PAllen
Science Advisor
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The value at a point is the result of a limit. Thus, you can’t measure it at a point. However, classically, you could measure geodesic deviation in a ball a billionth of a plank length with tiny instruments of arbitrarily great precision.atyy said:So if we have infinite precision, are we able to detect deviations from flatness, even at a point? For example, could geodesic deviation be detected? In other words, is there a physical counterpart to the objection to the terminology of "local flatness"?
I don’t have any real objection to local flatness treated as a name for math that both @Orodruin and I agree on. But I can also sympathize with the objection. Thus I am open to agreeing to other terminology as preferred for this site. I am not enamored of having to say something involving coordinates, because the local behavior is coordinate independent. I have suggested “locally Minkowski” as a possibility.
Note, unlike some, I have no problem with practical definitions of coordinate independent features (e.g. asymptotic flatness or spherical symmetry) that involve the existence of coordinates in which the metric takes a certain form. However, I want a name to emphasize that the feature itself is coordinate independent.