I just finished teaching two introductory (elementary) courses on relativity, one in English and another in Finnish. While revising my notes on the equivalence principle, I wondered how different formulations of the principle could be derived from each other. One would expect this if the formulations really were equivalent. Incidentally, there is just a paper on this topic recently published
in AJP:
<http://scitation.aip.org/content/aapt/journal/ajp/83/1/10.1119/1.4895342>
and an arxiv.org version of the same paper is here: <http://arxiv.org/pdf/1310.7426v1.pdf>
It turns out that the standard formulations are not equivalent, and they can be used in analyzing competing theories of gravity.
Cheers,
Antti
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