Einstein s Three Mistakes in Speial Relativity Revealed Copyright Joseph A. Rybzyk Abstrat When the evidene supported priniples of eletromagneti propagation are properly applied, the derived theory is the author s Cause and Effet Theory of Light Propagation and not Einstein s Speial Theory of Relativity. In order to derive the Speial Theory of Relativity, Einstein had to apply the priniples of eletromagneti propagation in an inonsistent, selfonfliting, manner that violates the very priniples the theory is postulated on. The resulting theory is in disagreement with its own priniples and does not orretly predit the observed behavior of eletromagneti propagation as laimed. The three mistakes Einstein made in the derivation proess are presented in simple terms that even a layperson should be able to omprehend. It is inoneivable that any redible physiist an ontinue to support Einstein s theory in view of the findings presented in this paper. 1
Einstein s Three Mistakes in Speial Relativity Revealed Copyright 2014 Joseph A. Rybzyk 1. Introdution The Speial Theory of Relativity 1 is prediated on two postulates. 1. The laws of physis are the same in all inertial systems. 2. The speed of light in empty spae has the same value in all inertial systems regardless of the speed of the soure. Whereas the first postulate is reasonable and appears to be self-evident, the seond postulate violates the onventional laws of physis. For light to have the same speed in all inertial systems regardless of the speed of the soure it would have to vary its speed in the frame of the soure in a ompensatory manner. But, that is not the ase aording to the theory. Light simultaneously has a speed in the frame of the soure in whih ase time must vary between the frame of the soure and the frame of the observer in whih the soure is moving at speed v. It was in Einstein s attempt to onfine the propagation behavior of light to the seond postulate that his three distint mistakes were made. The first mistake involves the failure to identify the wavelength and transverse angle dependent distane effet that results from the priniple that light does not take on the speed of the soure. The seond mistake involves using the priniple that light does not take on the speed of the soure to define the lassial Doppler effet while onversely using the priniple that light does take on the speed of the soure to define the Lorentz redshift effet 2. The third mistake involves using the Lorentz redshift effet to orret for the missing redshift at the 90 degree angle of propagation that resulted from use of the priniple that light does not take on the speed of the soure in the first plae. Even then, however, with all the orretions in plae, the results differ from that of the Cause and Effet theory 3 that is based on the evidene supported priniple that light does take on the speed of the soure. These three mistakes will now be disussed in detail. 2. The Speial Relativity Inorret Doppler Effet at 90 Degrees Before proeeding with the intended subjet matter it is important to note that a main ause of onfusion involving the Speial Relativity Doppler effet is the many different forms that the Doppler formula is given in. It should be understood that all the different forms of the formulas are the same formula as that derived by ombining the Classial Doppler effet with the relativisti redshift effet given as the Lorentz redshift fator. Using that approah we an begin the presentation by attempting to derive the Classial Doppler effet omponent of the omplete formula from the relationships given in Figure 1. 2
o S λ e λ o θ r θ a e v soure + v - v Figure 1 Propagated Light Wave The sphere S in Figure 1 represents the leading edge of a light wave emitted at point e in the stationary frame of the observer that the speed v of the light soure is referened to. As the sphere expands away from stationary point e in all diretions at speed, the soure, moving to the right, reahes its urrent loation where the trailing edge of the wave along with the leading edge of the next wave will be emitted. Sine, aording to the priniples of speial relativity, light does not take on the speed of the soure, the emitted wave will be strethed in the diretion of reession to the left and ompressed in the diretion of approah to the right as illustrated. That is, the emitted wave will have a wavelength defined by the length of the line λo that extends from the urrent loation of the soure to the point of observation o on the surfae of the sphere. This line will inrease in length as the angle of reession θr dereases to 0 and onversely derease in length as the angle of approah θa dereases to 0. As should be obvious, however, ontrary to the priniples of Speial Relativity, it does not give a zero Doppler effet at the angles where θr and θa = 90 as illustrated. That is, for a zero Doppler effet at 90 the line λo representing the observed wavelength would have to be equal to the line λe representing the emitted wavelength that extends from the point of emission e to the same point of observation o shown in the illustration. Suh a relationship is illustrated in Figure 2 as disussed next. Referring now to Figure 2 it an be seen that a orret zero Doppler effet, where the length of λo equals the length of λe does not our when θr and θa = 90. In fat, unless v = 0, a zero Doppler effet an only our when θr is greater than 90 and θa is less than 90 as shown. Yet, in Speial Relativity it is laimed to take plae when the vertial line that extends upward from the enter of the sphere at point e is at 90 relative to the path of motion of the soure along the horizontal x axis. It is true, however, that from a suffiient distane above the points of emission (i.e. point e and the urrent loation of the soure) the differene between angle θa and the 90 angle at the middle of the base of the triangle shown in Figure 2 will be indistinguishable and thus, θa and therefore θr essentially equal 90. This distintion is not mentioned in speial relativity and therefore has never been properly addressed as will be done here. Consistent with the priniples of speial relativity, if light does not take on the speed of the soure, the wave, represented by sphere S, propagated at emission point e in Figure 2 will stay entered on that stationary point as it expands at speed in the stationary frame that the soure s speed v is referened to. The same will be true of the next wave that will propagate 3
from the urrent loation of the soure as the soure ontinues its motion to the right while emitting a ontinuous series of suh waves. S o λ e = λ o = L θ r θ a e v soure + v - v Figure 2 Zero Doppler Effet Referring now to Figure 3 we have an example of how the radial distane of the expanding light spheres affet the wavelength at the 90 angle to the point of emission of the reeived wave. o S 1 S 2 L θ r θ a e 1 e 2 v soure + v - v Figure 3 Distane Effet on Doppler In the example e1 is the point of emission of the wave of whih the leading edge is represented by sphere S1, and e2 is the point of emission of the next wave of whih the leading edge is represented by sphere S2. Although a ontinuous number of sueeding waves from a ontinuous number of sueeding points of emission follow as the soure moves to the right, it is only these two waves that are neessary for the analysis. In this ase the soure is moving at ½ the speed of light and therefore the wavelength is inreased to 1.5 wavelengths in the θr = 0 diretion of reession and dereased to 0.5 wavelengths in the θa = 0 diretion of approah. This shift of ½ wavelength is equivalent to the distane the soure moved during the period of emission and is represented by the distane between points e1 and e2. As the angle of 4
observation inreases toward the transverse angle of 90, however, there is hardly any differene in the distane between the two spheres as measured along the line from e1 to the observer or the line from e2 to the observer. If the soure were not moving at all, these spheres would be one wavelength apart in all diretions, inluding at 90. When the soure is moving, however, the distanes between them is less affeted as the angle inreases toward 90, and if the distane from points e1 and e2 to the point o of observation is suffiient, there will be no detetable differene from one wavelength at 90. In other words, unlike the ase involving Figure 1, there will be no Doppler effet at 90. A formula for determining the distane at whih a zero Doppler effet ours at 90 an be derive from the relationships shown in Figure 4. o xλ e h θ r θ a e 1 vλ e / e 2 Figure 4 90 Degree Distane Relationships In the illustration the vertial side of a Pythagorean triangle represents the distane from point of emission e1 to observation point o in terms of xλe emitted wavelengths where x an be any hosen quantity. The base of the triangle is the distane between e1 and e2 given by expression 1 that represents the distane the soure moved in terms of speed v and wavelength λe emitted during the emission period. I.e. if the soure was moving at the speed of light, the distane between e1 and e2 would be equal to one emitted wavelength λe. If the soure was not moving at all, the distane would be zero. With that understood, the hypotenuse of the triangle is found by solving 2 for h to obtain 3 in its simplified form. Using the value of h from the just derived formula we an ompare the length of h in Figure 4 to the length of vertial side xλe using an additional formula 5
4 where df is the propagation distane fator. That is, formulas (3) and (4) an now be used to determine at what distane from points e1 and e2 to observation point o will the hypotenuse distane h virtually equal the vertial distane xλe. In onduting the just desribed analysis using the longest wavelength of visible light where λe = 700 x 10^-9 meters, and soure speed v = it is found that distane h will equal distane xλe to within 17 deimal plaes when x = 10^7.9. That translates to a distane of h = 55.6 meters. At that distane and greater from the point of emission the lassial omponent of the speial relativity Doppler effet is given by os 5 where θ an represent either θr or θa as appropriate, and the sign for v is + for reession and for approah. As an be seen in referring to the just given formula, sine the osine of 90 = 0, the fration redues to 1 resulting in λo = λe for that angle of observation and thereby yielding a zero Doppler effet. This formula, however, is inonsistent with the relationships inherent in the illustration given in Figure 1 that are typially used to demonstrate the behavior beause, as already shown, the distane to the point of emission is also a fator. Only when the distane to the point of emission equals or exeeds 10^7.9 wavelengths of the emitted light is the speial relativity lassial omponent virtually orret for all angles of observation inluding the transverse angle of 90. At loser distanes a formula introdue in a previously work 4 by this author must be used. 3. The Confliting Corretion Fator for the 90 Degree Doppler Now that we have a orret understanding of the lassial omponent, equation (5), of the speial relativity Doppler formula, we have to orret it with the Lorentz redshift omponent. In so doing it beomes apparent that the Lorentz redshift is based on light taking on the speed of the soure ontrary to the priniples of the lassial omponent and the priniples of speial relativity in general. And to make matters even more onfusing, the Lorentz redshift will not only ause a Doppler effet at 90, but the exat same Doppler effet at that angle that results if light does take on the speed of the soure. To understand all of this, let us now go about the proess of developing the Lorentz redshift omponent of the final speial relativity Doppler effet formula. The Lorentz redshift fator is postulated on the priniple that an emitted point of light moving in the perpendiular diretion relative to the horizontal motion of the light soure will travel a longer diagonal path in the stationary frame that the soure s motion is referened to. This is demonstrated in Figure 5 where the moving frame of the light lok is at the left and the stationary frame that its motion is referened to is on the right. As is well known, the straight up and down path of a point of emitted light between the light soure and mirror in the moving frame of the soure and mirror light lok, is seen as a longer diagonal path from the point of emission e in the stationary frame, upward to the mirror and bak down to the soure s new position in the stationary frame that the soure is moving through at speed v. Sine, aording to the priniples of speial relativity, the light has the same speed in the moving frame of the 6
soure and the stationary frame that the soure is moving through, time is dilated and distane is ontrated in the moving frame relative to time and distane in the stationary frame. mirror mirror soure e v soure Moving Soure Frame Stationary Frame Figure 5 SR Light Clok And, as is also well known, the differene in time and distane between the two frames is given by the Lorentz fator whih is given as 1 1 6 in its reiproal gamma form. In regard to the speial relativity Doppler effet, this fator is referred to as the Lorentz redshift fator and an be redued to the simpler form of 7 for our use here. Before proeeding, however, we will first take a moment to emphasize the onfliting behavior of the speial relativity light lok illustrated in Figure 5. The propagation behavior of the light lok is learly and indisputably that of light taking on the speed of the soure. A point of light, emitted in the diretion perpendiular to the soure s path of travel, that goes straight up and down at speed relative to the soure while simultaneously traveling with the soure to the right at speed v has indisputably taken on the speed of the soure in the stationary frame. Yet, the mathematial fator that defines this behavior will now be used to orret a Doppler effet formula that is prediated on and defined by the opposite behavior that light does not take on the speed of the soure. And to make matters even more onfusing, this final step results in the very same Doppler effet at 90 that ours if light does take on the speed of the soure as will be shown. 4. The Complete Speial Relativity Doppler Effet To derive the omplete speial relativity Doppler effet formula we simply fator the lassial omponent given by the fration in equation (5) with the Lorentz redshift gamma fator (7) to obtain os 7 8
where the roles of both omponents are learly indiated. I.e. regardless of what value is obtained by the lassial omponent of equation (8) whether in the diretion of reession or approah, the resulting Doppler effet will be inreased in the diretion of a greater redshift by the Lorentz redshift fator. With that understood, the simplified version of the formula an be given as os 9 whih is the same as the more ompliated version often given in the literature as 1 os 1 10 where in both ases, the sign is + for reession and for approah. So there, we have it. Inonsistent treatment in light propagation behavior between the lassial Doppler omponent and the Lorentz redshift fator omponent, inonsistent treatment between the longitudinal and transverse Doppler effet*, and the use of the Lorentz redshift to ause a transverse Doppler effet at 90 that should have been there from the beginning. It is important to note here that the Cause and Effet Theory of Light Propagation based on the priniple that light does take on the speed of the soure, gives exatly the same Doppler effet as the Speial Theory of Relativity at 90 for any soure speed v without the need for any orretion fators as in the ase of Speial Relativity. That is, the Speial Relativity formulas (9) and (10) above, and the Cause and Effet formula (12) given in Setion 5 that follows, all redue to 11 90 for an angle of observation of 90. This strongly implies that Speial Relativity is nothing more than a pathwork theory designed to bring preoneived theoretial onepts into agreement with the evidene. (* The longitudinal lassial omponent an be diretly derived from the relationships given in Figure 1. The distane from the soure is not a fator as it is with regard to the angular diretions greater than 0.) 5. The Cause and Effet Doppler For referene purposes the author s Cause and Effet Doppler formula based on light taking on the speed of the soure is given as os os 12 where θ is 0 to 90 for approah and 90 to 180 for reession. 8
6. Conlusion What s it going to take for the mainstream sientifi authorities to admit that Einstein s Speial Theory of Relativity is wrong? Don t they realize that it is now they who appear uninformed and inept at applying the evidene supported priniples of physis and astrophysis to properly explain the observed behavior of the universe? Don t they realize that they are saying things and showing things on TV siene shows that are embarrassingly inorret? Yes, I will be the first to admit that it is not easy to arrive at the truth. We start out aepting what we are taught and then run into one brik wall after another struggling to determine if what we were taught is really true. Only after years of wasted time do we finally dare to question authority and seek out the real truth. And, when we do, no one wants to listen. When time permits, I will write another paper that shows how ertain aspets of Speial Relativity seem orret and onsistent with the evidene when in fat they aren t. I.e. some of the preditions of Speial Relativity are supported by the evidene but for different reasons than given in the theory. Till then, wake up world sientists. For the times they are a-hangin' REFERENCES 1 Albert Einstein, the Speial Theory of Relativity, originally published under the title, On the Eletrodynamis of Moving Bodies, Annalen der Physi, 17, (1905) 2 Hendrik A. Lorentz, Duth Physiist, disovered a new way to transform distane and time measurements between two moving observers so that Maxwell s equations would give the same results for both, (1899, 1904), Einstein further refined the transformations for use in his speial theory of relativity. 3 Joseph A. Rybzyk, Cause and Effet Theory of Light Propagation, (2011), Longitudinal Cause and Effet Formulas for Light Propagation, (2011), both papers available at www.mrelativity.net 4 Joseph A. Rybzyk, The Relativisti Transverse Doppler Effet at Distanes from One to Zero Wavelengths, (2006), available at www.mrelativity.net Einstein s Three Mistakes in Speial Relativity Revealed Copyright 2014 Joseph A. Rybzyk All rights reserved inluding the right of reprodution in whole or in part in any form without permission. Millennium Relativity 9