PACS numbers: g, Ds, Kc

Transcription

1 General Physics PCS nubers:..-g,..ds,.5.kc The Correlation of the Fine Structure Constant with the Redistribution of Intensities in Interference of the Circularly Polarized Copton s Wave (The Possible Solution of the -th Century Mystery []) Gevorg Shawarshovich Kirakosyan P.O. Box, Dubai, UE E- ail: gevorge@inbox.ru Key words: Fine Structure Constant, Eleentary Charge, Huygens Fresnel s principle, Copton s Wave, Eleentary Particle, Standard Model. bstract: It is shown that the Fine Structure Constant is correlated with the redistribution of intensities in the interference of circularly polarized Copton s wave, in classical representation. The theoretically obtained nuber coincides with easured value of α in the accuracy range of last easureent: -. INTRODUCTION s known, there are no theoretical or conceptual interpretations of the nature of Fine Structure Constant α /37 in conteporary physics. ccording to standard foralis, its value can be obtained exclusively by experiental easureents. We will just reind that any of genius physicists (such as P. Dirac and R. Feynan) had attepted to deterine α theoretically; which continues to be an open question. It is possible to judge the extree iportance and all the coplications related to this diensionless constant fro []. The continuous attepts of representing α by eans of artificial cobinations of other known constants (nuerological representations, etc.) are not considered as theoretical interpretations. We can refer to Feynan s known critical reark [] on this question. The unsuccessful efforts to deduce this iportant nuber fro quantu theories or fro other fundaental physical constants of a icrocos analytically, force us to look back to the wavy phenoena and classical representations. We have looked at the proble of Fine Structure Constant in conjunction with the global proble of revealing the physical essence of the eleentary particles, since it appears indivisible fro those, as their deep property. Mentioning the large circle of phenoena in icrocos where α participates as an iportant paraeter, we will bring the expressions below, related to description of Hydrogen s ato, which help us to realize the essence of this constant. Using known relations e=(ε αhc).5 and e =h/cλ e we can express the speed of an electron (v ) on the first Bohr s orbit, the orbit s radius (a ) and the Rydberg s constant (R) by the following siple expressions, containing α, c and Copton s wave length λ e of the electron only: v = αc, a = λ e / πα,53, R 5 = c / e 3,3 s Fro these expressions we can conclude that α is an independent universal nueric constant defining the dynaical, geoetrical and wavy properties of localized particles as well as photons. This conclusion allows us to accept the general principle of construction of all kinds of eleentary particles and to link α to the unique nature of all possible particles (as localized or non-localized quantu objects) although it sees to contradict to the Standard Model. Our interpretation of Fine Structure Constant corresponds to the wavy-field principle of the substance. Einstein, Schrodinger, Heisenberg and other physicists of past century were convinced supporters of such approach. The large group of experiental, theoretical and cause-logical arguents is pointing on the naed concept [3]. We can reark [] as a recent work pointing to this direction. α λ

2 The wave-particle duality principle allows us to consider localized particles and photons as wavy forations. In this work it is shown that in the interference of circularly polarized waves a constant relation appears between the intensities. This relation is closely correlated to the value of the Fine Structure Constant.. THE STTEMENT ND SOLUTION OF THE PROBLEM The purpose of the presented work is to prove the following relation:.5 I / I.85 e* = α /37 () Where: I is the intensity of peak. I is the total intensity of interfering waves. α /37 is the Fine Structure Constant, e * is the value of the eleentary charge in the syste of units: (c = ħ = ). To prove () we represent the eleentary particle as a standing wave appearing as a result of interference of Copton s circularly polarized waves. We have chosen described odel of particle analogical to the standing de Broglie s wave on the first Bohr s orbit, ipleenting the following replaceents: l orb = λ c (where λ c is the Copton s wave length) and v orb = c. We consider nuber n of interfering waves as uch greater than one, which corresponds to existing classical representations of quanta. We have used handbook equations and vectorial representation to describe the relations between aplitudes and intensities [5]. I = ( + )π, I ( + ) π () Where: is the aplitude of peak. is aplitude of peak (ain), =,, 3 n. Since the equation () is an approxiation, suitable for sall angular distribution, we use the Kirchhoff s function, considering aplitude s dependence fro direction, according to Huygens Fresnel s principle [5]: F ( ) =,5( + cos ) (3) The Kirchhoff s function satisfies conditions: F ( ) = at = (axiu of aplitude on direction forward ) and F ( ) = at = π (the aplitude becoes zero on direction backward ) (fig. ). Using (3) in equation () we obtain: + cos ( + ) π () ccording to entioned condition of interference the angular distance between first and ain peaks will be equal to a phase difference of the interfering waves. The angular distances between two consecutive peaks will be consequently decreasing as described further. The angular distribution of the peaks according to initial condition of interference is illustrated in the diagra (fig. ) where: φ is the average value of a phase shift between interfering waves, is the angular shift of peaks.

3 Considering that aplitudes of the secondary peaks differ fro each other by (±πn) per phase [5], we can write: I = I + I I n = n (5) Fro equations () and (5) follows: I n + cos I π = + (6) Considering that the secondary peaks coincide and differ by (π/±πn) fro the ain peak, we can represent the redistribution of intensities by the equation: Fro above we can write: I ( = I + I ) Using (7) fro (6) we obtain: ΣI / I = tan ϕ, / I = sin ϕ I, I / = cos ϕ (7) I n + cos tan ϕ π = + (8) To find the functional link between and φ we have used the vector diagra (fig. 3). 3

4 pplying equation () instead of (), sall changes of vectors of interfering waves rise as a function of. fteraths, each angular distance between two peaks also changes as illustrated in the above diagra. With the reduction of the vector according to () a respective reduction of the angle occurs. The change of the angle as a consequence of replaceent () by () is defined as: δ + cos ϕ ϕ [ ] ϕ ( + ) π ( + ) π ϕ ( cos ϕ) π ( ) + (9) Using the equation (9) and considering the relative change of angle φ the equation () becoes: + cos ϕ ( δ / ϕ ) ( + ) π () Siultaneously, as a consequence of reduction of angle between directions and -, the vector will slightly turn to the right, as a result of which it will becoe. For this reason the projection of on - increases, that leads to relative increase of their su by value: + (δ / φ). This factor leads to new sall change of the angle and brings new sall increase of the su of the vectors. We can continue this reasoning infinitely which brings to aendents in the for of McLaurin s flows, for the angle and for the vector accordingly: ( ϕ ) = ϕ δ [ + ( δ / ϕ) + ( δ / ϕ) n + + ( δ / ϕ) ] = ϕ δ /( δ / ϕ) [ ( δ / ϕ ) ] n / + ( δ / ϕ) + ( δ / ϕ) + + ( δ / ϕ) = / = L () Considering relations () we have replaced in (8) resulting to below equation: n = + cos[ ϕ δ /( δ / ϕ)] ( + ) ( δ / ϕ) Where: δ φ (-cos φ)/ (+) π (9) π tan ϕ ()

5 By ethod of insertion, using the nueric calculation, the value satisfying above equation has been found: ϕ (3) ccording to representation (7), using the result (3) we obtain: I / I = sin ϕ e This value in the achieved accuracy range of easureents coincides with the eleentary charge in relative units and corresponds to the value of Fine Structure Constant: / sin ϕ e * / a () Here are results of last easureents of / α: / a [6, 7] 3. PROPOSL OF N EXPERIMENTL MESURE OF α S N INDEPENDENT CONFIRMTION OF THE CONCEPT The proposed concept of Fine Structure Constant deands soe correction in the distribution of intensities. ccording to initial equations () we can obtain: n Σ / = tan I I ϕ, (5) π ( + ) = This value corresponds to φ.933 that differs fro (3). The task of experients should be to define the actual value of φ and, by the sae to check the accuracy of deduced results (3), (). For such easureents we propose to use Fraunhofer s Single Slit Diffraction. The total intensity of the bea of light and intensity of ain peak are necessary to establish by experient: using photoetric easureents with the sae (P) photoeter (or two calibrated ones) behind the slits S and S (fig. ). It is necessary to define the constant relation between its values. The exactness of results will be conditioned by exact coincidence of the sizes of the slit S with the displayed sizes of ain peak of interference. (The direct easureent of the total intensity of secondary peaks for a full angle of redistribution sees difficult fro technical viewpoint). * 5

6 By easured values of I and I we can define: I / I = cos φ For the cause (5) that will be: I / I (6) For the cause (3) that should be: I / I = cos(arcsin e * ).9963 (7) The relative difference of two nubers is about δ 8* - which sees possible to easure with ipleentation of conteporary collaboration technique. The experiental confiration of (7) will deonstrate the wavy origin of the eleentary charge, as well as the localized particle in general. Calculation: The purpose of calculation is to confir the equation () for the value of φ (3). We count up the right side of equation (): π tan( ) (a). We applied the following progra designations filling coluns in a siple contest of EXCEL sheet, according to the equation (): = =,, B = φ = C = δ = B*(-COS (B*))/((*+)*PI ()) D = δ /(- δ / φ) = C/(-C/(*B)) E=(+COS(*B-D))/((*+)*(-POWER (C/(*B), ))) F = POWER (E, ) 3. We counted up the su of colun F for the first 5 ebers only: = F (a). We defined the value of reaining eber R - of a flow (a) as follows: Noticing, that a descending flow (3a) is asyptotical for the sae in (), we defined its su for an interval ( ). For this purpose we preliinary opened it in the following for: ( / + ) = [ / /() ] = (.75 / ) (3a) The su of standard flow (a) is presented in textbooks: / = π / (a) In view of (a) fro (3a) we got: ( / + ) = (5a) We counted up the su of (5a) for the first ebers only: /( + ) = = (6a) By difference (5a) and (6a) we found the reaining eber of the flow (6a): R -.* -5. We count up the sus for ebers for both flows (a) and (5a) for an interval: = (9 - ): S * -7, S 9-.* -6. We defined their ratio: k = S/S.378. This nuber corresponds to the average ratio of ebers of two flows with identical nubers, in cause >>. The residual ebers of two flows will have the sae ratio. Further to this, we can define a residual eber of the first flow: 5 6 R ( ) k * R( ).378 *. * 3.75 * (7a) We define the su of the first flow by adding (7a) to (a): 6

7 = F This result does not differ fro (a) by - accuracy, which was required to prove. Conclusions and discussion:. It is revealed that there is a constant relation concerning exclusively to a wavy properties, which has not been considered yet. Its value correlates with the electroagnetic coupling constant α, which is currently conceptually inexplicable. The obtained coincidence could confir the beliefs of faous physicists of past century in the field-wavy nature of all possible eleentary particles, as different kinds of wave forations.. ccording to this identification, the universality of α and its participation in the extreely large group of phenoena in icrocos becoe obvious; as the constant exposing the wavy-dynaic character of substance (analogical to π). The entioned circustance indirectly confirs the suggested interpretation. 3. The absolute stability of α becoes clear, which eans that it is really a constant and it can t vary with the tie, as soe researchers are inclined to see.. This interpretation shows the deep roots of wavy-corpuscular duality principle and its applicability at the level of quantu electrodynaics. It points on the unique nature of aterial world and on the possibility of unifying quantu and the classical representations, although it sees uniaginable fro nowadays doinating foralistical viewpoints. This approach ay open an alternative way to study the icrocos, independent fro the currently developing Standard Model. By the sae, it ay provide physical eaning to foral-atheatical and phenoenological theories. cknowledgent: This paper has been welcoed and supported by H. Khorchazyan - PHD, Professor of Physics Departent, state Pedagogical University Yerevan. The calculations were verified by. Khachatryan - PHD, Professor of Physics Departent, state Engineering University Yerevan. The valuable advice of Professor M. uci [) is considered. uthor is deeply grateful to naed scientists. References:. Jaes G. Gilson, Fine Structure Constant, Richard P. Feynan, QED: The Strange Theory of Light and Matter, ISBN G. Kirakosyan, Natural representation the basis of a substance (Rus.), Yerevan 9, ISBN Massio uci, Guido Deatties, n pproach to Unifying Classical and Quantu Electrodynaics, // International Journal of Modern Physics B, Vol. 3, No (999), B. M. Yavorsky,.. Detlaf, Directory of the Physics (Rus.), Science 985, BBK.3 Я УДК D. Hanneke, S. Fogwell and G. Gabrielse,"New Measureent of the Electron Magnetic Moent and the Fine Structure Constant", Phys. Rev. Lett., 8 (8) and arxiv:8.3v [physics.ato-ph]. 7. G. Gabrielse, D. Hanneke, T. Kinoshita and others, New Deterination of the Fine Structure Constant fro the Electron g Value and QED - Phys. Rev. Letters 97, 38 (6). 7