Элементарные частицы как вихри полей.
The physical meaning of the de Broglie wavelength and the Heisenberg uncertainty relation.
The physical meaning of the de Broglie wavelength and the Heisenberg uncertainty relation.
The successes of quantum mechanics in many areas of atomic physics are obvious. It is difficult to find another theory that with such tremendous accuracy would be consistent with experimental data. But, despite the almost century-old existence of this theory the basic principles underlying it, as wave-particle duality, Heisenberg uncertainty relation essentially remained unappreciated and not substantiated. But these basic principles lies a lot of interesting information to shed light on some of the problems faced by modern fundamental physics. Consider these principles in more detail.
The wave properties of the elementary particles.
All calculations are performed
in quantum mechanics, made the assumption that
elementary particles possess this mysterious property, as the wave-particle
duality, are the point. That is not true, known to many physicists. Modern
ideas, in particular in string theory, based on the fact that at very high
energies there, having a length of string, and the fluctuations that determine
the diversity observed in nature of stable and unstable particles. In order to
understand the question, what is actually determined by the wave properties of
microscopic objects, this paper will also be postulated that elementary
particles are not point and have a more dense core, but unlike the physical
concepts of string theory the diameter of the core determined by the
Each particle having rest mass, in addition to the postulated core is also a potential field that decreases at infinity. If the particle is charged, it is electric and gravitational fields. If the particle is neutral, it is only the gravitational field.
Consider a particle diameter equal to the
passage of the same particle with the size of the
Due to its potential field, the particle will interact with the walls of the slit, and experience some acceleration. Let this acceleration will be small and the velocity of the particle after passing through the slit, as before can be considered equal. The acceleration of particles will cause a wave of indignation own field, which will be distributed with the speed of light. During the passage of a particle, this wave will extend the gap at a distance:
With regard to (1) and (2) we get:
Thus, the introduction of
quantum mechanics in a non-zero particle size allows you to automatically
obtain an expression for the de Broglie wavelength. The physical meaning of the
de Broglie wavelength becomes clear. This is not an aggregate function, as is
commonly believed, but a real wave, which arises in the potential field in the
accelerated motion of a particle having a core equal to the Compton wavelength.
The first conclusion from this can be done, that the
Second. Since the wave properties of particles are determined by the potential field, the wave properties of macroscopic body can have a strong potential field, for example, the planets and stars. Substituting the expression (2) and (3) instead of the postulated in this paper a particle diameter size or macroscopic body l get a more general expression for the de Broglie wavelength:
As you can see the de Broglie wavelength for the armatures differs from the expression (4) and can have a wavelength depending on their size is much larger than it had been assumed previously, focusing only on the formula (4). Disclosure of the physical meaning of the de Broglie wavelength provides a key for constructing a quantum theory of gravity. All you have to do this, it is a necessity given that Planck's constant, which is widely used in quantum mechanics, for the gravitational field can have a different meaning. To determine this value, we use the expression (1), which will be considered more fundamental than Planck's constant. From (1) follows:
As seen from (6), Planck's constant contains three parameters: the size of the core particle, mass and velocity of light. This allows you to write an expression for the Planck constant, which can be used for the armatures having the potential field, if the expression (6) instead of the diameter of the core particle and its mass to substitute the appropriate diameter and mass of macroscopic body:
That in turn allows us to formulate the Schrodinger equation for the motion of the planets in the central gravitational field of the Sun:
Where m - a mass of the planet;
M a mass of the Sun;
G the gravitational constant.
The procedure for the solution of equation (8) is no different from the procedure of solving the Schrodinger equation for the hydrogen atom. This avoids the cumbersome mathematical calculations, and immediately writes down the solutions of this equation:
Since the presence of the trajectories of the planets moving in orbit around the Sun is no doubt, the expression (9) is convenient to transform and present it through the radiuses of the quantum orbits of the planets. Consider that in classical physics, the energy of the planet in an orbit is given by the expression:
- the average radius of the orbit of the planet.
Levelling (9) and (10) shall get:
Quantum mechanics does not allow an unequivocal answer, in which the excited state may be related to the system. She just lets you know all the possible states and the probability of finding each of them. Equation (11) shows that for every planet there are an infinite number of discrete orbits, where it can be. Therefore, we can try to determine the principal quantum number of the planets by comparing calculations made by the formula (11) with the observed radii of the planets. The results of this comparison are presented in Table 1.
The Table 1.
As can be seen from Table 1, each planet can be attributed to what is the principal quantum number. And these numbers are quite small compared to those that would be obtained if the Schrodinger equation instead of the minimum quantum of action, defined by the formula (7) would be used Planck's constant, commonly used in quantum mechanics. The discrepancy between the calculated and observed values of the radii of the orbits of the planets are considerable. Perhaps this is because the derivation of equation (8) was not taken into account the mutual influence of the planets, leading to a change in their orbits and, consequently, the quantum numbers. But the main show - the orbits of the planets in the solar system are quantized, just as is the case in nuclear physics. This is supported by astronomical observations. The ancient astronomers noticed that the positions of the planets in the solar system is not chaotic, but is subject to certain laws, which is expressed by the Titius-Bode rule. These data clearly show that quantum effects occur in gravity.
Thus, it can be argued that a theory of quantum gravity is possible, but it should be noted that the elementary particles have a size greater than zero and the minimum quantum of action for the armatures is given by (7).
second consequence, which can make the assumption that elementary particles
have a core is equal to the
the interaction of two identical particles of the nucleus equal to the
k- the coefficient of elasticity of the string
The Schrodinger equation for stationary states of a harmonic oscillator can be written as:
The exact solution of equation (13) leads to the following expression for the discrete values
, где n = 0, 1, 2, … (14)
In the formula (14) unknown coefficient of elasticity of elementary particles is k.
It can be approximately calculated from the following considerations. The collision of the particles when they stop all the kinetic energy is converted into potential energy. Therefore, we can write the equation:
If the momentum is transferred inside the particle with the highest possible speed equal to the speed of light, from the beginning of the collision and before the divergence of the particles pass the time necessary in order to spread the momentum of a particle diameter of the whole is equal to the Compton wavelength:
During this time, the deviation from the equilibrium state of a particle due to deformation can be:
In view of (17), expression (15) can be written as:
Substituting (19) into (14) we obtain an expression for the possible values , suitable for practical calculations:
Tables (2, 3) show the values of for electron and proton, calculated on formula (20). In the tables is also specified energy, liberated at disintegration of the agitated conditions when turning
and full energies of the particles in agitated condition .
The Table 2.Oscillatory spectrum of the electron е (0,5110034 МэВ.)
The Table 3.Oscillatory spectrum of the proton P (938,2796 МэВ )
Let us consider the spectrum of excited states for the proton (Table 3). As can be seen, the energy of some of the transitions is comparable with the energies of the rest of the particles, which are observed in experiments. For example, the energy released in the transitions between adjacent levels of a harmonic oscillator (149.58 MeV) is comparable with the rest energy of the charged pions (139.57 MeV). The discrepancy is 7.2%. Therefore, we can assume that the decay of the excited states of the proton can form pi mesons. What is actually happening, according to the results of experiments in inelastic collisions of protons. A characteristic feature of the vibrational spectra is that the decay of the excited states is predominantly cascade, that is, energy is released between two adjacent levels. So excited to high energy protons, moving in the ground state, will form many identical particles, the rest energy is comparable with the energy between two adjacent levels. A similar phenomenon is observed in experiments with high-energy collisions of protons and pionization called hadron jets, since most of the secondary particles produced in collisions of protons, pi mesons are. And it can serve as a confirmation that this manifested vibrational spectra.This effect can be further tested in elastic collisions of electrons at the same time if you study the emission spectrum of electrons in collisions. In this case, the production of new particles occurs. But, as seen from the table (2) line emission spectrum of electrons close to the 0.081 MeV, has a good show through. More detailed information can be found in the work (www.mtokma.narod.ru / string.doc), which shows that excitation of the vibrational spectra of the particles may be formed all unstable particles observed in experiments, and the need for the existence of quarks, there is no . Thus, for the construction of all open in the nature of the involvement of unstable particles of quarks is not required. Therefore, the future of physics might come to believe that quarks do not exist, and this is just a successful mathematical model to explain the existing patterns at this level in the structure of hadrons.
Heisenberg uncertainty relation.
In 1927, Heisenberg, as a result of numerous thought experiments came to the conclusion that it is impossible to accurately measure both the position and momentum of the particle. This conclusion is given by:
Niels Bohr showed that a similar relation holds for the energy uncertainty and uncertainty since the interaction of the object with the measuring instrument:
In addition to these relations
in a microcosm, there are other additional values to each other. These
relations are confirmed by numerous experiments. But what they are due remains
unknown. Let's draw for the explanation of this phenomenon is made in
this paper, the assumption that elementary particles have a core equal to the
Substituting (23) into (1) and noting that - an energy rest particles, get:
As can be seen in this case the Heisenberg uncertainty
relation is exactly satisfied. Thus, it becomes clear that this ratio is due to
the presence in the microcosm of elementary particles of the nucleus equal to
- the Einstein tensor;
- the gravitational constant;
- energy-momentum tensor;
- indexes running values from 0 to3
Cosmological term in (25) is omitted because of its small value, and for analysis in this paper it is needed. A few months after the publication of a German scientist GR Schwarzschild  was the first solution of equations (25). This solution describes the gravitational field of a spherical mass in the surrounding area. If the radius of the sphere in which the concentrated mass, the gravitational radius coincides with the solution (25) has the form:
R the radius of the curvature space; G the gravitational constant; M the spherical mass.
Let us check what happens if the equation (25) instead of the gravitational constant G substitute any other value of the same dimension .
Successively repeating all the steps for solving equations (25) carried out by Schwarzschild at one and the same value of energy-momentum tensor can come to the same solution as (26).
In contrast to (26) in equation (27), the Schwarzschild radius will have a different meaning, and the curvature of space-time is also different. In essence, this is a completely different universe, having its four-dimensional space-time continuum, whose properties may differ significantly from the universe, which is determined by the gravitational field. Since on value was not assessed any restrictions, then it can take any importance in interval . From this it follows that, substituting in equation (25) each time a new value , we will be getting a new universe and these universes may be infinite. How this may be true? In formulating his theory, Einstein's curvature tensor of space-time is proportional to the energy-momentum tensor through the coupling constant G. And that is uniquely tied them to the gravitational field. But the energy and momentum have other physical fields existing in nature. This fact allows the use of equations of the theory of general relativity with the same success in this case. Consider how will be (27) if we make the coupling constant so large that it will comply with the forces that act on the level of elementary particles. Then the value will be:
- the constant Plank,
- the mass of any elementary particle.
Justification of (28) is given in (www.mtokma.narod.ru/kvant.doc).
Substituting (28) in (27) shall get:
With such a large value of the
coupling constant, which is given by (28), the Schwarzschild radius in the
Einstein equations is minimized to the size of the
As can be seen, the
From the above we can draw several conclusions:
1. The modern physical concepts of string theory that high-energy particles are variations of some strings or branes may be incorrect. At the same time obtained in the framework of this theory, the findings of the possible existence of an infinite number of universes (the so-called problem of the landscape) can be confirmed, although modern theorists make every effort to resolve this infinity.
2. Quarks do not exist. Standard model - this is only an intermediate step in understanding the world.
3. Wave properties possessed by all objects with the potential field, not just the elementary particles.
4. The minimum quantum of action is not a universal constant is suitable for all known interactions in nature.
6. The orbits of the planets in the solar system is also quantized, as well as the energy states of electrons in atoms. Mathematical formalism of quantum mechanics can be fully applied in gravity, provided that the Planck constant in this case will be determined by the expression (7), and not the value that is used in quantum mechanics today.
7. The equations of general relativity can be applied to all fields that exist in the universe, not just for the gravitational field. Einstein was very close to the creation of a unified field theory. In essence, he created it and because its equation suitable for describing all the interactions that exist in nature. Perhaps, but do not have time during the life of a formulated more precisely.
All of the above conclusions
follow only one assumption that elementary particles have a dense core with a
diameter equal to the
The cited literature:
A. Schwarzschild K. On the gravitational field of a point mass in Einstein's theory of / / Albert Einstein and the theory of gravity. 1979. //.pages 199-207.
* * *
Dear Nikolay Saynyuk,
* * *
John A. Macken wrote on Aug. 26, 2012 @ 23:51 GMT
Sergey G Fedosin wrote on Aug. 27, 2012 @ 19:09 GMT