Space reflection

The space reflection , also called inversion , is a term from physics. It denotes a point mirroring of the space in which all points are mirrored at the origin. That is, a position vector turns into . ${\displaystyle {\vec {r}}}$ ${\displaystyle -{\vec {r}}}$

In Cartesian coordinates this means that the signs of all coordinates are reversed. This distinguishes spatial reflection from reflection on a plane , e.g. B. on a flat mirror. Here only the coordinate along the mirror normal is reversed. The full spatial reflection is obtained if, after the reflection on a plane, a rotation of 180 ° around the normal is carried out. If one also considers time as a dimension in connection with space- time, the space reflection only changes the signs of the spatial coordinates, time remains unchanged.

Applications

In physics, a distinction is made between polar and axial vectors in three-dimensional space . (The latter are also called pseudovectors .) The former change their sign when the space is reflected , the latter do not. For example, the location and the force are polar vectors. The torque , however, is an axial vector. (Since both factors of the cross product undergo a sign change when mirroring in space, the sign of the torque is retained). ${\displaystyle {\vec {r}}}$ ${\displaystyle {\vec {F}}}$ ${\displaystyle {\vec {M}}={\vec {r}}\times {\vec {F}}}$

When a physical object changes into itself in space reflection, it is in a state of positive parity ; however, the signs are swapped, which is the case with objects such as B. force field , oscillation , wave , quantum mechanical state vector is possible, it is in a state of negative parity.

Of the four fundamental forces in physics, gravitation, electromagnetism and strong interaction are invariant under reflections in space. This means that the processes they cause would convert the system in question to the mirrored end state in the same time after mirroring the initial state. The weak interaction violates the mirror invariance (see parity violation ). This was postulated in 1956 by the physicists Tsung-Dao Lee and Chen Ning Yang and confirmed experimentally by CS Wu, among others, during the beta decay . However, all four fundamental forces are invariant under the extended CPT symmetry (space reflection, time reversal, charge reversal or exchange of particles and antiparticles).

Individual evidence

1. ^ H. Vogel: Gerthsen Physik , 18th ed., Springer 1995, ISBN 3-540-59278-4 , Section 13.4.10: Symmetries, Invariances, Conservation Laws.