H.Petin. New Ideas in Phisics

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HENRY PETROVICH PETIN

DE BROGLIE WAWE AND SPECIAL THEORY OF RELIATIVITY

(Hypothesis)

INTRODUCTION

The quantum mechanics can explain so many experimental regularities correctly enough. Doubting its validity is unnecessary. Understanding is impossible why the world arranged as the quantum mechanics can explain it. The laws of the quantum mechanics appeared as a result from the generalization observable plenty of the experimental regularities without clear understanding of it origin.
Overall, the laws of the quantum mechanics should appear from viewing the processes occurring inside the elementary particles. In addition, these laws should appear from the processes of interaction of the elementary particles, viewing their interior device, with the exterior world. Modern science does not know until now even how the elementary particle - an electron is arranged. Consequently, the laws of the quantum mechanics should be taking on belief. Having some visual model would be desirable, and several regularities of the quantum mechanics would even gain.
The attempt made to create such a model in the given work. This model cannot give anything new for the quantum mechanics. However, it can be very important from the cognitive point of view, development of the field theory at level of an interior structure of the elementary particles and for the theory of the elementary particles.
The principle of the corpuscular-wave dualism is one basic principle of the quantum mechanics as known. These undular properties of the elementary particles describe the associated de Broglie wave. On the other hand, reveals that a given particle makes the simple harmonic oscillations in coordinate motionless system comparatively to a given particle. We find out easily it using the equations of the special theory of relativity. A particle should be motionless in this system, but a particle loses the undular properties and makes the simple harmonic oscillations in fact.
Recognizing in the opposite fact, that the elementary particles make those mechanical harmonic oscillations, so their motion in space explain a wavy trajectory. In view of the equations of the special theory of relativity, this trajectory expresses automatically the mathematical equation that is coinciding the equation de Broglie wave. Therefore, unknown until now some bridge occurs pairing the classical physics and the quantum mechanics.
A particle oscillates at a motion and their vibration amplitude or an initial phase unknown then a reason of an origin of the principle of the determinacy becomes clear completely. De Broglie wave in a motion describe every particle. The motion of the particles’ stream creates the conditions for the various diffraction and interference phenomena.
The interference bands at a dispersing of the particles on two slits arise from a superimposition of the two periodic structures from each slit with various angular phase modulations and displays the moire effect. Any interference between the separate particles does not occur.
Let us accept that a particle has not only simply an oscillation, but also a gyration of a partial charge on a circular trajectory. The estimate of a radius of this trajectory for an electron has given value greater in 137 times than a classical radius of an electron. In addition, the estimate velocity of a motion on a circle is coinciding with value velocity of light.
A motion of a charge on a circle gives in occurrence of a moment of magnet. Besides the rotating partial charge has some mass. This mechanical moment appears as a result. These exact values of the mechanical and the magnetic moments of an electron showed. For the explanation values of mechanical and magnet moments of the heavy, elementary particles are necessary to use the quark’s model of their structure.

THE WAVE IN A STREAM

In the elementary case of a motion of a not so prompt particle, its motion in the quantum mechanics can explain de Broglie wave

(1)
Let us tries describe its motion in coordinate system together propelling with a particle that is in a coordinate motionless system comparatively to a given particle. According to the special theory of relativity, changing time to is necessary.

(2)
A wave function gets a view in a result

(3)
If to accept for frequency known value, we will receive the equation

(4)
To substitute this value in the equation (1), then the wave function of some particle degenerates in the simple harmonic oscillations

(5)

Here we did not fall outside the limits of the usual quantum mechanics. The sense of the received equation is as difficult to understand like everything else in the quantum mechanics. Inverse transformation of a coordinate system is difficult to understand probably too. In a coordinate motionless system comparatively to a particle, a particle makes the oscillation express in the equation (5). Then after transformation of coordinate system, according to the equations of the special theory of relativity, the motion of a particle expresses the equation of the associated waves. That is according to the equations of the special theory of relativity. The received result brings an idea that the radiants of the associated wave are the eigentones of the elementary particles.
Let us depart a little from the usual quantum mechanics and we will return to the classical physics. Allow us to consider a case of the elementary particles making the natural mechanical harmonic oscillations. That the elementary particles make those oscillations not anybody can negate. The radiant of these oscillations lays in interior structure of the elementary particles. However, nobody knows how the elementary particle - an electron is even arranged.
The following equation (6) can present the own oscillations of a particle overall view. Naturally, a particle is in a coordinate motionless system comparatively to a particle.

(6)
where - quantity of bias from a center of the coordinates, - amplitude of bias. At a motion of this oscillating particle along axis x it will draw in space a wavy or a spiral trajectory depending on orientation of a vector concerning direction of motion. Shape of this trajectory can be found easily. For transition to coordinate system in which this particle moves in correspondence with the special theory of relativity for a propellent particle slowly, changing time with the equation is necessary.

(7)
As a result, a wavy trajectory of a propellented particle describes the following equation

(8)
Having accepted for frequencies value of the equation (4), we will receive the equation

(9)
where de Broglie wavelength is .
The equation for the associated wave with these odds turned out that the peak factor has the concrete physical sense of amplitude of the mechanical bias. We will receive it from the equation (9) for waves’ velocity.

(10)
Although a trajectory of a motion looks like a wave, it does not mean that a particle is smearing along a trajectory. It moves along this trajectory with velocity . The value of group velocity equal , determining velocity of a motion of an undular package, bound with a propellented particle testifies also to it. Phase of velocity easily determined from the equation (8), exceeded velocity of light and equal .
In 1924, de Broglie entered viewing his waves as a hypothesis. Our viewing gives quite understandable from the classical physics view explanation to an origin of the associated waves. A particle makes eigentones and simultaneously moves, drawing in space a wavy trajectory. An essence of the corpuscular-wave dualism for a separate particle is in it.
Therefore, the motion of one oscillating particle described the associated wave. Difference of the waves (9) and (10) from the associated de Broglie waves figuring in the quantum mechanics consists in interpretation of the peak multiplier. The peak factor is vector quantity in our understanding. Quantity of this vector is constant and depends on the interior device of an elementary particle. Now the science cannot tell us it is equal to what. Direction of this vector is unknown also. Therefore, currently is an indeterminacy of the principle of a particle within to sphere of a . radius. It explains an origin of the principle of indeterminacy known in the quantum mechanics. At the practical application of the received equation, treating the peak factors with probability of the positions is necessary, as it made in the quantum mechanics.
Giving the estimate of quantity of vibration amplitude is possible. We will take advantage of a relation of indeterminacy from the quantum mechanics for this purpose , =. We will receive in our case = . The result is . This value for an electron appears greater in 137 times than a classical radius of an electron. Value of amplitude velocity of an oscillatory motion appears equal to velocity of light. It can seem somehow strange. However, later it shows that is necessary to view not simply an oscillatory motion, but more complicated case of a rotary motion. Therefore, a particle rotates on a circle with stationary value of velocity. Velocity of a particle is equal to velocity of light. It is impossible in the Macro world, but at a level of an interior structure of particles, the usual laws of physics do not operate apparently. The calculated above equations describe a case of a motion of one particle along axis x. A particle is one of many particles creating a stream and velocity of a stream motion guide in arbitrary direction and determined direction of a vector of velocity . The vector as arbitrary determines direction of propagation of a wave. Then is possible to receive the equations describing the processes in a stream as

(11)

(12)

(13)

(14)
These equations are useful for viewing various interference or diffraction processes. Optic for viewing of the similar problems is using the coherent radiant. The coherence of a radiant of the particles is provided with that the particles initially leave from some solid body, where they interact one way or another between themselves and with a crystalline lattice. These particles, taking off from a radiant, are dependent, their initial phases and polarization completely or partially appear ranked. This stream of particles forms the associated de Broglie waves.

A PROBLEM OF TWO SLITS

Let us examine our interpretation of the solution of a known problem of the two slits. Figure 1 explains geometry for the chosen solution.

Figure 1

Distance between the slits is equal d. The particles impinge perpendicularly to the planes of the slits. Width of a slit is much lesser than de Broiglie wavelength. Therefore, we consider that after a slit a diversion of the particles from a tentative direction is equally probable for any direction. The screen that fixing hitting of the particles placed so much far from the slits, so r>>d, Therefore we consider that the angels . Give permission that the oscillations of all the particles occur perpendicularly to the direction of the propagation. It is extremely important to consider that the particles getting in the first and second slits come from the coherent radiant. The equitation (15) illustrates their oscillations.

(15)
A particle transits the first slit at the arbitrary moment of time with the phase of oscillations at the moment of time . Other particle transits the second slit at other moment of time and phase of its oscillations at this moment of time. Therefore, the oscillations of the particles passed the first slit described by the equitation.

(16)
Through the second slit –

(17)
By virtue of the coherence

(18)
However, from these equations follow importantly for the future viewing relation

(19)
If the given particle deviated after passage of a slit on an angle , as effect of the oscillations an angle describes the resulting diversion

(20)
The ambassador passages by the first particle of the first slit and an angle

(21)
The ambassador passages by the second particle of the second slit, in these expressions: and moments of time of a passage by the first and the second particles of the relevant slits, and an oscillation phase of the particles during the moment of a passage of the slits, - time of motion of the first particle from a slit up to the screen, time of motion of the second particle from a slit up to the screen. Seeing it from the given formulas is uneasy, that the presence of two slits gives in occurrence of additional angular phase modulation. Figure 2 evidently shows conveniently for visualization results of a qualitative calculation in an arbitrary gauge. The results of a calculation and - for the first and second slits are postponed on a horizontal axis through each degree. Limits of change of an angle are from zero up to 60 degrees. and Presence of phase modulation is hardly visible. If only one or another slit would be working, then from use of the fixing screen as a photo plate would be found out a uniform blackening on a corner. However, at geometrical superimposition of a pattern from the first and from the second slit, as effect of a presence of angular phase modulation, a presence of the lighter and darker strips is found out. .

Figure 2

The known moire effect shows. Interesting is that the angular standing of moire light and dark strips does not depend on distance to the screen. It does not depend on initial phases of the oscillations and times of a motion of the particles from the slits to the screen. It coincides with deductions of undular treatment of interference on two slits. The equitation of interference looks in our case as

(22)

Combining formally the last equations (20) and (21) we will receive the equations (23). ;

(23)

(19) (22) We will receive the same equation (22) as from an undular viewing it with a relation to the equation (19). However, using this equation is difficult to explain an origin of interference bands for the particles getting on the screen at the different moments of time.

ORBITAL MODEL OF A STRUCTURE OF AN ELECTRON

A hundred years ago classic said: “an electron is as inexhaustible like an atom.“ Since then, the science managed not so badly to explain an interaction of an electron with exterior for world for an electron. However until now is completely unclear what is an electron or what is its interior device. Whereas until then would be no answer to this simpler question, constructing the theory of the more composite elementary particles or the general field theory is impossible. The quantum mechanics and the theory of Dirac are viewing an electron as whole and describing the processes with a participation of an electron with probability of the positions. However, neither the quantum mechanics, nor the theory of Dirac can give an answer to a question what is going on inside an electron or other elementary particles. Various attempts to understand this question did not give a desirable result yet. In a development of the theory of an electron, some idea determined a direction of the searches is important first. Let us assume that at an electron a presence of a gyration not around of its own axis, but a gyration of a partial point charge on some circle. O ur hypothesis can give us the exact values of the mechanical and the magnetic moments. Agree to accept that an electron has some interior structure. The laws of the physics in limits of this structure are still unknown. Let us assume that those are the classical laws. Greatest composite question is a question of an origin of a partial charge of an electron. In the classical theory of the electromagnetic field, the charge is a radiant of a field, but its existence does not appear from this theory. Having more thorough field theory is necessary, possibly some general field theory that no one creates yet. Not anybody solved yet a problem about an origin of a charge. We will not solve it either. Presume to think that: - a mass of an electron, , - a mass of a point charge, - velocity of its motion on a circle, - - a radius of this circle, - quantity of a charge, - velocity of light. The mechanical moment of a motion of an electron

(24)
Its moment of magnet

(25)
The equations (24) and (25) cooperative if only

(26)

Only half of the mass of an electron bound to a point charge. The second half of the mass is bound to those processes that retain a point charge on a circular orbit. On our hypothesis, the rotaries’ charges will retain on a circular orbit by a gyrated electromagnetic field. The second half of the mass bound to this gyrated electromagnetic field. Other variants of an explanation of orbital gyration are possible also. Give permission to accept that the charge has bodily electromagnetic origin. Gyration of a charge is the distribution of some local electromagnetic field on a circular orbit. The distribution with velocity of light is natural to electromagnetic fields. Therefore, velocity of gyration of a charge can be equal to velocity of light. Objections can be concerning a motion of a point charge with velocity of light at an ending mass of a charge. Inside structure of an electron, the motion of a charge with velocity of light is already incorporated. For a motion of an electron as a whole, as a result some restrictions of the private theory of relativity apply. For a motion inside structure of an electron, as this motion of an electromagnetic field in a coordinate motionless system, as we view it, the special theory of relativity does not operate. Let us give a more understandable example. Allow us to imagine a rectangular or other shape, a vacuity with ideally reflecting walls. The electromagnetic waves can spread with velocity of light rereflecting from the walls of this vacuity. Some energy and a mass are applicable to the energy that is bound to a field of these waves. This is an ending mass. Any theory of relativity is unnecessary for evaluation of this mass. If vacuity can with a field force to move, then at evaluation of its mass is necessary to use the equations of the special theory of relativity. If to consider that the velocity of a motion of a charge on an orbit is equal to velocity of light, then for a radius of an orbit from aforesaid equations is gain

(27)

In relation to a classical radius of an electron

(28)
A radius of an orbit appears greater in 137 times A radius characterizes field of space where an electron is like "smeared," as the precise value of the standing of a point charge unknown. However, an underload radius of activity of the Coulomb forces of a point charge should determine a classical radius of an electron that testifies by the experimental results of a dispelling of the electrons. Angular velocity of gyration

(30)

П The projections of the parameters of a motion of a charge on a circular orbit on an axis of coordinate system have a time factor . If an electron, as whole, moves with velocity in a direction of an axis x, then in space the point charge of a spirally moving electron makes an undulation with circular polarization. This motion describes the associated de Broiglie wave about what said earlier with more details.
The model structure of the elementary particles examined in the given work is nevertheless a hypothesis. That hypothesis gives some visual representation how an elementary particle - an electron can be overall arranged. The author based on introduction in viewing the hypothesis of the quarks looked through the model structure of the proton and the neutron. He received the encouraging preliminary results. So that the offered model turns out to the rigorous theory is necessary first improving the field theory in the way that streams from it an existence of a partial electrical charge. Creation of that theory is obviously difficult.

REFERENCES:

1. Max Born. Atomic physics. London – Glasgow, 1963.
2.M. Lifshits2. L.D. Landau and E.. The theory of a field, (1967), “SCIENCE”, Moscow.
3. 3. Andre Angot. Complements de mathematiques. PARIS. 1957. .

ABOUT THE AUTHOR:

HENRY PETROVICH PETIN has a PhD in Physics and Mathematics Sciences.
He is working as a Senior lecturer of the Facility of the Radio-Physics of the SOUTHERN FEDERAL UNIVERSITY.
RUSSIA, 344015, Rostov - on-Don, 60/6 Eremenko St, apt. 247.
Telephone # (863) 225-4287
E-mail: sashapet@mail.ru
Copyright ©2007 Henry Petin
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