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The Geodesic Spacetime Equation-video/printing
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The Geodesic Spacetime Equation-video/printing

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A body’s motion in a gravitational field over the "shortest curve" or "straightest" possible world timeline for the extremal maximum proper transit time for the most efficient use of energy means that gravity indeed slows an attached clock to the utmost in the body’s geodetic transit. And hence the parallel transport of gyroscopes within fields of gravity physically traces out and thereby demonstrably reveals the actual geometry of spacetime curvature caused by gravity or its equivalent amount of acceleration.

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Gravity in Einstein's World
Gravity according to Einstein is best understood as space-time (or spacetime) woven as an imaginary "fabric". That is, Einstein employs the idea of geometry in an expanded sense in order to demonstrate the effects of gravity. However what exactly is gravity is again another matter for future mathematical physicists to discern.