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What does the following statement mean and why is it true?

The Weak Equivalence Principle (WEP) implies that in general curved space-time there is no privileged coordinate system.

I have looked up the WEP -- as far as I can see, it is more or less the Universality of free fall (?) My (probably totally missing the point) interpretation of the statement is that in general curved space-time, you can't do away with the Gravitational Field everywhere simultaneously... But like I said, I am probably barking up the wrong tree here. Grateful if someone could explain!

Context: This was to justify the use of tensor calculus in GR.

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Where is the quote from and what is the context? –  Ben Crowell Apr 10 '13 at 19:15
    
@BenCrowell: This is taken from some notes taken during a lecture.,as an introduction into tensor calculus/analysis. –  Gene Apr 10 '13 at 19:31
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But what is the context? Don't force us to peer through a keyhole. This sentence is presumably taken from a lengthy argument that explains what your prof had in mind. Taken in isolation, the quote overstates the logical link. You can have diffeomorphism invariance without the EP, and ordinary Galilean relativity already forbids the existence of a privileged coordinate system (although some equivalence classes of coordinate systems may be nicer than others). –  Ben Crowell Apr 10 '13 at 21:42
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Long shot, since lack of context, but here is my attempt.

Any event can be described with 4 coordinates [x,y,z,t], where [x,y,z] point in some coordinate system and [t] - synchronized clock at event point.

WEP is same thing as universality of free fall.

The universality of free fall, states that all bodies fall with the same acceleration in a gravitational field, independently of their mass and composition, Theory and Experiment in Gravitational Physics, by Clifford M. Will

That means trajectory depends only on its position and velocity. If we need to describe position there is no privileged coordinate system, that will give to us some additional information about event, each coordinate system differ only by some transformation.

In same time we need to combine geometrical properties with physical, position and time, this can be done by use of tensor, which combine spatial position of event [x,y,z] and time. This technique also used in analysis of electromagnetic fields.

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Thank you, Sigrlami! –  Gene Apr 13 '13 at 18:55
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