| Start of section
Production, amateur Radio amateurs Aircraft model, rocket-model Useful, entertaining |
Stealth Master
Electronics Physics Technologies Inventions |
Secrets of the cosmos
Secrets of the Earth Secrets of the Ocean Tricks Map of section |
  |
| Use of the site materials is allowed subject to the link (for websites - hyperlinks) | |||
INTERRELATION BETWEEN QUANTUM AND CLASSICAL PHYSICS
Mirgorodsky Alexander Illarionovich
WAVE DE BROILLE
In the article "The Interpretation of Quantum Mechanics" by Louis de Broglie about the wave named by his name, wrote:
"I tried to imagine the corpuscle as a very small local disturbance included in the wave, and this led me to regard the corpuscle as a kind of a small clock, the phases of which should always be coordinated with the phases of the wave with which they are united.
... I was able to establish the following basic formulas between the energy E and the amount of motion p of the freely moving corpuscle, on the one hand, the frequency y and wavelength λ of the associated plane monochromatic wave, on the other hand:
| E = hv, | Λ = | H | (1) |
| P |
Where h is the Planck constant. These formulas, applied to the photon, contained, as a special case, the light quantum formulas (what we now call photons) / Philosophical issues of modern physics. Under the editorship of IV Kuznetsov and ME Omelyanovskii, GIPL M., 1953, Louis de Broglie's article "Interpretation of wave mechanics", pp. 80-81 ).
Formulas (1) can be equally successfully applied to a freely moving corpuscle having a velocity less than the speed of light, and to a photon having a velocity equal to the speed of light.
On the basis of formulas (1), the energy and momentum of a freely moving corpuscle can be expressed in the following analytical form:
| E = | H | and | P = | H | (2) |
| T | Λ |
It should be noted that the ratio of the energy E and momentum p of a freely moving corpuscle and the ratio of its wavelength λ to the period T of its oscillations are the uncertainty relation. In other words, any physical system can not be in states in which its energy and momentum, wavelength and period simultaneously take completely definite, exact values.
A freely moving corpuscle must have its own energy and momentum, and a wave in which the corpuscle is incorporated must have its own energy and momentum. The phases of the harmonically oscillating corpuscle and the phase of the wave must always be matched, which causes the existence of a common period T of vibrations of the corpuscle associated with the wave and the wave.
De Broglie was very concerned about the exact shape of the wave amplitude associated with the corpuscle. "We tried to admit - by analogy with the waves considered by classical mechanics - that this amplitude continuously changes in space without a noticeable violation, but I considered it dangerous to accept this postulate, because then the wave would have no local feature that could serve To represent the corpuscles " / s. 83 /.
He could not find a satisfactory answer to the question that bothered him, because there was no answer to him and could not be in principle. For a certain period of time T, the proper space of the system, the wavelength and its amplitude, can not have a definite exact value at any one time, and the corpuscle can not have an exact image in the wave. At the time, de Broglie did not know that the ratio of the system's own space to its own time period is a universal form of expression for the uncertainty relation. Therefore, he continued to think to himself that the amplitude of the wave "should represent a kind of local singularity," it should grow a little.
According to de Broglie, the solutions of the Schrödinger equation (1) should be considered solely as solutions of the wave equation of a continuous amplitude propagating in the configuration space. Schrödinger proposed to consider physical reality only a wave and abandon the concept of corpuscles. Against this proposal, Schrodinger de Broglie objected because he believed that a continuous wave of continuous amplitude existing in an abstract definite space can only be a pure abstraction. Completely abandon her, from her equation and from the solutions of the equation, de Broglie did not and decided to keep the solutions of the Schrödinger equations for the purpose of their further use.
De Broglie supplemented the solutions of the Schrödinger equations with other solutions on the basis of his theory of a double solution, in order to "preserve along with the idea of a wave the idea of a strictly localized corpuscle . " He supplemented Schrödinger's continuous wave with a wave into which the corpuscle was incorporated, and expected that double solutions of the two-wave equation would indicate in their structure, in a very small area, a very small local disturbance.
Instead of the expected very small local disturbance in the structure of two waves by means of double solutions of the wave equation, a very small region was identified, in the center of which a "mathematical singularity with infinite value (valeur)" was discovered . In other words, an infinite set of finite solutions of the wave equation contained one solution with an infinite value.
Since the value of each solution was the magnitude of the wave amplitude, and the magnitude of the amplitude represented a failure in the energy of the wave, de Broglie made an erroneous conclusion that at the center of a very small wave region the energy of the wave increases to infinity.
Thus, De Broglie's practical application of his theory of the double solution of the wave equation led him to a stunning, unintelligible explanation and understanding, the result.
The existence in the continuous wave of energy, the magnitude of which increases to infinity, contradicted not only common sense, but also some ideas of Einstein, whose authority was at that time indisputable for de Broglie. In particular, it contradicted Einstein's assertion that the total internal energy of any physical system is equal to its mass multiplied by the square of the speed of light:
| E = mc2. |
The value of the energy of the system can only be finite. De Broglie could not explain the increase in wave energy and wave amplitude to infinity. As a result, he replaced the infinite value with a very large finite value, the explanation of which was also not received by him. The replacement did not resolve the contradiction, but only diminished its sharpness.
De Broglie did not find an explanation for his discovery because he did not know the relation of space and time as a universal ratio of uncertainties. He did not know that the problem of preserving, along with the idea of a wave, the idea of a localized corpuscle has no solution. The corpuscle, included in the wave, is "distributed" along its entire length and can not form in the structure of two waves a very small or very large local disturbance.
The solutions of the time Schrödinger equation for any of their additions by other solutions describe both waves existing for a certain period of time in an indefinite space, which has neither specific dimensions nor definite directions. The coordinates (x, y, x) shown in the time equation of Schrodinger are coordinates of an indefinite space and can not take completely definite, exact values.
De Broglie's inclusion of corpuscles into a plane monochromatic wave could not be the reason for the appearance in its double solution of the wave equation of a mathematical singularity with infinite value. The infinite value of one of the solutions appeared for another reason. A continuous Schrödinger wave and a plane monochromatic wave associated with a freely moving corpuscle were united by de Broglie into one single whole, after being called the de Broglie wave. It had to act and interact with three forces, two of which were internal forces of the vibrational system, and the third - an external force, at a certain time entering the system from the outside and at a certain time exiting the system from outside.
In other words, in the de Broglie wave there are constantly present quantitatively equal and qualitatively different two forces - variable and constant, wave and associated corpuscle. Within a certain time, under certain conditions, the third force intertwined in the interaction of the two forces belongs to the field of the external space. It is a continuous wave of continuous amplitude that has passed from the outer space to the internal space of the system. She enters the vibrational system by an uninvited guest, remaining to belong and serve the field of outer space.
The external third force included in the interaction of internal two forces, quantitatively equal to each of them and qualitatively opposite to them, puts them in a subordinate relation to themselves, adapts their interaction to change and transform the form of their quantity of movement that exists in the original unified form of the impulse. Since the amount of motion of the third force necessarily enters the quantum of the action of the harmonic oscillator of quantum mechanics, it also exits with the same necessity outside in the center of a very small region and finds itself in double solutions of the wave equation by a single solution with infinite value.
Replacing it with a large finite value, de Broglie unconsciously and unwittingly "buried" for many years his scientific discovery, which could make an invaluable contribution to the further development of the theory of quantum mechanics. His rediscovery turned out to be long and hard for me.
print version
Author: Mirgorodsky Alexander Illarionovich
Honored teacher of the school of the RSFSR
PS The material is protected.
Date of publication 17.11.2006гг
Comments
Commenting on, remember that the content and tone of your message can hurt the feelings of real people, show respect and tolerance to your interlocutors even if you do not share their opinion, your behavior in the conditions of freedom of expression and anonymity provided by the Internet, changes Not only virtual, but also the real world. All comments are hidden from the index, spam is controlled.