The Geodesic Spacetime Equation-printing

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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Parallel Transport

The astronaut in Skylab with his toy gyroscope is physically demonstrating the concept of parallel transport where a gyroscope when set in motion traces out a geodetic path of parallel motion or transport.

If you now substitute for the astronaut the effects of gravity, you can easily imagine how a gyroscope traces out the physical geometric outlines of spacetime itself and how its axial spinning rate under the same influence of gravity indicates time!! That is to say, that the spinning axis of a gyroscope under the influence of a gravitational field also behaves as a clock!! Therefore, space + time or spacetime!

And it's all called parallel (or gyroscopic) transport!