No abstract

The simplest model of a black hole, the massive point source generating a static spherically symmetric gravitational field, is examined using the Schwarzschild coordinate frame. A brief review is given of this coordinate frame external to the Schwarzschild surface. Greater attention is paid to an interpretation of this frame inside the Schwarzschild surface. Here the roles of space and time are reversed in the sense that the external radial coordinate becomes an internal temporal coordinate, and the external temporal coordinate becomes an internal spatial coordinate. An internal universe is constructed from this frame, and a few simple kinematic phenomena are described in terms of it. The internal and external coordinates are connected graphically by using Kruskal coordinates and physically by considering the world lines of photons and freely moving particles which transit the Schwarzschild surface.

An argument is given that teaching relativity from the beginning using four-vectors provides a powerful and correct way of thinking that also conforms to everyday methods of making measurements. In particular, it is pointed out that the emphasis on the relativistic mass is both undeserved and misleading.

The kinematic concepts of special relativity seem best understood by the beginning student if they are presented in purely geometric form. The description of events in space-time is given geometrically as viewed from different coordinate systems in relative motion with one another, both from the classical and relativistic points of view. These geometric representations differ somewhat from those usually seen. Some justification is given the Lorentz transformation by requiring that the velocity of light be the same for all observers and that in the limit of small velocities, the Lorentz transformation reduce to the Galilean transformation. The relativistic contraction of lengths and the dilation of time intervals are deduced.

It was suggested by Einstein and later greatly elaborated on by others that the methods used to synchronize distant clocks are a matter of convention. The standard method, in which it is assumed that the speed of light is isotropic, obviously yields an isotropic light speed when such clocks are involved in determining the speed of light. Another method, in which clocks travel symmetrically but otherwise arbitrarily in opposite directions, may also be used to synchronize distant clocks. This method establishes whether or not the clocks are synchronized in a physically significant way in the sense that it allows a distinction to be made between a contrived anisotropic light speed and an anisotropic speed that is physically significant or real. Specifically, a contrived anisotropic light speed results in laws of physics that are not symmetric, whereas a true anisotropic light speed does not affect the symmetry of physical laws. Furthermore, when invariance in the speed of light is imposed, the invariant interval may be identified with the lapse of proper time in the case in which anisotropy is contrived. But, in the case of true anisotropy, this identification is not possible. Experiment reveals that, on the basis of symmetry in physical law, any anisotropy in the speed of light is contrived and not physically significant.