Chapter 15 establishes the concept of a spacetime reference Frame field where local future-pointing, timelike integral curves of this field model the local histories of idealised observers in an arbitrary Lorentzian spacetime. It is explicitly shown how the use of instantaneous relative rapidity parameters explains why instantaneous observation of local massive particle speeds by different observers will always detect bounded particle speeds in sharp contrast to the “law for the addition of collinear velocities in Newtonian non-relativistic physics”. The chapter exploits the concept of observer fields to give criteria for the existence of locally synchronisable Frames, based on previous discussions of the Frobenius condition (Sect. 5.13 ). This leads to the notion of a “time function” and the possibility of synchronising “idealised clocks” between different observers in the same reference Frame in an arbitrary spacetime. Section 15.2 is devoted to a geometrical discussion of “clocks” and “rods” in Minkowski spacetime (i.e. \(\mathbb {R}^{4}\) with a globally flat Lorentzian metric tensor field and Levi-Civita connection \(\nabla \) yielding a spacetime free of Einsteinian gravitation). Such a spacetime admits global inertial (geodesic) Frames with well-defined “time functions” and idealised clocks that are synchronisable. The redundant notion of “material rods” for measuring “spatial length” is replaced by observable “spatial separations”. These then yield the traditional descriptions of “time dilation” and “length contraction” without any reference to Lorentz transformations or properties of “light” (null geodesics) (Sect. 15.2). In Sect. 15.2 we also return to arbitrary Einsteinian spacetimes to define the notion of Fermi-Walker transport (Sect. 15.3) and (in Sect. 15.4) set up the mathematical machinery for defining the notion of the “neighbours” of an observer field. This is followed by five subsections that implement this notion in the context of different types of observer Frames in various Einsteinian spacetimes.