Life in a rotating world

We imagine a group of people living on the inner surface of a huge rotating cylinder in flat spacetime. Their experiences are described and calculated. Thus we introduce gravimagnetic effects and the connection between gravitational time dilation and gravitational acceleration. Gravimagnetic effects such as the force on moving particles and the precession of gyroscopes are derived. The Thomas precession is obtained. These observations illustrate GR ideas that are applicable more generally. Some properties of the general stationary metric are introduced.

Reexamining the Thomas precession

We review the Thomas precession exhibiting the exact form of the Thomas rotation in the axis-angle parameterization. Assuming three inertial frames S, S', S'' moving with arbitrary velocities and with S, S'' having their axis parallel to the axis of S' we focus our attention on the two essential elements of the Thomas precession: (i) there is a rotation between the axis of frames S, S'' and (ii) the combination of two Lorentz transformations from S to S' and from S' to S'' fails to produce a pure Lorentz transformation from S to S''. The physical consequence of (i) and (ii) refers to the impossibility of arbitrary frames S, S', S'' moving with non-paralell relative velocities have their axis mutually parallel. Then, we reexamine the validity of (i) and (ii) under the conjecture that time depends on the state of motion of the frames and we show that the Thomas precession assumes a different form as formulated in (i) and (ii).

Einstein’s accelerated reference systems and Fermi–Walker coordinates

We show that the uniformly accelerated reference systems proposed by Einstein when introducing acceleration in the theory of relativity are what is known at present as Fermi–Walker coordinate systems. We then consider more general accelerated motions and, on the one hand we obtain Thomas precession and, on the other, we prove that the only accelerated reference systems that at any time admit an instantaneously comoving inertial system belong necessarily to the Fermi–Walker class.