Lorentz contraction of rigid bodies and time dilation of observers’ clocks is what most laymen consider the essentials of Einstein’s Special relativity. And admittedly they were featured as essential by Einstein himself. But they are not essential; They are not factual; they represent a misinterpretation of the more relevant transaction interval that is the distance and duration of an electrodynamic energy transfer. The transaction interval is a length and duration consequence of electrodynamics, not just a mathematical artifact to solve a problem resulting from an erroneous interpretation of the Lorentz equations.
Of course there are reasons why those concepts were embedded into the extended dogma of the special theory. They result from forcing frame independence on the coincident detection of what are constrained to be frame independent coincident emissions. Einstein considered there to be a a direct connection between frame-independent indivisible events as a resolution to what he saw as the kinematics problem since events are located on objects to which they occur. However, his interpretation of frame independence did not support that agreement without altering the shapes of rigid bodies and times of occurrence in one of the two uniformly moving frames of reference.
The primary difference between the observations of two observers in uniform relative motion is the extent of the difference in the transaction intervals c Dt’ and c Dt of two co-located observers. Holding the velocity of light constant, this difference of a factor of gamma must either reflect a difference in when separated events occurred or in how long it takes light to propagate between indivisible coincident events. The ambiguities of frame independence illustrated in the previous post we include here as illustration.
Any (and every) one of the six observers could detect the coincident emission event in which all six of the light source objects were coincident when their respective emission events took place. But these six detections of the coincident emission from the six sources are not observed from the perspective (angle) of their coincidence as indicated by the blue circle. The perspective of each observer is from that of the respective black circles. The essential difference between frame independent emission and detection is that the sources paths begin at emission. It will be detected by the observer as if he were at a position when that emission took place even though it will not actually be observed until he is at the location at the end of his path of the same duration as the light path. So sure, there is frame independence of coincident detection, but the detected coincident emission event will not be indivisible in that sense. It will be in different directions with differing amounts of red and blue shift for each coincident observer.
Einstein ignored this difference as denying his interpretation of frame independence that he saw as implying indivisibility of coincident events at both the emission and detection ends of each transaction. That interpretation of the transaction interval demanded that the observers account differently for time and distance of the differing transactions they observe.
Since events, whether emission or detection, occur on objects – sources and observers. When and where individual events on an object occur must be when and where that part of the object happened to be located at that instant. That is what Einstein considered to be the kinematics problem. The problem exists exclusively with his interpretation of how coincident events are to be handled. His interpretation requires Lorentz contraction of otherwise rigid bodies and clock time dilation throughout the other observer’s reference frame rather than just applying to the individual transactions. Let us analyze the implications of his interpretation using a rigid ring in the x-y plane – a cross section of a sphere of radius R = c T. The inner side of the ring has a mirrored surface. The ring is in motion at half the speed of light and moving to the left. At the center of the ring at time zero an instantaneous burst of light is emitted by either observer – one that is situate at that location of initial emission and the other at the center of the ‘moving ‘ ring. White arrows in the following diagrams indicate how far the center of the ring has traveled at each of the nine stages of progress of the experiment. The wavefront of the emitted light is shown with progress of Einstein’s ‘rays of light’ in the various directions.
As shown in snapshot i, the light will converge after reflection off the mirrored surface back to the center of the ring and (Einstein evidently believed) to a relatively stationary detector at a coincident distance 2 v T from the original source location all at time 2 T.
The problem – Einstein’s ‘kinematic problem’ – is that using the Lorentz equations, reflection does not occur at the inner surface of the ring at any location on the ring except directly overhead and below the center. This is shown in the diagrams. That is a real problem to be solved. Right? Every light path is extended by a factor of gamma = 1 / root( 1 – (v/c)2 ). To solve this problem he assumed a moving sphere (ring in our case) would be contracted along a direction of relative motion by an inverse gamma facror of root( 1 – (v/c)2 ) and clock time of an observer associated with the ring would be dilated by the gamma factor. And yes, that does solve the ‘kinematics problem as you can see in the similar thought experiment below (and as justified by Penrose in demonstrating that Lorentz contraction can never be observed.) All reflections occur at the inner surface of the contracted ring. But so what? That is how you fudge experiments to make things fit the data. It’s not how God would have done it.
The ‘problem’ isn’t with rigid bodies or observers’ clocks it’s with lack of the recognition of the properties of transactions. Transactions are not rays of light shot out into the ether. They are the conjoined relationships between objects with an emission event at one end and a detection event at the other. For a transaction between relatively moving objects the duration of the transaction is longer by a factor of gamma. The distance traveled by the transaction is less than the helical light path by a factor of the inverse of gamma.
In the ring thought experiment, there is a real difference in which observer emits the light. If it is emitted from a frame of reference including a rigid association of the center of the ring, there is no relative movement between the emission and the detector (reflector) on the inner surface of the ring or on the reverse transaction back to the center of the ring. So the combined transaction time duration is 2 T, and the center of the ring will have traveled 2 vT. However, the coincidence of the center of the ring with a ‘stationary’ emitter when it emits a burst of light poses a different situation. Emission and reflection will occur on relatively moving objects as well as the reversed transaction direction. So the gamma factor applies to the transaction between the ‘stationary’ observer and the ‘moving’ mirrored surface. In both cases reflections occur at the inner surface of the ring and there is no kinematic problem.
The implications should be obvious.
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