Matolcsi T. Spacetime Without Reference Frames 2020

Textbook in PDF format

In this book, nonrelativistic spacetime and special relativistic spacetime are modelled by a four dimensional affine space endowed with further structures, among which the fundamental ones distinguishing between them are absolute time and absolute light propagation, respectively. In both cases, the same mathematically well-defined notions are introduced: observer and its space, synchronization and its time, reference frame, splitting of spacetime by a reference frame into synchronization time and observer space, splitting of classical fields into timelike and spacelike components. Coordinate systems which form a starting point of the usual treatments and are intuitive notions there, get mathematically exact and clear definition here. Transformation rules, regarded as postulates there, are assertions here. The book contains lots of examples with detailed calculations which help the reader to see how these models work, and it calls attention to some significant errors arising form the traditional way of thinking in terms of coordinates. The symmetry groups of spacetime, the Noether group and the Poincaré group, respectively, are also treated in these models.The mathematics involved is fairly simple and is summarized in the second part of the book