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- Is a violation of the Equivalence Principle proven by the following calculation?

Alan Macdonald claims in "4 Appendix: The Equivalence Principle" of his text "Special and General Relativity based on the Physical Meaning of the Spacetime Interval", that his calculation regarding a 2D-surface of a sphere proves, that the equivalence principle is violated.

He defines the local measurement of

## M = ({3 \over \pi}){2\pi r - C(r) \over r^3}##

with ##C(r) = 2 \pi R \sin{ \Phi } = 2 \pi R \sin{ (r/R) } = 2 \pi R [r/R - {(r/R)}^3 /6 + ...]##.

He argues, that the equivalence principle is violated because of ## \lim_{Area \rightarrow 0} M = 1/R^2## instead of zero.

The calculation of the limit is correct. But can his argument regarding violation of the equivalence principle be correct?

Source (see under "4 Appendix: The Equivalence Principle"):

http://www.faculty.luther.edu/~macdonal/Interval/Interval.html

He defines the local measurement of

## M = ({3 \over \pi}){2\pi r - C(r) \over r^3}##

with ##C(r) = 2 \pi R \sin{ \Phi } = 2 \pi R \sin{ (r/R) } = 2 \pi R [r/R - {(r/R)}^3 /6 + ...]##.

He argues, that the equivalence principle is violated because of ## \lim_{Area \rightarrow 0} M = 1/R^2## instead of zero.

The calculation of the limit is correct. But can his argument regarding violation of the equivalence principle be correct?

Source (see under "4 Appendix: The Equivalence Principle"):

http://www.faculty.luther.edu/~macdonal/Interval/Interval.html