* 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.