Rethinking the Principles of Relativity. Copyright 2010 Joseph A. Rybczyk

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1 Rethinking the Principles of Relativity Copyright 2010 Joseph A. Rybczyk Abstract An analysis of all of the principles involved in light propagation lead to the discovery that the relativistic principle that light does not take on the speed of the source is invalid. A subordinate finding then places a new limit on the maximum speed at which an object in recession can be observed. These findings taken together with another recent finding involving stellar aberration lead to an entirely new understanding of relativistic theory. 1

2 Rethinking the Principles of Relativity Copyright 2010 Joseph A. Rybczyk 1. Introduction Examination of scientific principles so fundamental as to be self evident leads directly to a discovery that invalidates the principle that light does not take on the speed of the source. It is found instead that the evidence supported principle that light propagates from the stationary point where it was emitted by a moving source is causally dependent upon the stationary point of detection intercepting the light that propagates directly from the source. This discovery then leads to a second discovery that places a new limit on the maximum speed at which a receding object can be observed. This is the second recent finding 1 by this investigator that has major implications with regard to the proper application and interpretation of relativistic principles. 2. Definition of an Inertial Reference Frame Since the first step in the examination process is to ensure a proper understanding of an inertial frame based upon a proper interpretation of Newton s three laws of mechanics, the laws are given below directly from a physics textbook: Newton s first law law of inertia: There are frames of reference, identified as inertial frames, in which any body will have zero acceleration if there is no net force exerted on it by other objects. Newton s second law: (Where F is force, m is mass and a is acceleration) Newton s third law: If one object exerts a force on a second, then the second exerts a force on the first; these forces have equal magnitudes and opposite directions. Strict interpretation of Newton s three laws of mechanics shows clearly that there is only one fundamental inertial state an object can be in and that is a state of complete rest. Such an inertial state is one in which the object is not undergoing any form of acceleration. This includes linear acceleration, rotational acceleration and orbital acceleration since all involve a change in direction in one form or another that in turn involves a change in velocity in that regard. 3. The Principle of Relative Motion If one object is moving at a uniform rate of speed relative to the another object and neither object is under any kind of acceleration then either object can be declared to be in a state of rest relative to which the motion of the other object is referenced. It is of ultimate importance here to understand that the standard textbook treatment of Newton s laws of mechanics can be misleading since, as in the case here, the same textbook that gave the definitions of the previous section can additionally give the following alternate definition for Newton s first law where it is also applied to objects in motion: Newton s first law: If an object has zero acceleration (that is, the object remains at rest or moves with constant speed along a straight path), the vector sum of the forces on the object is zero. 2

3 The problem with this second interpretation of Newton s first law is that is implies that uniform motion is another state that an object can be in. According to the principle of relative motion, however, uniform motion is not a state that an object is in but rather a relative condition between objects in different rest states. Thus, two objects that are not under acceleration of any kind but are in motion relative to each other are in identical states where either can be defined as a state of rest relative to which the speed of the other object s motion is referenced. Whereas the direction of motion for each object is the opposite of the direction of the other, the speed of each object relative to the other is identical as are their rest states. The important thing to understand here is that neither rest state has privilege over the other and though identical in that regard are different by the very fact that the objects are moving relative to each other. If the rest states are fundamentally the same then both objects can be used as the point of origin for the inertial reference frame in which they are at rest. This also means that both objects can be used as the point of reference in the moving inertial frame whose motion is referenced to the other inertial frame that serves as the stationary frame to which the motion is referenced. Now let us discuss how the laws of physics apply to such inertial frames. 4. The Laws of Physics are the same in all Inertial Frames The first postulate of Einstein s special theory of relativity 2 can be stated as: Einstein s special theory of relativity, postulate 1: When properly formulated, the laws of physics have the same form in all inertial systems. Although this postulate can be expanded to include all systems including those under various forms of acceleration, for our purposes here we will limit our examination to only its relevance to inertial systems. Base on our understanding of the laws of physics and the prevailing evidence, there is not only no reason to believe that the laws of physics would differ from one inertial frame to another, but it would seem to defy common sense if they did. For that would not only get us back to the question as to why one inertial frame should have precedence over any other, it would provide the reason for it; i.e. because the laws of physics are different in each frame. But there is no evidence to support such a claim and subsequently there is no reason to assume that the laws of physics should differ from one frame to the next. While on the subject, however, we can take a second look at an inertial frame and raise the question as to what it is in its purest form. If we say it is a frame of reference without an object at rest within it, we have a condition that might be valid but seems to lack meaning. For we have nothing more than a condition of empty space with nothing to compare or reference anything to. For example, how can some object have a speed v relative to empty space? And what purpose would it serve to define things in such a manner? No, it makes far more sense to refer to a reference frame as being attached to an object that physically exists, meaning an object that has detectable properties of one kind or another. And that gets us back to the description we used in the previous section as discussed next. On the assumption that an inertial reference frame has as its basis, a physical object that is at rest within it, we not only have something physical to reference the motion of something else that has physical existence, but we have something to relate the laws of physics to. For example, assume that a particle, object, or body that gives off light constitutes the basis of the inertial system under discussion. Now it is quite valid to raise the question as to why this object 3

4 should exhibit different behavior in emitting light than any other object? And, of course, there are many different reasons as to why it could. For example, the color of the emitted light depends on the chemical properties of the object that emits the light. So, the real question becomes why the light from one object should be different in any way from light emitted by an identical object in a different frame of reference. Now we will have a far more difficult time coming up with an answer that makes sense. While it might be true that the light received from a moving source will be Doppler shifted relative to light emitted by the stationary source in the frame of the stationary source, it would follow that the same Doppler shift will be detected for the light from the stationary source when received in the frame of the moving source. In other words, if both sources are identical in every way, then each would receive the light from the opposite source with the same speed and Doppler shift. And that gets us to the heart of the matter as will be explained next. From what was just discussed it seems perfectly reasonable that the physical behavior of two identical objects under identical conditions will be the same as determined in their own inertial frames of reference and also as determined in the inertial frame of the other object assuming they are in motion relative to each other. If there is any difference between the two objects of any kind, it would then be reasonable to assume that any changes in the detected behavior will be the same if the circumstances are reversed. This then is what is meant by the laws of physics being the same in all inertial systems. Now let us proceed to the next step in our analysis. 5. The Michelson and Morley Interferometer Experiment The Michelson and Morley interferometer experiment 3 involved splitting a beam of light from a common source into two streams that were made to travel back and forth along two different paths of the same length that were set at a 90 degree angle to each other. The returning light was recombined and checked for a shift in the fringe pattern that would result if light traveled thorough a medium called aether. Taking into consideration the Earth s orbit around the Sun of about 60 km/sec in addition to the Sun s unknown speed through space the experiment was conducted throughout the year to ensure that the effects of one motion was not cancelled by the effects of the other. As is well known, although the experiment was conducted many times by different investigators over the years, the expected shift was never detected. This proved conclusively that the speed of light is not affected in the frame of the light source by the speed of the source through space. This finding is consistent with the relativistic principle that no experiment conducted in a moving inertial frame of reference will give evidence of that motion through space. Contrary to many of the claims made regarding different interpretations of the null results of the experiments, the two things the experiments proved is that light travels in all directions at the same speed relative to the source and as stated previously, no experiment conducted inside an inertial system will give evidence of that system s motion through space. This means that light from a symmetrical source in an inertial state propagates at the same speed in all directions relative to that source. More specifically, a wave of light given off by such a source will propagate in all directions away from the source in the form of a perfect sphere centered on the source whose radius at any instant is the same in all directions as determined in the frame of that source. Moreover, to prove that such a perfect sphere will have an unsymmetrical appearance in the stationary frame to which its source s motion is referenced requires the identification of the causal agent for such change in symmetry. Since no such causal agent has ever been discovered 4

5 it is perfectly reasonable to treat such a sphere of light propagating from a point source that is in uniform motion relative to a stationary frame of reference as a symmetrical sphere of light as observed in that stationary fame also. In conclusion such a sphere is symmetrical in appearance and effect whether viewed from within the inertial frame of its source or from without in the stationary frame that its motion is referenced to. 6. The Transverse Doppler Effect for Light If a sphere of light propagating in all directions at speed c from an inertial light source of the kind just defined in the previous section takes on the speed v of the source relative to the inertial frame that the source s motion is referenced to then an observer directly in the path of approach will detect the light at a speed of c + v while another observer directly in the path of recession will detect the light at a speed of c v. Although it may seem so, this behavior is not actually an alternative interpretation of the standard longitudinal Doppler shift that is detected from such sources when all of the different factors are taken into consideration. Referring to Figure 1, in the case of the standard explanation for the longitudinal Doppler shift the light does not take on the speed of the source. Thus the expanding propagation sphere stays centered on the stationary point in the stationary frame where it was emitted by the source as the source passed that point along its path of travel. Subsequently an observer in the path of approach detects an increase in frequency (a blueshift) because the wavelength of the received wave while emitted in his direction at speed c is compressed by the speed v of the source coming at him, i.e. (c v). Conversely an observer in the path of recession detects a decrease in frequency (a redshift) because the wavelength of the received wave while emitted in his direction at speed c is stretched by speed v of the source moving away from him, i.e. (c + v). Transverse 90 - stationary observer measures c (no effect on wavelength) Light Propagation Sphere Recession - stationary observer measures c + v effect on wavelength v source Approach - stationary observer measures c v effect on wavelength Figure 1 Light Speed Not Affected by Source Speed Referring next to Figure 2, notice that the Doppler behavior associated with a moving source is exactly opposite the behavior associated with the premise that light does not take on the speed of the source. In the previous case of light received from the stationary point where the light was emitted, we have c v for approach and c + v for recession. In the case of light received directly from the source we have c + v for approach and c v for recession. 5

6 Transverse 90 - stationary observer measures speed Light Propagation Sphere Recession - stationary observer measures c v light speed v source Approach - stationary observer measures c + v light speed Figure 2 Light Speed Affected by Source Speed Given that light does take on the speed of the source when detected in the stationary frame to which the source s motion is referenced if we wanted to compare the emission speed of light in the moving frame to the emission speed of the light in the stationary frame we have to use light that is neutrally effected by the motion of the source. Such light is that which travels in a perpendicular direction to the source s path of motion in the frame of the source. Obviously if the light received in the stationary frame is affected in the manner of c + v for an approaching source and in the manner of c v for a receding source then light received at the transverse angle of 90 degrees to the source s path of motion will be unaffected by the speed of the source. This finding is of utmost importance in determining the relativistic behavior of one inertial frame relative to another to which its motion is referenced. We will see why in the next section. 7. The Millennium Relativity Light Clock If a point of light moving in the perpendicular direction to the direction of motion of the source is unaffected in the stationary frame by the speed of the source then the distance it travels in the source frame can be directly compared to the distance it travels in the stationary frame to determine the relationship between time in the two frames since by definition the speed of that particular point of light is the same in both frames. This principle forms the basis of the millennium relativity 4 light clock illustrated in Figure 3 which is an abbreviated form of the special relativity light clock. apparent propagation sphere centered on stationary frame point of emission ct ct real propagation sphere centered on moving source emission point vt source Figure 3 Millennium Relativity Abbreviated Light Clock By using only the first half of the special relativity light clock the distances ct and ct traveled by the same point of light in stationary inertial frame and moving inertial frame respectively can be 6

7 used along with the distance vt traveled by the source in the stationary frame in place of the clock ticking principle of Einstein s theory to relate the time in one frame relative to the time in the other frame. Of great importance involving this particular principle of the behavior of light is to understand that it involves light that transitions between two different inertial frames. Unlike the light used in the Michelson and Morley interferometer experiments discussed previously, this light is detected in one frame from a source that emitted it in another frame that is moving relative to the receiver frame. And since the received light at the stationary frame point of detection (where ct and ct intersect) traveled a greater distance in the stationary frame in comparison to the distance it simultaneously traveled in the moving frame of the source even though its speed was unaffected by the source s motion, time must vary between frames. That is, if the distance traveled by light is the product of its speed and time of travel and the distances are different even though the speeds are the same then it must be the time that varied between frames. Moreover, in consideration that the three distances (the distance traveled by the light source, and the distances traveled by the perpendicular point of light in both the source s frame and the stationary frame) form a Pythagorean triangle, the variance in time between frames is easily determined from the Pythagorean Theorem. 8. The Millennium Relativity Dual Light Propagation Spheres Given the principle that light propagates from a point source at the same speed c in all directions it then follows that any such radial path from the source represents the radius of the resultant sphere of light that in turn represents the same wave front in all directions. This principle can be applied directly to the perpendicular distance traveled by the point of light in the source frame without further justification. In the case of the diagonal (hypotenuse) distance the same point of light traveled in the stationary frame there are other considerations that must be taken into account. Based on the special relativity principle that light does not take on the speed of the source we are justified in claiming that this distance represents the radius of the light propagation sphere centered on the point in the stationary frame from which the light appears to propagate from as shown in Figure 3. This, however, is a faulty conclusion because the specified radial (hypotenuse) distance is correct only for the point of light that traveled the perpendicular distance in the frame of the source. Points of light elsewhere on the surface of the expanding light sphere centered on the source will describe a different radial distance in the stationary frame resulting therefore in a smaller or larger sphere centered on the same stationary frame point as shown in Figure 4. Thus, no single stationary frame sphere can represent all of the corresponding points of light on the surface of the moving frame sphere and their corresponding paths in the stationary frame. And more importantly, only stationary observers contacted by the sphere of light centered on the source will see the light coming from the stationary point in the stationary frame to begin with. Stationary observers within any of the described stationary frame spheres but outside of the moving frame sphere will have no reason to believe that any light is propagating at all. This, however, does not preclude the use of an appropriately defined equivalent propagation sphere in the stationary frame as will be discussed next. 7

8 apparent propagation spheres centered on stationary frame point of emission emission point ct ct vt source real propagation sphere centered on moving source Figure 4 Multiple Stationary Frame Spheres Based on the principle that the hypotenuse path that corresponds to the perpendicular path traveled by a single point of light in the source s frame represents the distance traveled by light at the same speed c in the stationary frame, the hypotenuse path represents the radius of a corresponding sphere of light emitted by a second source at the stationary point where the hypotenuse intersects the path of travel of the source in the stationary frame as shown in Figure 3. Since time is the same throughout an inertial frame, such a sphere represents time in the stationary frame in all directions relative to the corresponding time that the sphere centered on the moving source represents in all directions in the source frame. In short, the dual Millennium Relativity light spheres related time and distance in the stationary frame to the corresponding time and distance in the moving frame. The full significance of this new definition is beyond the scope of the present paper and will require future investigation. Of greatest importance at this time is the discovery that the special relativity principle that light does not take on the speed of the source is invalid. 9. The Source Speed Dependent Limitation Principle Given the apparent fact that with regard to the universe most objects are receding directly away from the stationary frame point of observation the relativistic effects on light involving longitudinal recession are of great interest. In such regard the question becomes what if any are the changes in view regarding light from that direction if only light from the moving source is actually observed. The answer to that question is nothing short of stunning. Referring to Figure 5 the relationship of source travel distance equals light propagation distance is given. The significance of this relationship is based on the resultant fact that the light emitted by the source will never propagate beyond the stationary frame point of emission in the direction of longitudinal recession. Subsequently a source traveling at such speed or greater relative to the stationary frame will never be observed in the longitudinal direction of recession. Still referring to Figure 5 we can use the Pythagorean relation to determine source speed v in terms of light speed c. Using that relationship we obtain 1 8

9 where v is the speed of the source in the stationary frame and c is the speed of light in both the moving frame of the source and the stationary frame of the observer and where t is the dilated time in the frame of the source that corresponds to stationary frame time T. apparent propagation sphere centered on stationary frame point of emission to observer emission point ct ct vt source real propagation sphere centered on moving source Then, given the proposition that Figure 5 Source Distance Equals Propagation Distance 2 we obtain by way of substitution of the left side of this equation with the term ct of equation (1) 3 that when solved for v gives and finally for the formula that gives the light speed limit in terms of c for longitudinal recession. This final result, of course, reduces to 9

10 which is absolutely stunning. If applied directly to the universe this implies that the edge of the observable universe is receding away at only 0.707c and not light speed c as currently believed. There is, however, another consideration as will be discussed next. 10. The Local Nature of Relativistic Principles Recent research 5 by this investigator showed that the supposed evidence supported proposition that light does not take on the speed of the light source is valid only at local distances that do not exceed approximately light years from the source. This finding is based on the discovery of a new principle called distance perspective that in turn is based on the newly introduced principle of inverse stellar aberration 6. These findings in themselves change our entire understanding of the universe for they limit all related relativistic principles to such local distances. Now, however, based on this latest research the very proposition that light does not take on the speed of the source is shown to be invalid. More specifically, according to this latest research light will be seen to propagate from the stationary frame point of emission only if light propagating directly from the source is intercepted by the observer. This places the proposition that light does not take on the speed of the source into the cause and effect area of scientific consideration. Perhaps not as clear is the question as to which of the two different findings, the newly discovered source speed dependent limitation principle or the previously discovered local distance limitation principle apply to objects at the edge of the observable universe. Resolution of that question is beyond the scope of this present work and is therefore deferred to a future investigative effort. 11. Longitudinal Light Speed Propagation Before concluding this present work it seems appropriate to include a brief discussion of the overall behavior of light propagating in the longitudinal direction of recession and approach. Referring now to Figure 6 we will conduct a brief analysis in that regard. S 2 S 1 ct ct light from receding source ct A B vt C source ct light from approaching source Figure 6 Longitudinal Light Speed Recession and Approach 10

11 In referring to Figure 6 assume that a point light source moving from left to right at a uniform speed v relative to a stationary frame of reference that contains the stationary points A, B, and C emits a single wave of light at point A while continuing its travel to its present location at point C. The smaller sphere of light S 1 represents the size of the single wave of light emitted at point A at the instant the source reached point B in its travel to the right. The larger sphere of light S 2 represents the size of that same single wave of light at the instant the source reaches its present location at point C. Since the wave of light shown is the wave in the moving frame of the source it is shown centered on the point occupied by the source for the two instances being discussed. In other words, it expands from size 0 at point A where it was emitted at the instant the source was at point A and then reaches size S 1 when the source reached point B and later reaches size S 2 when the source reaches point C. Thus, the wave stays centered on the source as the source travels to the right at speed v and will continue to expand in size as the source continues its travel to the right beyond point C. Now let us derive the basic formulas that will give the stationary frame speed of the light propagating from the source at speed c in the source frame as it will be observed in the stationary frame in the direction of recession and also in the direction of approach. As for sphere S 1, its radius increased to a distance of ct as the source traveled distance vt from point A to point B. Since the sphere is moving to the right along with the source, the distance its surface travels in the direction of recession to the left is given by 10 where D r is the light propagation distance in the direction of recession, ct is the distance traveled by the light relative to the source in source terms and vt is the distance the source traveled in the stationary frame in stationary frame terms. In a similar manner, since the surface of the light sphere S 1 is propagating to the right relative to the source while the source is also moving to the right, the distance its surface travels in the direction of approach to the right is given by 11 where D a is the light propagation distance in the direction of approach and the other terms have same the definitions previously given. Source frame time t is then given by 12 where T is the corresponding time in the stationary frame during which the distances were traveled. In the millennium relativity version of the Lorentz transformation factor to the right of time interval T in the just given equation (12), c is the constant speed of light, and v is the speed of the source in the stationary frame. Given the standard formula for equating speed to distance and time, we have 13 11

12 where L is the stationary frame variable speed of light that takes on the speed of the source, D is the stationary frame propagation distance, and T is the stationary frame time interval during which the propagation takes place. By substituting the right side of equation (10) in place of D in equation (13) we obtain 14 where the r subscript is added to light propagation speed L r to show it is the speed of light in the direction of recession. Substituting the right side of equation (12) in place of time interval t in equation (14) and simplifying, gives where again, L r is the light propagation speed in the direction of recession. By placing the right side of equation (16) over c we obtain the alternate equation 17 for expressing the light speed L rc in terms of c which, interestingly can be expressed as 18 where the Lorentz factor is obvious. Doing similar for equation (11) involving the direction of approach gives 19 where L a is the light propagation speed in the direction of approach. Then by placing the right side of equation (19) over c we obtain the alternate equation 20 for expressing the light speed L ac in terms of c which, like before can be expressed as 21 12

13 showing the Lorentz factor. 11. Conclusion While it is true that the principles involved in light propagation can be used to show that light appears to propagate from the point in the stationary frame where it was emitted by the moving source, it is not true that this proves that light does not take on the speed of the source. If light truly did not take on the speed of the source it would propagate in all directions from the stationary frame point where it was emitted. This means that all observers in the path of the expanding propagation sphere centered on the stationary frame point of emission would detect the light. According to the findings presented here, however, only stationary frame observers in the path of the light propagation sphere centered on the source are able to detect the propagated light at all and even then, only when the speed of the source does not exceed 0.707c relative to an observer who is in the direction of recession. There were two important discoveries made in the preparation of this paper. The first involves the contradictory nature of the special relativity light clock. The whole point of using only the light propagating in the perpendicular direction to the direction of source motion is to relate the distance traveled in the moving frame by a point of light not affected by the motion of the source to the distance it simultaneously travels in the stationary frame. Since the speed of light for the chosen point was unaffected by the source speed, the difference in distances is theoretically caused by a difference in time between the two frames. This then is an admission that light speed is affected by the speed of the source which is a contradiction of a main premise of relativistic theory. The second important discovery involves the cause and effect nature relating the light in the moving frame to the light propagating from the stationary point in the stationary frame. It appears that the latter cannot be detected independent of the former. On the basis that these findings are found to be valid, our entire understanding of relativistic theory and everything it involves, including the nature of the observed expansion of the universe is affected. Given the dramatic differences imposed by the new findings, they may contain the answer to what is really behind the dark matter, dark energy, and most recently, the dark flow mysteries involving the universe that have yet to be resolved. This investigator makes no pretence that the findings presented in this paper are not strange, yet they follow from principles that seem beyond reproach. REFERENCES 1 Joseph A. Rybczyk, Stellar Aberration, Relative Motion, and the Lorentz Factor, (2010), Section 5. The Principle of Distance Perspective was the first finding, 2 Albert Einstein, On the Electrodynamics of Moving Bodies, now known as the Special Theory of Relativity, Annalen der Physik, (1905) 3 Albert Michelson and Edward Morley, conducted the interferometer experiments in 1887, the null results of the experiments is considered proof that light does not require a medium for propagation. 4 Joseph A. Rybczyk, Millennium Theory of Relativity, (2001), 5 Joseph A. Rybczyk, Stellar Aberration, Relative Motion, and the Lorentz Factor, (2010), 6 Joseph A. Rybczyk, The Complete Nature of Stellar Aberration, (2010), 13

14 Rethinking the Principles of Relativity Copyright 2010 Joseph A. Rybczyk All rights reserved including the right of reproduction in whole or in part in any form without permission. Note: If this document was accessed directly during a search, you can visit the Millennium Relativity web site by clicking on the Home link below: Home 14