The Weak Equivalence Principle has any one of the following forms:
- the inertial mass is equal to the gravitational mass
- there exists a preferred class of trajectories through spacetime, known as inertial or freely-falling trajectories, on which unaccelerated particles travel - where unaccelerated means "subject only to gravity"
- the motion of freely-falling particles are the same in a gravitational field and a uniformly accelerated frame, in small enough regions of spacetime
and the Einstein Equivalence Principle has the following form:
In small enough regions of spacetime, the laws of physics reduce to those of special relativity; it is impossible to detect the existence of a gravitational field by means of local experiments.
The difference between the WEP and the EEP lies in the fact that WEP considers only the motion of freely-falling particles whereas EEP considers any local experiments.
The following extract describes a theory that respects the WEP but violates the EEP:
we could imagine a theory of gravity in which freely falling particles begin to rotate as they moved through a gravitational field. Then they could fall along the same paths as they would in an accelerated frame (thereby satisfying the WEP), but you could nevertheless detect the existence of the gravitational field (in violation of the EEP). Such theories seem contrived, but there is no law of nature that forbids them.
In the theory mentioned in the extract, what does it mean for the particles to fall along the same paths as they would in an accelerated frame and how does that satisfy the WEP? Similarly for the EEP?
P.S.: The extract is copied verbatim from Sean Carroll's textbook.