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Let's say there is a way to get position of all particles of human with perfect accuracy.

When random human jumps, can it alter position of someone who is on the other end of earth?

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Yes, the acceleration of a freely falling particle anywhere else would be slightly altered.

If the person jumping would be right next to the freely falling object, and one could neglect the maximum speed of propagation $c$, the falling object would be slightly pulled towards the jumping person. And thus change its falling acceleration. If this happens at a greater distance, the effect would still be there but even more weaker.

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  • $\begingroup$ It would be best to elaborate. As it stands, this doesn't give any physical insight as to why/how/etc. $\endgroup$ – Kyle Oman May 19 '16 at 8:57

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