Suppose we have a test mass located at some point above the earth. It is allowed to free fall down toward the earth. It passes through a closed surface. Prior to entering the surface it has an initial momentum pi and initial kinetic energy kei. After leaving the closed surface it has acquired a greater momentum pf and a greater kinetic energy kef. Clearly, the momentum and kinetic energy of the test mass has not been conserved.(adsbygoogle = window.adsbygoogle || []).push({});

Could we choose one of two explanations for this? The first one is there was no time and space translation symmetry during the transit of the test mass through the closed surface, and therefore, it follows that momentum and energy were not conserved.

Or during the transit within the closed surface the gravitational field imparted an impulse on the test mass and simultaneously did work on the test mass, and therefore, momentum and energy were conserved when we include the effects of the gravitational (curving of space-time) field.

If the second explanation is the correct one, how can this be if the test mass is weightless as general relativity asserts? That is, there was no force acting on the test mass during its transit within the closed surface, yet it still acquired momentum and kinetic energy.

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# Gravity and time and space translation asymmetry

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