Weinberg's cosmology book stated that Einstein Equivalence principle implies that at any spacetime point in an arbitrary gravitational field there is a “locally inertial” coordinate system in which the effects of gravitation are absent in a sufficiently small spacetime neighborhood of that point.
So if I underatand this correctly, irrespective of being free-fall, one can always find a locally inertial frame. I have two questions:
How is EEP related to Weak Equivalence principle relating inertial & gravitational mass? It seems to me that the most intuitive way to think of EEP is to imagine a tangent surface at an arbitrary point on curved manifold. However it is purely geometrical and has nothing to do with mass.
Based on EEP, human sitting on Earth can also come up with a locally inertial frame around him/her (assuming the size of human can be considered as local). I forgot its name, but one experiment proved that a rest frame on Earth is not inertial since we can observe redshift (which makes sense because at rest in the presence of gravity is not inertial in GR). How can we reconcile these two? Is it because the experiment setup was not small enough to be considered local or something more profound?