Advanced Electromagnetism and Vacuum Physics (World - download pdf or read online

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By Patrick Cornille

ISBN-10: 9812383670

ISBN-13: 9789812383679

This publication is aimed toward a wide viewers: scientists, engineers, professors and scholars clever adequate to maintain a severe stance each time faced with the chilling dogmas of latest physics. Readers will discover a tantalizing volume of fabric calculated to nurture their options and arouse their suspicion, to a point at the least, at the so-called validity of contemporary such a lot celebrated actual theories.

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Extra info for Advanced Electromagnetism and Vacuum Physics (World Scientific Series in Contemporary Chemical Physics, 21)

Sample text

In the general case, it is not possible to find an explicit solution to this integral equation enabling to define the trajectory of a point particle observed in the plan r,t. We we shall see later on, especially in the relativistic ADVANCED ELECTROMAGNETISM AND VACUUM PHYSICS 24 case, how it is possible to solve explicitly this integral equation. It results from the preceding integral relation that the function U has for expression: U[r(t'), A = U[r 0 + [ U[r(i"), t"]dt", t'} Jo (96) The term integral in the equation given above explains the non-local character of velocity at time t' which results from the addition of velocity between instants 0 and t1.

Third transformation The transformation relating coordinates ro,to and r,t defined in the same reference frame is, now, the Lorentz transformation: r = [l + ^ (7 - 1)UU] • r 0 + e 7 Ut 0 (132) t = j{to + 4 U • r 0 ) (133) where the velocity U is constant. In this case, we obtain: V 0 r = I + -Jo ( 7 - 1)UU V 0 ct = - 7 U 1 dr e dt - ^ - = -7U ~r = 7 c dto c dto This results in the Lagrangian space-time derivatives having for expression: (134) (135) «-» 1 e 9$ Vo$o = [ I + ^ 2 ( 7 - l ) U U ] - V $ + ?

In order to do that, we just have to write the following relations: k 0 = 7(ki - -J o>i) = 7(k 2 + -J w2) (38) wo = 7(^1 - U - k i ) = 7 ( w 2 + U - k 2 ) (39) Those equalities enable us to verify the phase invariance for waves propagating in opposite directions: u0t0 - k 0 • ro = u\t - ki • r (40) uj0to + k 0 • r 0 = uiit + k 2 • r (41) provided that the vectors ki,k2,U are all directed in the same direction. If a sum of two progressive waves defines a standing wave, reciprocally, the sum of two standing waves can describe a progressive wave as illustrated by the following example: cos(w£ — k • r) = cos(wt) cos(k • r) + sin(cjt) sin(k • r) (42) As a result, when a summation over standing waves is performed in a Fourier integral, one may expect to obtain, after integration, progressive wave-like solutions.

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Advanced Electromagnetism and Vacuum Physics (World Scientific Series in Contemporary Chemical Physics, 21) by Patrick Cornille

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