Classical Electromagnetic Doppler Effect Redefined. Copyright 2014 Joseph A. Rybczyk

Transcription

1 Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk Abstrat The lassial Doppler Effet formula for eletromagneti waves is redefined to agree with the fundamental sientifi priniples it is founded upon. The purpose of the derivation is to show that the Speial Relativity Doppler Effet formula was inorretly derived in the form of an inorret lassial omponent that has to be fatored by a relativisti omponent in a failed attempt to bring it into agreement with the sientifi interpretation of the evidene. On the finding that the orretly derived formula, as presented here, is in onflit with the priniples of Speial Relativity that it is based upon we are left to question the validity of the Speial Theory of Relativity itself.

2 Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk. Introdution The lassial Doppler Effet is one of two omponents that make up the Speial Relativity Doppler Effet. The other is the Lorentz fator that is fatored into the lassial omponent to arrive at the omplete Relativisti Doppler Effet formula. On lose examination of the derivation proess used to derive the lassial omponent it is apparent that the underlying priniples are not orretly applied. It appears that the lassial omponent was formulated to agree with the priniples that it will represent in the main theory and not the priniples that are fundamental to its underlying sientifi relationships. The same is true with regard to the Lorentz fator that is then applied to bring the ompleted formula into apparent agreement with the underlying priniples of Speial Relativity. The result is a Doppler Effet formula for eletromagneti waves that is invalid in both regards. It neither agrees with the fundamental Doppler Effet priniples it is supposedly postulated upon nor the relativisti priniples of the Speial Theory of Relativity. These findings add to a growing list of theoretial evidene in opposition to the Speial Theory of Relativity and in favor of the Cause and Effet Theory of Light Propagation 4.. The Inorret Speial Relativity Doppler Effet The Speial Relativity Doppler Effet is mathematially defined by a formula that onsists of two separate omponents as will be demonstrated. For the purposes of our investigation in suh regard we need only to analyze the wavelength version of the referened Doppler Effet formula. That version of the formula an be stated as os where λo is the observed wavelength in the stationary frame of the observer, λe is the emitted wavelength in the moving frame of the soure, v is the speed of the soure, θ is the angle of propagation, and is the onstant speed of light. The sign, where indiated, is + for reession and for approah. This formula an be restated as os where the fator in brakets to the left is the lassial omponent, and the fration to the right is the relativisti omponent. The relativisti omponent is otherwise known as the reiproal form

3 of Lorentz fator and is often represented by the Greek γ gamma fator. For the intended purpose of sientifi analysis the lassial omponent of the formula an be restated as os that beomes even more funtionally learer when given in the form v os 4 where it is apparent that the os θ ats diretly on the speed v of the soure. With that understood we an proeed with an examination of the sientifi rationale that the lassial omponent is based upon. Referring to Figure, we begin the proess by reviewing the fundamental basis of the Classial omponent. Aording to the priniples of Speial Relativity, light, as with all eletromagneti waves, does not take on the speed of the soure. S θ r θ a e v soure Figure Classial Component of SR Doppler Effet This priniple is illustrated in Figure in the form of a single wave of light, represent by propagation sphere S, expanding away at speed from point e in the stationary frame of the observer where it was emitted by the moving soure, shown at its urrent position to the right. That is, sine light does not take on the speed of the soure it propagates at speed in all diretions from the point where it was emitted in the stationary frame that the soure s speed v is referened to. And on that basis, as the leading edge of the wave travels in the diretion reession, toward point in the illustration, the wave is strethed by the soure s travel in the opposite diretion to its urrent position at the right where it emits the trailing edge of the wave. The reverse is true in regard to the wave traveling in the diretion of approah toward point. In that ase the wave is ompressed due to the fat that the soure s motion is in the same diretion. On the basis of what was just disussed it is apparent that the wavelength will be affeted at all angles of propagation from point e to the observer as represented by the arrow from point e to point. Aording to the priniples of Speial Relativity, the angle of propagation θr determines the amount of strething that ours in the diretion of reession and the angle of propagation θa determines the amount of ompression that ours in the diretion of approah. This an be seen in referene to formula (4) for the Classial Effet. In formula (4), where the

4 sign is + for reession and for approah, the angle θ represents either reession or approah from the longitudinal angle of 0 to the transverse angle of 90. As the angle of propagation varies from 0 to 90 the os θ varies from to 0 and is used to fator the effet that speed v will have on the wavelength. That is, its effet will vary from v at the longitudinal angles of reession and approah to 0 at the transverse angle of 90. Suh mathematial treatment is selfontraditory and inorret, however, as will be shown in the next Setion.. The Corret Classial Doppler Effet The orret Classial Doppler Effet for wavelengths is defined by the relationships illustrated in Figure. In referring to Figure, it is seen that an additional fator w is inluded that defines the distane between the soure and the point of observation. S w θ e v soure Figure Corret Classial Doppler Effet The signifiane of this new fator is in the fat that it relates the next point of emission e to propagation point and in so doing ompletes the lassial Doppler Effet on the transmitted wave. To understand this, we have to onsider the propagation behavior during the period in whih a single wave is emitted by the soure. By definition, it is during that period that the strething and ompression of the wave takes plae. In viewing Figure, assume that the angle θ is at 80. This would be the same as 0 in the diretion of reession using the Speial Relativity Classial Effet just overed. In this ase, however, the strething of the wavelength is represented by the wave fator w in Figure. And, as should be apparent, sine w spans the distane between the soure and point on the propagation sphere we have the ondition where the wavelength fator w = + v. This is the same effet that would be obtained by the Speial Relativity Classial Effet defined by formula (4). In a similar manner, if we assume an angle for θ of 0, the wavelength fator w would span the distane from the soure to point on the propagation sphere giving a wavelength fator of w = v. This result is the same that would be obtained using formula (4) for longitudinal approah. But that is the extent of the similarity between the two effets. To understand the full impliations of the orret Classial Doppler Effet, we need to take a moment and derive the formula from the relationships given in Figure as will be aomplished next. By applying the Law of Cosines to the relationships ontained in the propagation triangle of Figure onsisting of angle θ and sides, v, and w, we obtain os 5 4

5 that when solved for w gives os 6 where w is the wavelength fator. Putting the wavelength fator w in terms of and applying it to the emitted and observed wavelength we obtain 7 for the orret Classial Doppler Effet for wavelengths. Substituting the right side of equation (6) for w in equation (7) then gives os 8 for the omplete Classial Doppler Effet formula. 4. Comparison of the Two Classial Formulas In omparing the results of the just derived formula (8) to the previously derive formula (4) for the Classial Doppler Effet it is found that both formulas give the same results for the longitudinal angles of 0 in the diretion of reession and approah as stated earlier. (I.e., with the understanding that 0 reession for the Speial Relativity formula (4) is equivalent to 80 for the orret Classial Doppler Effet formula (8)). But as the angle varies in either diretion toward the transverse angle of 90, the results will diverge in diret proportion to the speed v of the soure. Note, for ease of omparison, the results of Speial Relativity formula (4) an be diretly ompared to the results of formula (8) at all angles of propagation from 0 to 80 by simply leaving the sign at in formula (4). The main point to be understood during the omparison proess is that the Classial Doppler Effet is not null at the transverse angle of 90 as given by the Speial Relativity Classial omponent, formula (4). That is, aording to the priniples of Speial Relativity there is no Classial Doppler Effet at the transverse angle of 90. There is only the Lorentz redshift effet at that angle due to time dilation in the moving frame of the soure. The time dilation is not affeted by the angle of propagation and fators the Classial result given in the omplete Speial Relativity Doppler Effet formula, () with the same Lorentz redshift effet at all angles. Consequently, sine there is no Classial Effet in the Speial Relativity formula at 90, there will only be a Lorentz redshift effet at that angle. As shown here, however, suh Classial behavior is in violation of the priniples that follow from proposition that light does not take on the speed of the soure. If light does not take on the speed of the soure, it will propagate at speed in all diretion from the point where it is emitted in the stationary frame that the soure s speed v is referened to. But sine the entire wave is atually spread aross two points of emission in the stationary frame, and yet the 90 angle applies only to the first of those two points, there will be a Classial Effet at that 90 angle. This is ontrary to the behavior represented by the Speial Relativity formula in the fat that the two different points of emission are reognized only at angles less than 90 in the 5

6 diretion of approah or reession. To be lear on this disrepany in the Speial Relativity treatment, it should be understood that there is a point of null Effet even in the orret Classial Effet formula. Suh effet, however, properly ours when the two base angles inside the propagation triangle of Figure are equal. I.e., when the internal angle at point e is equal to the internal angle at the urrent loation of the soure, there will be no Classial Doppler Effet at the point where both sides of the triangle onverge at the upper edge of the propagation sphere. This ondition is illustrated in Figure. In referring to Figure it an be seen that when the two base angles, θ, are equal, w = and the propagation triangle an be divided into two equal but opposite Pythagorean triangles. S w θ e θ v soure Figure Valid Conditions for Null Classial Effet Determining the angle at whih that ours is easily aomplished using the osine relationships of either of the two triangles shown. Seleting the triangle to the left we have os 9 that simplifies into os 0 giving for the angle θ at whih there is no Classial Doppler Effet. As previously stated, the null effet does not our when θ = 90 as given by the inorret Speial Relativity Classial Doppler omponent. 5. Results of Comparison In the appliation of unbiased sientifi examination of the behavior inherent in eletromagneti propagation where the waves do not take on the speed of the soure, it is 6

7 unhallengeable to onlude that the Classial Component of the Speial Relativity Doppler Effet formula is invalid. This is not to say that the orret Classial Effet as giving in this paper is a valid interpretation of the atual propagation behavior that takes plae in the universe. In fat, the author stated suh at the end of Setion and firmly believes that the orret formula for the eletromagneti Doppler Effet is that whih is given in his Cause and Effet Theory of Light Propagation. For referene purposes that formula will be reviewed in the next Setion. What the author is saying, is that the Speial Relativity Doppler Effet is a ontrived attempt to define a Doppler Effet formula that agrees with the findings of Maxwell s theory 5. The formula is an invention that does not follow from the strit appliation of sientifi priniples and is therefore invalid. This in turn brings the overall validity of the Speial Theory of Relativity into question sine the Doppler Effet plays a key role in its appliation. 6. The Cause and Effet Doppler Effet For referene purposes the Cause and Effet Doppler Effet formula is based on the priniple that eletromagneti waves atually do take on the speed of the soure. This behavior is illustrated in Figure 4 where it is readily seen that the Soure, and not emission point e, is at the enter of the propagation sphere. The importane of this differene annot be over emphasized. In Speial Relativity the propagation sphere expands at speed, but does not move in the stationary frame of the observer. In the Cause and Effet Theory the propagation sphere moves along with the soure in the stationary frame of the observer. S L θ e v soure Figure 4 Cause and Effet Doppler Effet Thus, the emitted waves propagate away from the soure in all diretions at speed as the soure travels to the right at speed v relative to the stationary frame of the observer. The end result is that the waves do take on the speed of the soure and have a variable speed L relative to emission point e that is stationary in the frame of the observer. With that understood the Cause and Effet Doppler Effet formula an be derived by applying the Law of Cosines to the propagation triangle of Figure 4. This then gives os that when solved for L gives os os 7

8 where L is the variable speed of light dependent on the angle of propagation θ. Putting L in terms of gives a wavelength fator that when applied to the emitted wavelength gives 4 for the mathematial relationships, that in turn gives os os 5 for the omplete Cause and Effet Doppler Effet formula for wavelengths. The frequeny version of the formula is os os 6 where fo is the observed frequeny in the stationary frame and fe is the emitted frequeny in the moving frame of the soure. 7. Conlusion In view of what was shown here there an be no doubt that the Speial Relativity Doppler Effet formula was devised to agree with the priniples of Maxwell s theory and not the behavior assoiated with the onstany of light speed in empty spae. It appears that the development of the Speial Theory of Relativity follows a disturbing pattern of inventing reasons to explain away any evidene that is ontrary to the intended purpose of maintaining ontinuity with previous theories. This pratie most notably began with the invention of distane ontration to ounter the unexpeted null result of the Mihelson and Morley experiment of 887 and ontinues to this day. It is used to explain away a seemingly unending list of unexpeted findings involving the nature of the universe. Dark Matter, Dark Energy, Dark Flow are but a few examples. In the author s opinion it is time to get siene bak on trak in applying evidene supported priniples in an unbiased sientifi manner. Anyone who reads the author s earlier works will see that the author himself fell vitim to this pratie of maintaining agreement with previous theories. It was only after years of researh that inevitably, and ontinually, led to self-ontraditory priniples that he deided to question the validity of what was given by the sientifi establishment. In so doing, he has found no onvining evidene to support the priniple that light does not take on the speed of the soure. And therefore he is onvined that the Speial Theory of Relativity is invalid and his Cause and Effet Theory of Light Propagation is orret. Appendix An appendix is inluded at the end of the doument ontaining graphs of the Doppler Effets overed. 8

9 REFERENCES Christian Doppler, Austrian physiist proposed the Doppler effet for sound in 84. Hippolyte Fizeau disovered independently the same phenomenon on eletromagneti waves in 848 but the effet retains the name of Doppler. Sine this version of the effet does not ontain the relativisti redshift effet assoiated with Einstein s speial theory of relativity, it is normally referred to as the lassial Doppler Effet as opposed to the relativisti Doppler Effet that does ontain the relativisti redshift effet. Albert Einstein, the Speial Theory of Relativity, originally published under the title, On the Eletrodynamis of Moving Bodies, Annalen der Physik, 7, (905) 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, (899, 904), Einstein further refined the transformations for use in his speial theory of relativity. 4 Joseph A. Rybzyk, Cause and Effet Theory of Light Propagation, (0); Longitudinal Cause and Effet Formulas for Light Propagation, (0), Both on file at the US Library of Congress and available from the Millennium Relativity website at 5 James Clerk Maxwell, A Dynamial Theory of the Eletromagneti Field, Philosophial Transations of the Royal Soiety of London 55, (865). (This artile aompanied a Deember 8, 864 presentation by Maxwell to the Royal Soiety.) Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk All rights reserved inluding the right of reprodution in whole or in part in any form without permission. 9

10 Appendix Doppler Effet Graphs 0