# Equivalence principle

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## Main Question or Discussion Point

Einstein's equivalence principle states that:
The sets of inertial frames in the real world that correspond to (portions of) the ideal set of inertial frames discussed in special relativity consist of freely falling local frames.

In other words,can we say that since all the local frames are in free fall,i.e subject only to gravity so there is no relative acceleration between them and hence they are moving with constant velocities(which can be relative)?

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PeterDonis
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Einstein's equivalence principle states that:
The sets of inertial frames in the real world that correspond to (portions of) the ideal set of inertial frames discussed in special relativity consist of freely falling local frames.
This is not the usual way of stating the EP, but it seems ok.

an we say that since all the local frames are in free fall,i.e subject only to gravity so there is no relative acceleration between them
The fact that all of the local inertial frames are in free fall does not mean there is no relative acceleration between them. That would be true in the flat spacetime of Special Relativity, but the actual spacetime we live in is not flat; it is curved, because of the presence of matter and energy. And spacetime curvature means that there can be relative acceleration between objects that are in free fall.

This is not the usual way of stating the EP, but it seems ok.

The fact that all of the local inertial frames are in free fall does not mean there is no relative acceleration between them. That would be true in the flat spacetime of Special Relativity, but the actual spacetime we live in is not flat; it is curved, because of the presence of matter and energy. And spacetime curvature means that there can be relative acceleration between objects that are in free fall.
Sorry I forgot to state that I sm talking about free fall in the context of special relativity only.Thanks for the reply.I suppose I will get to study about curved spacetime more in General Relativity,right? Currently I am reading Introduction to special relativity by Wolfgang Rindler.

PeterDonis
Mentor
2019 Award
I forgot to state that I sm talking about free fall in the context of special relativity only.
But if that's the case, the equivalence principle is irrelevant. The only point of even thinking about the equivalence principle is to understand to what extent the flat spacetime physics of special relativity can still be used if spacetime is actually curved, as it is in general relativity. If you're only thinking about flat spacetime, there is no equivalence principle because there's nothing for flat spacetime to be locally equivalent to.

vanhees71