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Originally Posted by wisp
You are an observer fixed in absolute space...
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"Absolute space" is in violation of the conditions of relativity, where - by definition - everything is relative and nothing is absolute.
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We could make the radius bigger than 1 billion light years, which in turn would make it impossible for you to detect the curvature of the moving sagnac observer within the 1km window. ...
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But, no matter how much you flatten the circle and no matter how difficult it is to detect that circle over a finite distance, it is still a circle and requires acceleration. The circle traveller cannot be in an inertial frame.