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GeneSnider
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Rather than adding to this already long thread, I chose to start a new thread.
Thought Experiment
In this post, s is distance, t1, is the time of transmission, t2 is the time of reflection and t3 is the time of reception. All cases assume an orthogonal coordinate system.
Case 1:
From a God's eye point of view, a laser pulse bounced off of a retroreflector on the moon will have these time stamps:
t1=0, t2=1.25, t3=2.5
Case 2:
Coordinate Transformation
In transformed coordinates where the transformation is T = T' + T * C / S the time stamps are:
t1 = 0 = 1.25, t3 = 2.5
Case 3:
When C is C/2 away from the earth and C/0 towards the observer, the time stamps are:
t1 = 0, t2 = 1.25, t3=2.5
If we watch the clocks from a God's eye point of view, the only difference is that in Cases 1 and 2, the time of flight is equal on both legs of the journey. In Case 3, the time of flight on both legs of the journey is not equal.
Historical Perspective
Einstein, Riechenbach and Gruenbaum never mentioned coordinate transformations in their work. The earliest paper I can find proposing this thesis is Edwards 1963 paper in 'American Journal of Physics'. Winnie popularized the idea in his two paper article in the 1970 'The Philosophy of Science Journal Association'.
Equations
I would like to see someone derive the cavity resonator equation under the conditions of Case 3.
ω101=[(πc/a)2+(πc/d)2]0.5
This equation shows that it is theoretically possible to measure e using a missile projectile and only one clock.
Rearranging Reichenbach's equation e = (t3 - t1) / (t2 - t1).
e = t3 / (t2 - 2 * t1))
Supporting article
The only supporting paper I've found so far is:
R. Anderson, I. Vetharaniam, and G. E. Stedman, Conventionality of synchronization,
gauge dependence and test theories of relativity, Physics Reports 295, 93180 (1998).
He provides no supporting evidence or a proof. This purpose of this post is to fill in the blanks.
Minkowski Diagram
To construct a Minkowski diagram, start with an XY plane and an orthogonal T axis. Obviously for the case where the speed of light C/2 away from an observer located at the origin and C/0 toward the observer located at the origin, the slope is C/2 for the forward light cone and the slope for the backward light cone is C/0. This corresponds to Einstein's alternate synchrony convention published in his 1905 paper.
A Paradox
Consider observer 1 located at the origin. Another observer is located at event 2 sometime in the future of observer 1. When an event occurs at observer 2's location, observer 1 will never be aware of it. However any event occurring at the location of observer 1 will always be seen by observer 2.
The only symmetrical case is when the light cones are parallel, which means the only possible solution is that the speed of light is isotropic.
Conclusion
A coordinate transformation is not equivalent to a change of synchrony convention.
Respectfully,
Gene Snider
Thought Experiment
In this post, s is distance, t1, is the time of transmission, t2 is the time of reflection and t3 is the time of reception. All cases assume an orthogonal coordinate system.
Case 1:
From a God's eye point of view, a laser pulse bounced off of a retroreflector on the moon will have these time stamps:
t1=0, t2=1.25, t3=2.5
Case 2:
Coordinate Transformation
In transformed coordinates where the transformation is T = T' + T * C / S the time stamps are:
t1 = 0 = 1.25, t3 = 2.5
Case 3:
When C is C/2 away from the earth and C/0 towards the observer, the time stamps are:
t1 = 0, t2 = 1.25, t3=2.5
If we watch the clocks from a God's eye point of view, the only difference is that in Cases 1 and 2, the time of flight is equal on both legs of the journey. In Case 3, the time of flight on both legs of the journey is not equal.
Historical Perspective
Einstein, Riechenbach and Gruenbaum never mentioned coordinate transformations in their work. The earliest paper I can find proposing this thesis is Edwards 1963 paper in 'American Journal of Physics'. Winnie popularized the idea in his two paper article in the 1970 'The Philosophy of Science Journal Association'.
Equations
I would like to see someone derive the cavity resonator equation under the conditions of Case 3.
ω101=[(πc/a)2+(πc/d)2]0.5
This equation shows that it is theoretically possible to measure e using a missile projectile and only one clock.
Rearranging Reichenbach's equation e = (t3 - t1) / (t2 - t1).
e = t3 / (t2 - 2 * t1))
Supporting article
The only supporting paper I've found so far is:
R. Anderson, I. Vetharaniam, and G. E. Stedman, Conventionality of synchronization,
gauge dependence and test theories of relativity, Physics Reports 295, 93180 (1998).
He provides no supporting evidence or a proof. This purpose of this post is to fill in the blanks.
Minkowski Diagram
To construct a Minkowski diagram, start with an XY plane and an orthogonal T axis. Obviously for the case where the speed of light C/2 away from an observer located at the origin and C/0 toward the observer located at the origin, the slope is C/2 for the forward light cone and the slope for the backward light cone is C/0. This corresponds to Einstein's alternate synchrony convention published in his 1905 paper.
A Paradox
Consider observer 1 located at the origin. Another observer is located at event 2 sometime in the future of observer 1. When an event occurs at observer 2's location, observer 1 will never be aware of it. However any event occurring at the location of observer 1 will always be seen by observer 2.
The only symmetrical case is when the light cones are parallel, which means the only possible solution is that the speed of light is isotropic.
Conclusion
A coordinate transformation is not equivalent to a change of synchrony convention.
Respectfully,
Gene Snider
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