoid of “common sense”. In a system consisting of two oppositely charged particles – the electron and the nucleus of the atom, oscillations of the electron are not possible, just as, incidentally, no forces other than those of electrostatic and gravitational interaction are possible. And yet the idea of the existence of a ponderomotive field in the atom is not a supposition requiring proof or refutation. This idea is an inference of certainty, whose truth is grounded in the fact of the being of the atom: since the atom exists over the duration of eternity, there exists in the atom also a ponderomotive field, as a necessary condition of its being.
After Schrödinger's equation, behind which stands the whole experience of modern quantum mechanics, the question now is whether this new form of matter reveals itself not indirectly but directly, in a specially designed experiment?
11. If white-hot solids give, as is known, a continuous spectrum of radiation, then “blazing” rarefied gases, heated or excited by an electric discharge, give an entirely different spectrum. Analysis of their radiation, essentially of the emission spectra of individual atoms, shows that light of most colours is absent from the spectrum, and there are only very narrow and very bright strips of definite colours, i.e. the spectrum consists of bright “lines”, each of which corresponds in practice to one wavelength. Each gas has its own characteristic set of lines. The wavelengths of the bright spectral lines have a quite definite magnitude for the atoms of each element. The lines of each element are grouped along the spectrum in regular series with a varying step, so that in the arrangement of each series some system is plainly observed.
Studying the line spectrum of the hydrogen atom, the Swiss scientist J. Balmer established (1885) a rule reflecting such a system. Balmer established [2] that the wavelengths λ of the nine lines of the hydrogen atom spectrum known by that time satisfy a formula he selected empirically
Изображение
where R` = 10973731.77 m-1.
The constant R` was determined by the Swedish scientist J. Rydberg and is called the Rydberg constant. Since λ = c/v, formula (19) can be rewritten for the frequencies v:
The constant R` was determined by the Swedish scientist J. Rydberg and is called the Rydberg constant. Since λ = c/v, formula (19) can be rewritten for the frequencies v:
Изображение
where R=R`c = 3.2931193*1015 s-1– is likewise called the Rydberg constant.
At the beginning of the 20th century four more series of spectral lines, showing an analogous regularity, were detected in the ultraviolet and infrared regions of the spectrum of the hydrogen atom. This circumstance made it possible to describe all the series in the spectrum of the hydrogen atom by one formula, justly called the generalised Balmer formula:
At the beginning of the 20th century four more series of spectral lines, showing an analogous regularity, were detected in the ultraviolet and infrared regions of the spectrum of the hydrogen atom. This circumstance made it possible to describe all the series in the spectrum of the hydrogen atom by one formula, justly called the generalised Balmer formula:
Изображение
where m has a constant value in each series, m = 1, 2, 3, 4 (it determines the series), and n takes integer values, beginning with m + 1 (it determines the individual lines of that series).
According to Planck's radiation law, the hydrogen atom emits electromagnetic energy in quanta. Therefore, multiplying the right and left sides of equation (21) by the Planck constant h , we obtain the generalised Balmer formula for the energies of the spectral lines:
According to Planck's radiation law, the hydrogen atom emits electromagnetic energy in quanta. Therefore, multiplying the right and left sides of equation (21) by the Planck constant h , we obtain the generalised Balmer formula for the energies of the spectral lines:
Изображение
As a result of applying the quantum law of radiation, the generalised Balmer formula acquired an expressiveness that makes it possible to determine its physical meaning unambiguously: the emission or absorption by the atom of a quantum of energy hv is a process of change of its internal energy. Here the change of the internal energy of the atom is to be understood as a discrete transition of the atom from one energy state Wm to another state Wn, so that on absorption the atom passes into a state of greater energy, on emission – into a state of lesser energy.
Since the values m and n form a series of integers starting from 1, this makes it possible to collapse equation (22) in such a way that the energy of the hydrogen atom in the n-th state, up to an arbitrary additive constant, is expressed by the formula:
Since the values m and n form a series of integers starting from 1, this makes it possible to collapse equation (22) in such a way that the energy of the hydrogen atom in the n-th state, up to an arbitrary additive constant, is expressed by the formula:
Изображение
From equation (23) it follows that the values of the internal energy of the hydrogen atom, which it can assume as a result of emission or absorption of electromagnetic energy, form a discrete series of “allowed” values:
Изображение
Thus the application of the quantum law of radiation to the line spectra of atoms leads us to the thought that every atom is a system whose main peculiarity is that interactions with the external environment cannot change its internal energy continuously, at the will of the external environment. The internal energy of an atom can change only discretely. The law of discreteness is due to the structure of the atom and for the hydrogen atom is expressed by formula (23).
However, this thought is only a supposition, for there remains the doubt whether the discrete character of the change of energy of atoms is not a specific feature of their interactions with radiant energy. Experimental confirmation was required that the discrete character of the change of the internal energy of atoms is preserved in other interactions too, and such confirmation was obtained by the German physicists J. Franck and Gustav Hertz in the middle of 1913.
12. Franck and Hertz studied collisions of atoms with electrons at various values of the kinetic energy of the electrons. They firmly established [3] that, depending on the magnitude of the kinetic energy of the electrons, atoms can collide both elastically and inelastically. Mercury atoms collide elastically if the energy of the electrons does not exceed eφ<4.86 eV. But as soon as the energy of the electrons reaches the value 4.86 eV, inelastic collisions begin to occur, as a result of which the electron transfers all its energy to the atom and its velocity falls to zero.
Thus the discrete character of the change of the internal energy of the atom was confirmed: the atom either does not take up energy at all, or takes it up, but only in definite amounts.
This was a very important discovery; however, we ask the question of what the atom is as an object of collisions with an electron. If the atom is an aggregate of a nucleus and electrons united by the force of Coulomb attraction, then when it collides in an experimental apparatus with emission electrons there must necessarily occur either elastic electron/electron collisions without exchange of energy, or nucleus/electron collisions, with the inevitable annihilation of the atom. Given the difference in the geometrical sizes of the electron and the nucleus, it is precisely these atom-destroying collisions that should have an overwhelming advantage. However, the atoms were not destroyed, and therefore the emission electrons collided not with the nucleus and electrons of the atom, but with some physical reality which is the system-forming basis of the atom, i.e. with the ponderomotive field of the atom. It is by colliding with this field that the electrons transfer their energy to the atom.
Thus the Franck – Hertz experiments not only proved that the atom is a discrete system, but also revealed in the atom the existence of some physical reality, entirely unknown before. However, this objectively revealed fact not only did not receive due development but, judging by everything, was not even noticed by physical science.
13. The American physicist A. Compton, repeating (1922 – 23) the Franck – Hertz experiments, found that mercury atoms bombarded by electrons with an energy eφ=4.86 eV become a source of radiation of one ultraviolet line with λ=254 nm. This is to be understood as meaning that mercury atoms which received in the collision with electrons a quantum of energy eφ=4.86 eV pass into an excited state and, in order to return to the ground state, “shed” this quantum, emitting photons of the corresponding wavelength λ=254 nm. From which it necessarily follows that the photon, as an object of the material world, is a physical quantum of action h .
As a quantum of action h, all photons are identical, but while identical in action they differ, according to Planck's radiation law W=hv, in the magnitude of the energy proper to them.
According to equation (2), the energy of the action h is determined by the duration of the action in time T. Since the frequency of the photon v=1/T, for each photon the duration of the quantum of action in time is equal to T=1/v, and therefore the energy of the physical quantum of action is equal to
However, this thought is only a supposition, for there remains the doubt whether the discrete character of the change of energy of atoms is not a specific feature of their interactions with radiant energy. Experimental confirmation was required that the discrete character of the change of the internal energy of atoms is preserved in other interactions too, and such confirmation was obtained by the German physicists J. Franck and Gustav Hertz in the middle of 1913.
12. Franck and Hertz studied collisions of atoms with electrons at various values of the kinetic energy of the electrons. They firmly established [3] that, depending on the magnitude of the kinetic energy of the electrons, atoms can collide both elastically and inelastically. Mercury atoms collide elastically if the energy of the electrons does not exceed eφ<4.86 eV. But as soon as the energy of the electrons reaches the value 4.86 eV, inelastic collisions begin to occur, as a result of which the electron transfers all its energy to the atom and its velocity falls to zero.
Thus the discrete character of the change of the internal energy of the atom was confirmed: the atom either does not take up energy at all, or takes it up, but only in definite amounts.
This was a very important discovery; however, we ask the question of what the atom is as an object of collisions with an electron. If the atom is an aggregate of a nucleus and electrons united by the force of Coulomb attraction, then when it collides in an experimental apparatus with emission electrons there must necessarily occur either elastic electron/electron collisions without exchange of energy, or nucleus/electron collisions, with the inevitable annihilation of the atom. Given the difference in the geometrical sizes of the electron and the nucleus, it is precisely these atom-destroying collisions that should have an overwhelming advantage. However, the atoms were not destroyed, and therefore the emission electrons collided not with the nucleus and electrons of the atom, but with some physical reality which is the system-forming basis of the atom, i.e. with the ponderomotive field of the atom. It is by colliding with this field that the electrons transfer their energy to the atom.
Thus the Franck – Hertz experiments not only proved that the atom is a discrete system, but also revealed in the atom the existence of some physical reality, entirely unknown before. However, this objectively revealed fact not only did not receive due development but, judging by everything, was not even noticed by physical science.
13. The American physicist A. Compton, repeating (1922 – 23) the Franck – Hertz experiments, found that mercury atoms bombarded by electrons with an energy eφ=4.86 eV become a source of radiation of one ultraviolet line with λ=254 nm. This is to be understood as meaning that mercury atoms which received in the collision with electrons a quantum of energy eφ=4.86 eV pass into an excited state and, in order to return to the ground state, “shed” this quantum, emitting photons of the corresponding wavelength λ=254 nm. From which it necessarily follows that the photon, as an object of the material world, is a physical quantum of action h .
As a quantum of action h, all photons are identical, but while identical in action they differ, according to Planck's radiation law W=hv, in the magnitude of the energy proper to them.
According to equation (2), the energy of the action h is determined by the duration of the action in time T. Since the frequency of the photon v=1/T, for each photon the duration of the quantum of action in time is equal to T=1/v, and therefore the energy of the physical quantum of action is equal to
Изображение
From which it follows that the photon is not only an unchanging quantum of action h, but a quantum of action with a definite intensity of its active realisation, i.e. the photon is also a definite quantum of energy.
Taking into account that the speed of the photon in vacuum is equal to c, and the duration of the action in time is T, we obtain the dependence of the energy of the physical quantum of action on its extent in space in linear dimensions λ
Taking into account that the speed of the photon in vacuum is equal to c, and the duration of the action in time is T, we obtain the dependence of the energy of the physical quantum of action on its extent in space in linear dimensions λ
Изображение
Proceeding from experiments on the reflection of light from stationary mirror surfaces and on the diffraction of light, one can conclude that the quantum of action h has no preferential extent in space, and therefore it may be assumed that physically it is a sphere of non-substantial materiality of diameter λ.
Thus the quantum of action h should not be regarded merely as some finite quantity in the course of calculations – a universal constant of the physical world. The quantum of action h is, above all, a physical object, the photon, which is a certain non-substantial materiality, localised in space as a single and indivisible whole, which moves in vacuum with the absolute speed , being a definite quantum of energy.
It is precisely the physical wholeness of the photon that firmly determines its basic rule of interaction with matter: a photon never interacts with a part of itself, a photon always interacts “wholly”. From which it necessarily follows that the photon is indestructible, and it is precisely the indestructibility of its being, so to speak, its “instinct of self-preservation”, that conditions this rule. In other words, from the basic rule it necessarily follows that the photon is a quantum h-system, which in all interactions by its own causes preserves itself as an unchanging quantum of action h.
Since the speed of the photon is finite, and the photon is localised in space, the interaction of the photon with matter does not occur instantaneously. The interaction of the photon necessarily is a process having extent in space and duration in time. Therefore, from the point of view of interaction as a process of active realisation of the quantum of action h, the physical meaning of λ is the extent of the interaction in space (Δl), and of T the duration of the interaction in time (Δt). 14. At the same time, in exceptionally delicate experiments the Russian physicist P. Lebedev showed (1899 – 1910) that a flux of radiation exerts on matter a pressure whose magnitude is proportional to the energy density of the radiation. Lebedev's experiments showed that the pressure of light on an absorbing wall is equal to the quantity of energy in unit volume of the radiation. This fact allowed Einstein to obtain a relation connecting the energy of the radiation W with the magnitude of the momentum p which is imparted to matter on absorption:
Thus the quantum of action h should not be regarded merely as some finite quantity in the course of calculations – a universal constant of the physical world. The quantum of action h is, above all, a physical object, the photon, which is a certain non-substantial materiality, localised in space as a single and indivisible whole, which moves in vacuum with the absolute speed , being a definite quantum of energy.
It is precisely the physical wholeness of the photon that firmly determines its basic rule of interaction with matter: a photon never interacts with a part of itself, a photon always interacts “wholly”. From which it necessarily follows that the photon is indestructible, and it is precisely the indestructibility of its being, so to speak, its “instinct of self-preservation”, that conditions this rule. In other words, from the basic rule it necessarily follows that the photon is a quantum h-system, which in all interactions by its own causes preserves itself as an unchanging quantum of action h.
Since the speed of the photon is finite, and the photon is localised in space, the interaction of the photon with matter does not occur instantaneously. The interaction of the photon necessarily is a process having extent in space and duration in time. Therefore, from the point of view of interaction as a process of active realisation of the quantum of action h, the physical meaning of λ is the extent of the interaction in space (Δl), and of T the duration of the interaction in time (Δt). 14. At the same time, in exceptionally delicate experiments the Russian physicist P. Lebedev showed (1899 – 1910) that a flux of radiation exerts on matter a pressure whose magnitude is proportional to the energy density of the radiation. Lebedev's experiments showed that the pressure of light on an absorbing wall is equal to the quantity of energy in unit volume of the radiation. This fact allowed Einstein to obtain a relation connecting the energy of the radiation W with the magnitude of the momentum p which is imparted to matter on absorption:
Изображение
But if momentum is imparted to matter, and radiation is a flux of photons, then the photon possesses momentum. Comparing (25) and (26), we obtain the relation between the linear dimensions of the photon and its momentum
Изображение
The pressure which matter experiences on absorbing photons is not virtual but actually existing, twisting a torsion balance. Consequently, in the process of absorption of a photon, the duration of which is equal to T, some force F acts on the torsion balance, imparting to it a momentum equal to
Изображение
And the source of this force can only be the photon.
Momentum, by definition, is the quantity of motion of a particle of mass m moving with velocity v. But the photon is substantially realised by non-substantial materiality, and therefore cannot have mass, and consequently momentum either, but since it does have it, then formally, by analogy with particles of matter, it was defined as
Momentum, by definition, is the quantity of motion of a particle of mass m moving with velocity v. But the photon is substantially realised by non-substantial materiality, and therefore cannot have mass, and consequently momentum either, but since it does have it, then formally, by analogy with particles of matter, it was defined as
Изображение
where mΨ - the mass of the photon, the magnitude of which is determined so as to satisfy relation (27). Whence follows Einstein's remarkable relation:
Изображение
15. Thus in the photon there are two groups of attributes, but not corpuscular and wave ones, as is customarily held, but energetic and space-time ones. The distinguishing feature of these attributes is that they characterise different aspects of the corpuscularity of the photon.
The first group is formed by the attributes which characterise the quantum of action h as a process of reaching a result. These include the extent of the interaction in space λ, the duration of the interaction in time T, and the speed of interaction c, i.e. those attributes which are customarily regarded as wave ones.
The second group is formed by the attributes which characterise the quantum of action h from the point of view of the result of interaction with matter. These include the mass, energy and momentum of the photon, i.e. the properly corpuscular attributes.
It is quite evident that the process of reaching a result precedes and prepares the result, and therefore the space-time attributes of the photon necessarily condition its energetic attributes. The course of the interaction process itself, its separate stages, prove to be in principle inaccessible to direct observation, constituting an informationally closed cycle of internal changes of the photon, although it is precisely these changes that synthesise the various physical phenomena in which one or another property of the photon is manifested, and consequently the properties of the “substance” of the photon itself. But since we are considering the photon in the context of the quantum-mechanical system of the atom, we are interested above all in its basic rule of interaction with matter – the rule of interacting “wholly”.
16. The photon in question was obtained as a result of an inelastic collision of an emission electron with a mercury atom. In this connection, are we really to allow ourselves to think that by this chance collision the atom and the electron “created” it out of non-being. Would it not be more correct to think that by the collision the electron “knocked out” or “freed” the photon from the ponderomotive field of the atom, in which it already existed, and had existed as long as the mercury atom itself. Precisely “knocked out” or “freed”, as a part of the matter of the atom, for to suppose that the emission of a photon by matter has an electrodynamic nature is, after Planck's studies of the thermal radiation of solids [4] and Bohr's work on modelling the atom [5], altogether impermissible.
Since the emission electron interacts directly with the ponderomotive field of the oscillator, the motion of the electron in the process of the collision is necessarily determined by equation (5), provided that the inelastic collision is a finite event. Therefore, at a value of the kinetic energy W=4.86 eV the velocity of the electron at the moment of the collision is
ν=13.07*107cm/s,
extent of the collision in space
l=0.882*10-8cm ,
and the duration of the collision in time
T=0.135*10-15s.
For comparison [6], the radius of the mercury atom is taken to be r=1.6*10-8cm.
Since as a result of the collision the oscillator emitted a quantum of energy, its total energy W decreased and became equal to
The first group is formed by the attributes which characterise the quantum of action h as a process of reaching a result. These include the extent of the interaction in space λ, the duration of the interaction in time T, and the speed of interaction c, i.e. those attributes which are customarily regarded as wave ones.
The second group is formed by the attributes which characterise the quantum of action h from the point of view of the result of interaction with matter. These include the mass, energy and momentum of the photon, i.e. the properly corpuscular attributes.
It is quite evident that the process of reaching a result precedes and prepares the result, and therefore the space-time attributes of the photon necessarily condition its energetic attributes. The course of the interaction process itself, its separate stages, prove to be in principle inaccessible to direct observation, constituting an informationally closed cycle of internal changes of the photon, although it is precisely these changes that synthesise the various physical phenomena in which one or another property of the photon is manifested, and consequently the properties of the “substance” of the photon itself. But since we are considering the photon in the context of the quantum-mechanical system of the atom, we are interested above all in its basic rule of interaction with matter – the rule of interacting “wholly”.
16. The photon in question was obtained as a result of an inelastic collision of an emission electron with a mercury atom. In this connection, are we really to allow ourselves to think that by this chance collision the atom and the electron “created” it out of non-being. Would it not be more correct to think that by the collision the electron “knocked out” or “freed” the photon from the ponderomotive field of the atom, in which it already existed, and had existed as long as the mercury atom itself. Precisely “knocked out” or “freed”, as a part of the matter of the atom, for to suppose that the emission of a photon by matter has an electrodynamic nature is, after Planck's studies of the thermal radiation of solids [4] and Bohr's work on modelling the atom [5], altogether impermissible.
Since the emission electron interacts directly with the ponderomotive field of the oscillator, the motion of the electron in the process of the collision is necessarily determined by equation (5), provided that the inelastic collision is a finite event. Therefore, at a value of the kinetic energy W=4.86 eV the velocity of the electron at the moment of the collision is
ν=13.07*107cm/s,
extent of the collision in space
l=0.882*10-8cm ,
and the duration of the collision in time
T=0.135*10-15s.
For comparison [6], the radius of the mercury atom is taken to be r=1.6*10-8cm.
Since as a result of the collision the oscillator emitted a quantum of energy, its total energy W decreased and became equal to
Изображение
Thus, in an inelastic collision we are in fact dealing with a mediated interaction of the emission electron with the electron of the oscillator. An interaction in which the total energy of this electron decreased by the quantum of emitted energy, and therefore the atom not only did not receive energy but lost it, so that with a sufficiently prolonged repetition of such collisions all the energy of the atom will pass into radiation, and the “death” of the atom will occur. However, the “death” of the atom does not occur, and therefore formula (32) is not exact: in an inelastic collision the emission of a photon takes place without a change in the internal energy of the atom. The mechanism of such conservation is to be sought, evidently, in the nature of the ponderomotive field.