Special Relativity Simply Debunked in Five Steps!

Transcription

1 Speial Relatiity Simply Debunked in Fie Steps! Radwan M. Kassir Abstrat The speed of light postulate is losely examined from the perspetie of two inertial referene frames unprimed ( stationary ) and primed ( traeling ) in relatie motion, reealing that the speed of light postulate atually requires length ontration with respet to the unprimed referene frame, and length expansion with respet to the primed frame. It is shown that when symmetry is imposed on the inerse length transformation (i.e., to make it exhibit the same length ontration from the perspetie of the primed frame), the ommon length ontration fator beomes nothing but the Lorentz ontration fator. Howeer, this would neessarily result in, implying that the frames are being at rest with respet to eah other, and thus refuting the speial relatiity preditions! When the oordinate s transformation symmetry assumption is applied on the diret transformation resulting from the light speed postulate whih is shown inompatible with this assumption, the Lorentz transformation and its inerse are erroneously obtained; it is shown to be restrited to ertain oordinate relations, resulted in mathematial ontraditions, and thus demonstrated to be uniable. Keywords: Speial Relatiity; Speed of Light Postulate; Priniple of Relatiity; Coordinates Transformation Symmetry; Lorentz Transformation; Length Contration; Length Expansion. Introdution The Lorentz transformation, proiding interrelation between the oordinates of two inertial referene frames in relatie motion, forms the heart of the Speial Relatiity Theory. Einstein [] mainly deried the transformation on the basis of two priniples: - the priniple of relatiity, stating that the laws of physis are the same in all inertial referene frames, and - the speed of light priniple, postulating that the speed of light in auum is inariant with respet to all inertial frames of referene. Yet, another essential tool used in the Lorentz transformation deriation is that the diret and inerse transformations exhibit mutually symmetrial property; that is, the inerse transformation equation an be dedued from the diret one by swapping the oordinates and reersing the eloity sign. This is essentially the result of the isotropi property of spae, ombined with the first priniple of the speial relatiity. This assumption is rather intuitie. Howeer, in this paper, it is demonstrated that the speed of light priniple deiates from this law of transformation symmetry. That is, the speed of light priniple onsequent diret transformation from the perspetie of one frame is not symmetrial relatie to the orresponding inerse transformation from the perspetie of the other frame in relatie translational D.A.H. (S & P), Mehanial Dept., Verdun St., PO Box -759, Beirut 07 30, Lebanon Radwan M. Kassir 04

2 motion with respet to the first frame. It is shown that this fat has a fatal outome in regard to the oherene of the speial relatiity, in agreement with the findings of an earlier study. []. Steps to Fatal Consequene of the Light Speed Postulate and the Transformation Symmetry Let K( x, y, z, t) be a oordinate system attahed to a referene frame K, and let K( x, y, z, t ) be another oordinate system attahed to a referene frame K in relatie translational motion at a uniform eloity, with respet to K. A light ray is emitted when the two frames are oerlying at the instant of time t t 0, from a point at the oiniding frame origins, in the relatie motion diretion. Aording to the light speed priniple, after period of time t with respet to K, orresponding to t with respet to K, has elapsed, the light ray tip will hae traelled a distane x t with respet to K, x twith respet to K, where is the speed of light in empty spae. Step Sine, aording to the speial relatiity s seond postulate, the speed of light is the same with respet to both frames, the light ray trajetory drawn independently in K and K would appear as shown in Fig. in solid lines. Howeer, the light ray tip point L is atually pereied as point L (sine L and L ' represent the same eent in eah frame) with respet to K. Hene, the distane x must be ontrated with respet to K in order for point L to oinide with point L. Suppose the distane x is ontrated by a fator of (/ ), as shown in Fig. a with the gray dashed line, the following expression is inferred from Fig.a, relatie to K. x t. x t t t () where t is the distane traelled by K with respet to K during the trael time t. Step On the other hand, the light ray tip point L is atually pereied as point L, with respet to K (sine L and ' L represent the same eent in eah frame). Hene, the distane x must then be expanded with respet to K in order for point L to oinide with point L. Suppose the distane x is expanded by the fator of, as shown in Fig. b with the gray dashed line. Hene, the following expression is inferred from Fig.b, relatie to K. x Fig. Light ray tip point path from the perspetie of K (a), and K (b). Radwan M. Kassir 04

3 3 x t ; x x t. x t t t () Step 3 Equations () and () lead to. (3) Step 4 If we now impose that the length in K must by the law of symmetry be also ontrated with respet to K by the fator (/ ) (i.e., / ), then equation (3) redues to, (4) whih is the Lorentz ontration fator, in aordane with to the speial relatiity preditions. Step 5 Consequently, omparing equations () and (4), the symmetry requirement results in ; ; 0. ; (5) Or, the symmetry riteria / leads to from Eqs. () and (), or 0, implying the referene frame must be at rest with respet to eah other in order to satisfy the light speed priniple and the transformation symmetry. It follows that the speial relatiity is deemed to be refuted. Radwan M. Kassir 04

4 4 3. Coordinate Transformation and Verifiation of Findings Using Fig.a, the following transformation is dedued with respet to K. x x t, x ( x t). (6) Similarly, Fig.b leads to the following transformation with respet to K x x t, x ( xt ). (7) It should be noted that the spatial transformation equations (6) and (7) dedued from the speed of light inariane are in onformane with the Galilean transformation for the limit. Equations (6) and (7) lead to x x t (8) x x t. (9) Diiding equation (8) by equation (9) we obtain x t ; x t x ; ;, (0) erifying equation (3). Now, if equations (6) and (7) were to be symmetrial, in aordane with the speial relatiity assumption of transformation symmetry, then ; () Radwan M. Kassir 04

5 5 leading to (from equation (0)), () and equations (6) and (7) beome the spatial Lorentz transformation and its inerse. Howeer, this would neessarily lead to (from equations (), (), and ()) thus refuting the speial relatiity preditions. 4. The Speial Relatiity Blunder 0, Using the isotropi property of spae, and the Speial Relatiity first postulate stating that the laws of physis are the same in all inertial referene frames, the oordinate transformation with respet to the unprimed frame K, gien by equation (6) obtained from the onstany of the speed of light postulate would represent the inerse transformation (i.e., with respet to the primed frame K ), had we swapped in the equation the unprimed and the primed oordinates, and reerse the sign of the relatie eloity (as K is traeling in the opposite diretion with respet to K ). This will lead to the following transformation equation and its inerse. x ( x t); (3) x ( x t). (4) Obiously, equation (4) is inonsistent with the speed of light priniple, as it is not in line with equation (7) required by this priniple. Now, diiding both sides of equations (3) and (4) by, the speed of light, the following time transformation equations are obtained. t t, t t. (5) (6) Substituting equation (5) into equation (6) leads after simple simplifiation to. (7) Radwan M. Kassir 04

6 6 Replaing equation (6) in equation (3), and equation (5) in equation (4), returning, respetiely t x x t ; x and t x x t, x requiring x t and x t, to yield the transformation equations (4) and (3), respetiely. When this requirement (i.e., x t and x t) is applied to equations (5) and (6), the following equations are returned. x t t ; x t t. (8) (9) It follows that, equations (3), (4), (8), and (9), whih are nothing but the Lorentz transformation equations, are restrited to x t and x t, whih leads to arious ontraditions. In fat, when t 0, Lorentz transformation (8) leads to equation (8), yielding the ontradition t t /, or. t x /. But, as shown aboe, x t Similarly, Lorentz transformation (9) an lead to a similar ontradition for t 0 (i.e. ). Furthermore, substituting equation (8) into equation (9), returns in x x t t, (0) whih an be simplified to t x x. x () Sine, as shown earlier, equations (8) and (9) require x t; x t, then equation () an be written as Radwan M. Kassir 04

7 7 t x t. t () Now, for time, the transformed -oordinate with respet to would be, aording to equation (8). Consequently, for, equation () would redue to t t, yielding the ontradition,, or 0. It follows that the onersion of the time oordinate t 0 to t x /, for x 0, by Lorentz transformation equation (8), is proed to be inalid, sine it leads to a ontradition when used in equation (), resulting from the Lorentz transformation equations for t 0 (i.e. beyond the initial oerlaid-frames instant satisfying t 0 for t ' 0 ). A similar ontradition is obtained by substituting equation (9) into equation (8), and applying equation (9) for the onersion t 0 ; t x/. In addition, substituting equation (3) into equation (4), yields ; x x t t x t t ; x t. t t (3) Sine equations (3) and (4) along with equations (8) and (9) require (3) an be written as x t; xt, equation x x. x t (4) Now, for x 0, the transformed x -oordinate with respet to K would be x t, aording to equation (3). Consequently, for x 0, equation (4) would redue to x x,, or 0. Radwan M. Kassir 04

8 8 It follows that the onersion of the spae oordinate x 0 of K origin to x t, at time t 0, with respet to K by Lorentz transformation equation, is inalid, sine it leads to a ontradition when used in equation (4), resulting from Lorentz transformation equations, for x 0 (i.e. beyond the initial oerlaid-frames position satisfying x 0 for x 0). A similar ontradition would follow upon substituting equation (4) into equation (3), and applying equation (4) for the onersion x 0; x t. 5. Conlusions Considering two internal referene frames unprimed and primed in relatie translational motion, the diret oordinate onersion fator and its inerse were easily dedued from the onstany of the speed of light priniple, using simple diagrams for a light ray trael path from the perspetie of eah of the two frames. The diret length onersion fator was found to be in agreement with the orresponding speial relatiity predition. Howeer, the dedued inerse onersion fator was not symmetrial with respet to the diret length onersion that required that the spae in the primed frame be ontrated with respet to that of the unprimed frame, while the inerse length onersion fator showed the inerse relation (i.e., the length in the unprimed frame was expanded with respet to the primed frame). It followed that, to ahiee symmetry (i.e., length be mutually ontrated with respet to both frames and by the same fator), the onstany of the speed of light priniple required that the two frames be at rest with respet to eah other, thus inalidating the speial relatiity preditions. Moreoer, further analysis of the Lorentz transformation, following from the oordinate transformation symmetry assumption, showed fatal mathematial ontraditions leading to its refutation. Referenes. Einstein, A. "Zur elektrodynamik bewegter Körper," Annalen der Physik 3 (0), 89 9 (905).. Kassir, R.M. On Lorentz Transformation and Speial Relatiity: Critial Mathematial Analyses and Findings, Physis Essays 7 () (04). Radwan M. Kassir 04