On the Origin of the Special Relativity Anomalies

Transcription

1 On the Origin f the Speial Relatiity Anmalies Radwan M. Kassir February 2015 radwan.elkassir@dargrup.m ABSTRACT In this paper, the nlusie rigin f the Speial Relatiity (SR) mathematial nflits identified in the authr s prir related wrks will be presented and linked t these arius nflits. It is shwn that fr inertial referene frames in relatie mtin, the nstany f the speed f light pstulate inherently results in time transfrmatins independent f the spatial rdinates. The time f eents urring alng the lngitudinal rdinate axis is transfrmed with a different saling fatr than that f eents urring alng the transerse rdinate axes. The inrprated x rdinate (nsidering that the relatie mtin is in the X- diretin) in the Lrentz transfrmatin time equatin is the result f the SR assumptin fring the transfrmatin t take a linear frm as a funtin f the time and x rdinate. The SR deried Lrentz transfrmatin time equatin takes the assumed frm by the aid f the impsed nstany f the speed f light equatin, resling itself as x= t and x = t, t supply the x and x terms t the assumed time transfrmatin and its inerse, respetiely. The resulting time transfrmatin equatin (and its inerse) dependene n the x (and x ) rdinate is therefre fake, sine x ( x ) in the transfrmatin is nthing but t ( t ), making the transfrmatin time-dependent nly, yet ntraditing the time transfrmatin fr eents in the transerse Y -Z plane. ACTUAL TIME TRANSFORMATION RESULTING FROM THE SR SPEED OF LIGHT POSTULATE Cnsidering sme statinary and traeling inertial referene frames with rdinate systems Kxyzt (,,, ) and K ( x, y, z, t ), respetiely, in relatie mtin f elity, we will determine hw the relatie times f the fllwing eents will be related between tw bserers at the system rigins. A. E : Y A light wae frnt emitted frm a pint f psitie rdinate n the Y - axis f K at the instant f time t = t = 0, when the tw frame rdinate systems are iniding. B. E : X A light wae frnt emitted frm a pint f psitie rdinate n the X - axis f K at the instant f time t = t = 0, when the tw frame rdinate systems are iniding.

2 Using the SR nstany f the speed f light pstulate, the eents light wae frnts an be pltted n the frame rdinate systems as shwn in Figs. 1 and 2. At the instants f time t and t, the signal arries at K and K rigin, respetiely. The fllwing relatin an be dedued frm Fig. 1, where is the speed f light. Fig. 1 Eent E Y diagram frm the perspetie f K t = t + t ; t= t = γt (1) If the wae frnt was emitted in K frm a pint n the Y-axis, and lked frm K, then we wuld get the time pereied in K as t = γt. (2) It shuld be nted that the abe time transfrmatin is independent f the eent psitin n the Y- axis. Using a similar reasning, the same time transfrmatin wuld be btained fr eents urring n the Z- axis, independently f the eent spatial rdinates. Hene, the time transfrmatin fr eents urring in the YZ - plane is gien by Eqs. (1) and (2), independently f the spatial rdinates. On the ther hand, Fig. 2 leads t, frm the perspetie f K, t= t + t ; t= t 1 +. (3) If the wae frnt was emitted in K frm a pint n the X- axis, then we wuld get, frm the perspetie f K, Page 2 f 6

3 Fig. 2 Eent E X diagram frm the perspetie f K t= t + t; t = t 1. (4) Hweer, Eqs. (3) and (4) wuld lead t = 0, unless a time defrmatin fatr (say κ ) was assumed. Hene, Eq. (3) bemes t= κt 1 +, (5) whih is a time transfrmatin with respet t K. Based n Eq. (4) and the priniple f relatiity, the time transfrmatin with respet t K bemes t = κt 1. (6) Substituting Eq. (6) int Eq. (5), and sling the resulting equatin fr κ, we get κ= 1 = γ (7) Therefre, the SR nstany f the speed f light priniple as depited in Fig. 2, results in t= γt 1 +, (8) Page 3 f 6

4 t = γt 1, (9) Here t, the abe time transfrmatin fr eents urring n the X- axis is independent f the eent spatial rdinates. It shuld be nted the abe equatins are the same as the equatins btained in a different paper, 1,2 using Einstein s wn 1905 deriatin. Nw, as shwn abe, the same SR light speed priniple as depited in Fig. 1, leads t t= γ t, (10) t = γt. (11) It fllws that, sine the btained time transfrmatin fr eents n the X- axis, as well as the time transfrmatin fr eents n the ther system axes, are independent f the eent spatial rdinates, these transfrmatins ught t be idential. Therefre, we biusly get, frm the abe equatins, the innsisteny = 0. THE SR ANOMALY ORIGIN What happens in the SR is that the time transfrmatin is fred t be gien as a linear funtin f the prper time and the spatial X- rdinate. This is impliitly dne, in the transfrmatin deriatin press (e.g., Einstein s and deriatins), by splitting the time in Eqs. (8) and (9) int a time term and an X-rdinate-t-speed term, by indiretly using x = t and x= t, as fllws. t x t γ t γ = t + = + ; 2 t x t = γ t γ t =, 2 (12) (13) getting the Lrentz transfrmatin time equatins. The Lrentz transfrmatin fr the X- rdinates an be readily btained by multiplying the abe equatins by, and fring the SR desired, assumed linear frm by using x = t and x= t, getting x= γ ( x + t ) and x = γ( x t). In ther wrds, in the Lrentz transfrmatin deriatin predure in SR, the nstany f the speed f light equatin, suppsedly in the three dimensinal spae, x t x t = 2, ends up with its slutin in the X- diretin, x= t and x = t, being intrinsially emerged t inrprate the x and x terms int the time transfrmatin equatins with the SR impsed linear frm t = at+ bx (r t= at + bx ), sine the atual frm f the time transfrmatin, resulting frm the speed f light priniple, inrprates n spatial rdinates, as demnstrated abe. Hene, by replaing x and x by zer in Eqs. (12) and (13) fr eents urring in the YZ - plane, the time transfrmatin Eqs. (10) and (11) are btained. Hweer, Eqs. (12) and (13) are inalid fr x = 0 and x= 0, when t and t are different frm zer, sine they are based n Page 4 f 6

5 x = t and x= t, whih wuld result in t = t= 0. We an see frm Eqs. (12) and (13) that replaing x and x by zer eliminates the terms t / and t / frm the time transfrmatin Eqs. (8) and (9), althugh these terms are nt zer fr psitie t and t, errneusly trunating the latter equatins t the transfrmatin Eqs. (10) and (11) fr eents in the YZ - plane. This is the reasn why replaing x and x by zer in the Lrentz transfrmatin equatins, btained under x = t and x= t, leads t arius ntraditins, as demnstrated thrughut arius studies. 5-7 Anther nflit with the SR preditin t be pinted ut is that Eq. (9), the inerse f the time dilatin Eq. (8), shws a time ntratin. Furthermre, fr apprahing frames, Eq.(8) bemes a time ntratin, as reealed in earlier wrks: 8-11 t= γt 1, (14) Equatins (8) and (14) are in line with the relatiisti Dppler effet fr reeding and apprahing frames, respetiely, if the time t and t represented the pereied and emitted light wae perids, respetiely, sine in suh a ase, inerting Eqs. (8) and (14) leads the relatiisti frequeny shift equatins. Hweer, these equatins are in ntraditin with the SR time dilatin preditin, as demnstrated in ther related studies CONCLUSION It fllws that, the atual nsequene f the SR speed f light pstulate is the innsisteny = 0, r γ= 1, defying the iability f SR, and leading us bak t the lassial Galilean transfrmatin and Newtnian physis. 1 Kassir, R. M. Einstein's 1905 Deriatin f the Equatins f Speial Relatiity Leads t Its Refutatin. Vixra 14, (2014). 2 Kassir, R. M. Einstein's 1905 Deriatin f the Equatins f Speial Relatiity Leads t its Refutatin General Siene Jurnal, Jurnals/Essays/View/5838 (2014). 3 Einstein, A. Zur elektrdynamik bewegter Körper. Annalen der Physik 322, (1905). 4 Einstein, A. Einstein's mprehensie 1907 essay n relatiity, part I. English translatins in Am. Jur. Phys. 45 (1977), Jahrbuh der Radiaktiitat und Elektrnik 4 ( 1907). 5 Kassir, R. M. On Lrentz Transfrmatin and Speial Relatiity: Critial Mathematial Analyses and Findings. Physis Essays 27, 16 (2014). 6 Kassir, R. M. On Speial Relatiity: Rt ause f the prblems with Lrentz transfrmatin. Physis Essays 27, (2014). 7 Kassir, R. M. The Critial Errr in the Frmulatin f the Speial Relatiity. Internatinal Jurnal f Physis 2, , di: /ijp (2014). Page 5 f 6

6 8 Kassir, R. M. On the Test f Time Dilatin Using the Relatiisti Dppler Shift Equatin. Vixra 14, (2014). 9 Kassir, R. M. On the Test f Time Dilatin Using the Relatiisti Dppler Shift Equatin General Siene Jurnal, (2014). 10 Kassir, R. M. The Pereied Image f Time: Unraeling The Speial Relatiity Misneptins. Vixra 14, (2014). 11 Kassir, R. M. The Pereied Image f Time: Unraeling The Speial Relatiity Misneptins General Siene Jurnal, (2014). 12 Kassir, R. M. Speial Relatiity Refutatin Thrugh the Relatiisti Dppler Effet Frmula. Vixra 15, (2015). 13 Kassir, R. M. Speial Relatiity Refutatin thrugh the Relatiisti Dppler Effet Frmula General Siene Jurnal, (2015). Page 6 f 6