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There is a nice demostration picture concerning the propagation of gravity in finite time: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/#Starting

enter image description here

It says:

He (Einstein) examined gravitation theories, modified to allow for a finite time of propagation of effects, and found a result that aroused great suspicions in him. In the modified theories, the distance fallen by a body varies according to its sideways motion. In the simplest case, the body would fall a shorter distance if it has some sideways velocity.

However this explanation is vague and does not explain "why" the distance fallen by a body varies according to its sideways motion. Do they mean relativistic speeds or just any speeds? Why this happens?

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  • $\begingroup$ This doesn't happen, in reality. It apparently happened in some of the predecessors to general relativity that added a Lorentz-covariant propagational delay to Newtonian gravity. This is perhaps a better question for the History of Science and Mathematics stackexchange site, hsm.stackexchange.com. $\endgroup$
    – David Hammen
    Dec 31, 2016 at 17:27
  • $\begingroup$ Does that not describe a modified theory of gravity which resulted from Einstein's work on formulating general relativity? For most observations, components are independent, and I believe the article said the noticed effects in the diagram were deemed negligible. As a tool in developing general relativity, it seems like this modified gravity was set aside in favor of his argument on accelerating reference frames. $\endgroup$
    – bleuofblue
    Jan 1, 2017 at 23:30

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