A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in (...) coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

A theoretical device, which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined. The device, which we call a metrosphere, is simple enough that it can be introduced at the starting point of relativity theory and versatile enough that it can serve as an aid in the development and conceptualization of the theory. Relative to an inertial frame, a moving metrosphere undergoes a Lorentz-Fitzgerald contraction (...) and the associated clock exhibits a Lorentz-Larmor rate retardation. From this fact and the assumption that there exists one inertial frame, it is possible to generate the kinematical results of special relativity. A metrosphere provides an observer with a local frame of reference, hence it is well adapted to the needs of general relativity, allows the equivalence principle to be introduced in a straightforward manner, and permits a smooth transition from special relativity to general relativity. (shrink)

A rotating disk with angular acceleration is given a relativistic description as observed from the rotating rest frameR of the disk. It is shown how a non-Euclidean intrinsic spatial geometry develops inR, as the disk gets an angular velocity. The explanation of this as given by anR-observer is discussed. A recent description of the geometry inR presented by Grünbaum and Janis is criticized. The motion of light as described by use of coordinate clocks inR is discussed in connection with some (...) recent work by R. C. Jennison and coworkers. The significance of the difference between directed signals and circular waves when clocks inR are to be synchronized by means of light emitted from the axis inR is made clear. (shrink)

The use of the axial vector representing a three-dimensional rotation makes the rotation representation much more compact by extending the trigonometric functions to vectorial arguments. Similarly, the pure Lorentz transformations are compactly treated by generalizing a scalar rapidity to a vector quantity in spatial three-dimensional cases and extending hyperbolic functions to vectorial arguments. A calculation of the Wigner rotation simplified by using the extended functions illustrates the fact that the rapidity vector space obeys hyperbolic geometry. New representations bring a Lorentz-invariant (...) fundamental equation of motion corresponding to the Galilei-invariant equation of Newtonian mechanics. (shrink)