Instructor:  Dr. Tamás MATOLCSI

Text: T. Matolcs:  Spacetime without reference frames (the book is recently out of print; necessary parts of it  are sold as classnotes while the PostScript file of the entire book can be downloaded from here)

Prerequisite: linear algebra and calculus

Course description:   Mathematical physics is conceived as a theory of mathematical models of physical phenomena.
A mathematical model has to be a mathematically well defined structure which reflects the properties of the
physical phenomena in question. Since space and time appears in every physical theory, first of all we must build up
mathematical models of space and time which, in fact, are some aspects of a unique physical entity, spacetime.

Topics:

First part: nonrelativistic spacetime model
Measure lines. Spacetime as a four dimensional affine space.
Absolute time, absolute Euclidean structure. World lines,
absolute velocities and absolute accelerations. Observers,
splitting of spacetime into time and space. Inertial observers.
Comparison of different splittings. Motions relative to inertial
observers. Relative velocities and relative accelerations.

Second part: special relativistic spacetime models.
Spacetime as a four dimensional affine space.
Absolute light propagation. Lorentz structure. World lines,
proper time, absolute velocities and absolute accelerations.
Observers, synchronizations. Splitting of spacetime into time
and space. Inertial observers, standard synchronization.
Lorentz boosts. Comparison of different splittings.
Motions relative to inertial observers. Relative velocities
and relative accelerations. Time dilation, length contraction.
The twin paradox and the tunnel paradox.