PeterDonis
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Yes, you are. See below.HansH said:Then it means that I am not referring to the tem ''proper acceleration'
Such an "applied force" causes proper acceleration.HansH said:but to the accelleration as result of an applied force such as a rocket engine.
Not at all. Remember, in relativity "gravity" is not a force. The force you feel when you stand at rest on the surface of the Earth is not "gravity". It's the force of the Earth's surface pushing up on you. Just as, if you stand at rest on the floor of a rocket accelerating at 1 g, the force you feel is the force of the rocket's floor pushing up on you. The principle of equivalence says that you cannot distinguish these two cases by local observations, but that is not the same as saying that you can't distinguish "gravity" from the effects of a rocket engine in flat spacetime.HansH said:I think you are going to say that an observer cannot discriminate between gravity in curved spacetime and a rochet engine in flat spacetime due to the principle of equivalence.
Basically what the principle of equivalence is saying is that proper acceleration is proper acceleration, and by itself it doesn't tell you want kind of spacetime geometry the proper acceleration is occurring in.
There is no such thing as "the effect of curvature on the path of a worldline" if by "curvature" you mean "spacetime curvature". That is getting things backwards. It's not that you start out with a worldline, and then you put it in one spacetime geometry or another and see what happens to it. You have the spacetime geometry first, and then you look at the behavior of worldlines in it. There is no way to pick out "the same worldline" in two different spacetime geometries and compare the effects of one spacetime geometry vs. another on "the worldline". There is no way to even define a "worldline" at all independently of a spacetime geometry.HansH said:the equivalence principle that cannot isolate an external acceleration from the effect of curvature on the path of a worldline?