The True Nature of the Special Relativity Light Clock. Copyright 2012 Joseph A. Rybczyk

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1 The True Nature of the Special Relativity Light Clock Copyright 2012 Joseph A. Rybczyk Abstract It is generally believed that the light clock typically associated with special relativity correlates the relationship of light behavior in the frame of the moving source to its behavior in the stationary frame that the source s speed is referenced to. It is further believed that the specified behavior is consistent with and directly supports the principles of special relativity as defined by the first and second postulates of that theory. Here it will be shown that the light clock actually exhibits a previously unidentified anomalous behavior that in fact violates one of the defining principles of the theory it supposedly represents. 1

2 The True Nature of the Special Relativity Light Clock Copyright 2012 Joseph A. Rybczyk 1. Introduction The author was fully aware that the light clock associated with special relativity 1 does not follow directly from the principles of Einstein s theory at the time the author developed the principles of the millennium theory of relativity 2. In fact it is for that reason that the principles of the millennium theory differ from those of special relativity. It is not until now, however, that the full ramifications of this finding have been worked out. It will now be shown that the light clock not only violates the principles of special relativity but does not actually represent the behavior of light from a moving source. In fact, the light clock is based solely on the behavior of light from a stationary source as related to the moving frame and not the light from a moving source as related to the stationary frame. This behavior is consistent with its relationship to the Michelson and Morley interferometer experiment 3 and not the principles of special relativity. The significance of this discovery and another involving an anomalous mathematical based consideration regarding the Lorentz transformation factor 4 are such as to completely change our understanding of the behavior of light propagation. 2. The Special Relativity Light Clock In preparation for the analysis that will show the discrepancy in the special relativity light clock we will first review the principles that the light clock is founded upon as given in Figure 1. mirror y mirror light pulse clock D light path as seen in clock D stationary frame A v B x (a) (b) Figure 1 The Special Relativity Light Cock Note: To avoid confusion it should be understood that the millennium relativity mathematical convention is used in this work. In that regard T is used for stationary frame time and t is used for moving frame time. With that in mind, view (a) of Figure 1 shows clock D when it is at rest in the stationary frame that clocks A and B of view (b) are at rest in. Clock D has a light source at the center of the lower mirror that emits a pulse of light along the y axis in the direction of the upper mirror at tick 1. When the pulse reaches the top mirror it is reflected downward along the y axis and gives off tick 2 when it reaches the lower mirror. In view (b) clock D moves from left to right along the x axis at speed v relative to the stationary frame clocks A and B. At the beginning of stationary frame time interval T, (i.e., T = 0) clock D gives off a pulse of light in the direction of the upper mirror at tick 1 as it passes over clock A. The pulse reaches the upper mirror when clock D has traveled half the distance to clock B. The pulse is then reflected downward and gives off tick 2 when it reaches the lower mirror at the instant clock D passes over clock B. Let time interval t be the time interval between the ticks as read on clock D, and 2

3 let time interval T be the difference in time between the reading of clock B at the second tick and the reading of clock A at the first tick. In special relativity time interval t is referred to as proper time because it is the time interval between ticks as read on the clock doing the ticking. Referring now to Figure 2 an observer in the frame of clock D can determine the speed of light, which we label c, by dividing t into distance 2y traveled by the light pulse in clock D. y Figure 2 Path of light in stationary frame and moving frame That is, the observer in the moving frame of clock D calculates vt 2 1 for the speed of light in that frame. To determine the speed of light by measurements of the same light pulse in the stationary frame of clocks A and B the stationary frame observer divides the distance traveled by the pulse as seen in his frame by time T. In this case the path for the light is along the two adjoined hypotenuses of the two adjacent back-to-back Pythagorean triangles shown in the illustration. Since the distance along the base of a single triangle is given by vt/2 and the distance the light travels along one hypotenuse is therefore ct/2 we can define either of the two identical triangles by the equation and solve it for speed c as determined in the stationary frame of clocks A and B. This then gives which in turn gives for the speed of light c in the stationary frame. In viewing Figure 2 it can be seen that speed c in the moving frame as given by equation (1) can equal speed c as given by equation (4) only if T t because as is evident in Figure 2 the 3

4 distance traveled by the pulse is greater as seen in the stationary frame than as seen in the moving frame. To get an equation that relates T to t we first solve equation (1) for y and obtain 2 5 the right side of which can then be substituted in place of y in equation (2) to obtain that can then be solved for T in terms of t. This gives and finally 13 for the millennium relativity formula for relating stationary frame time T to moving frame time t. This formula is simply another form of the more familiar special relativity formula that can be obtained in a few more mathematical steps for relating T to t. 3. The Inconsistency of the Special Relativity Light Clock Now that we understand the underlying nature of the special relativity light clock it is easily shown that the true principles on which it operates actually violate the principles of the special theory of relativity that it is supposed to demonstrate. To make the analysis easier to 4

5 understand we will limit it to the behavior associated with a single Pythagorean triangle as used in the millennium theory of relativity. As just demonstrated in the previous analysis, the behavior is the same with respect to both triangles of the light clock. Referring now to Figure 3 assume that the light from the moving source that travels distance ct in the frame of the source simultaneously travels hypotenuse distance ct in the stationary frame that the distance vt traveled by the source is referenced to. ct ct e vt source Figure 3 Abbreviated Light Clock (Moving Source) In that case solving the mathematical relationships given in the illustration for stationary frame time interval T during which the moving source traveled distance vt gives 15 that leads to the previously derived equation (8) and therefore also to equations (13) and (14) that followed for the relationship of stationary frame time T to moving frame time t. If we then take equations (13) and (14) and solve for t in terms of T we obtain 16 and 1 17 for the alternative versions of the millennium relativity and special relativity formulas respectively. The important thing about these formulas is that they produce a value of 0 for moving frame time t regardless of the value of stationary frame time T for the case where speed v of the source reaches the speed of light c. In referring to Figure 3, or any of the previous illustrations for that matter, this results in the vertical side ct of the Pythagorean triangles to reduce to 0. But that means the distance y between the two mirrors of the special relativity light clock has reduced to 0 which in turn violates the special relativity principle of distance contraction only in the direction of motion, i.e., along the x axis. This finding was originally reported in the Millennium Theory of Relativity paper and has since been a defining principle that distinguishes the millennium theory from the special theory of relativity. But now we will look deeper into the nature of this difference between the two theories. 5

6 4. The Conflicting Principles of the Light Clock Upon further investigation it is found that there are three main problems with the special relativity light clock. First of all, the light clock is based on the behavior of light from a stationary source, and not the light from a moving source as claimed in the theory. Second of all, the behavior inherent in the light clock results directly from one of the behaviors inherent in the relationships of a Pythagorean triangle and thus represents a self-fulfilling proposition in that regard. And third of all, this then results in distance contraction in all directions in the moving frame of the source, and not just in the direction of motion, which is a violation of the principles of special relativity as previously stated. Let us now explore these claims in detail. In Figure 4 the light source is stationary at the left corner of the base of the triangle. Assume that an object (or moving source) that is traveling distance vt at speed v in the direction shown passes the stationary source at the instant the stationary source gives off a pulse of light that propagates away from it (in the form of an expanding sphere) in all directions at speed c. In such case there will always be a point of propagated light that travels the hypotenuse path ct while simultaneously staying directly above the moving object traveling path vt. Stated another way, the same point of light that travels distance ct in the frame of the stationary source simultaneously travels distance ct in the frame of the moving object. ct ct source vt object Figure 4 Abbreviated Light Clock (Stationary Source) With that being the case, and given the natural relations inherent in a Pythagorean triangle the angle between the base vt and the hypotenuse ct will reduce to 0 as v reaches the speed of light c. This is easily demonstrated mathematically by assigning the following labels, y = ct, h = ct, and x = vt, to the sides of the triangle of Figure 4, and solving the resulting Pythagorean triangle for side y. This gives 18 and therefore 19 for the vertical side y of the Pythagorean triangle shown in Figure 4. Quite apparent from equation (19) is the fact that side y becomes 0 if base x = hypotenuse h. Whereas this behavior is consistent with that involving the acceleration of an object relative to the stationary frame that provides the energy for the acceleration, it is not consistent with the special relativity principle of distance contraction only in the direction of motion. Therefore whereas the special relativity light clock exhibits a behavior that is consistent with the special relativity principle that nothing can be accelerated to the speed of light, it is inconsistent with the special relativity principle that distances in the frame of the moving object contract only in the direction of motion. Yet, it is 6

7 exactly this behavior that is imposed on the moving frame by the fundamental nature of the light clock when it is applied to the light from a moving light source as with clock D in Section 2 of this paper. There is, however, an alternative way to view the light clock behavior associated with light from a moving source. By taking equation (18) and solving for h we obtain 20 where it is easily seen that the hypotenuse will just keep increasing in length and always be longer than the base x if side y (the distance between the mirrors) is held constant, regardless of how large the value of x becomes. Another way of viewing this behavior is to relate it back to the time t in the frame of the moving source, i.e., clock D. If the distance between the mirrors is constant and defined by the product ct where light speed c is constant, then time t in the frame of the moving source must also be constant regardless of the magnitude of speed v. Referring back to equation (14), repeated below it then follows that stationary frame time T will increase toward infinity as speed v of the source approaches light speed c. This is contrary to the behavior given by equation (17) repeated below 1 17 where it is seen that time t approaches 0 as speed v approaches speed c regardless of the value of time T. That is, in the case of equation (14) time t is unaffected by speed v, even if v = c. It is only time T that is affected and in that case increased to infinity. But, in the case of equation (17) time t = 0 if v = c. Thus, our whole understanding of time in the frame of the moving object depends upon how we view the anomalous predictions of the equations that relate it to the time in the stationary frame. Nonetheless, even in the case just presented, where time t is held constant and therefore the distance between the mirrors of clock D are held constant, we have still violated the principles of special relativity. That is, as shown throughout the author s research, time is not dependent on direction and therefore if t is constant and c is constant then distances in all directions in the moving frame are constant including that in the direction of source motion. Thus, the special relativity proposition of distance contraction in the direction of motion is still violated. 5. Conclusion It has been clearly demonstrated in this work that the special relativity light clock actually violates the principles of the theory it is intended to illustrate. This in addition to a newly identified anomaly involving the Lorentz transformation factor raises some serious questions regarding the validity of special relativity in general. It is important to remember here that it is the light clock principle of time dilation in the frame of the moving source that makes up the 7

8 Lorentz redshift component of the special relativity Doppler effect formula for electromagnetic propagation. If the light clock principle is flawed, so then are the Lorentz time dilation equations given as equations (14) and (17) in this present work. In conclusion, what was shown in this present work gives increased credibility to the author s recent findings involving the cause and effect principles of light propagation. In view of these combined findings it is no longer acceptable to assume validity of Einstein s special theory of relativity based on the overly simplistic principles given in that theory. The time has come to evaluate such principles in terms of their specific cause and effect nature and base future acceptance of the theory on that basis when evaluating what the evidence appears to show. REFFERENCES 1 Albert Einstein, the Special Theory of Relativity, originally published under the title, On the Electrodynamics of Moving Bodies, Annalen der Physik, 17, (1905) 2 Joseph A. Rybczyk, Millennium Theory of Relativity, (2001), available at 3 Albert Michelson and Edward Morley, The interferometer experiments conducted in 1887 over a period one year in a failed attempt to detect the ether medium postulated by Maxwell as being required for the propagation of electromagnetic waves. (1887) 4 H. A. Lorentz, devised the distance contraction formula in 1895 to explain the null result of the Michelson and Morley interferometer experiment of The use of the so-called Lorentz factor was later expanded upon to also include time dilation as given by equations (14) and (17) in this work. The True Nature of the Special Relativity Light Clock Copyright 2012 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 8