You can have accelerating frames of reference in Special Relativity; for example, one can set Rindler coordinates on a body that is uniformly accelerating. Add

You can have accelerating frames of reference in Special Relativity; for example, one can set Rindler coordinates on a body that is uniformly accelerating. Addtionally, you can have locally inertial frames of reference that are inequivalent. Consider two space stations orbiting Earth at different altitudes. The occupants are in free-fall in both cases, but there is a relative acceleration between them. Rotating frames of reference tend to distract users into confusing coordinate artifacts with physical ones. As a trivial example, suppose we vary the Minkowski metric by introducing a rotation into Cartesian coordinates: dS^2 = -\left(1 - \omega^2 ({x}^2 + {y}^2) \right){dt}^2 + 2 \omega (- y dx dt + x dy dt) + {dx}^2 + {dy}^2 + {dz}^2. Here a non-massless object far from the origin will have |d\vec{x}/dt| > 1, or in other words a coordinate velocity greater than c. This is essentially the same as your last sentence. However, when we calculate the four-velocity \eta^\mu of any non-massless object, even far from the origin, we will see that dS^2 < 0 for all nearby points along its worldline. In other words, there is no superluminal motion -- there is just movement against a set of coordinates, and a different choice in coordinates will vary that. We can certainly do Standard Model physics (or classical particle dynamics) in a rotating system of coordinates, using a number of approaches. However, it is usually easier to use a different system of coordinates, and even better to abandon the idea of using any global system of coordinates in a spacetime that is not Riemann flat.