Born rigidity

The Born's rigidity is a concept of special relativity theory and was first proposed in 1909 by Max Born. It is one of the possible answers to the question of how the concept of the rigid body, which is in classical mechanics is of great importance, is also applicable in the context of special relativity.

Theory

The Born's rigidity is fulfilled, albeit in accelerated reference systems, the distance between two points locally remains the same, and is thus subject from the perspective of a movable relative to the inertial frame of the Lorentz contraction. This condition restricts the possible movements of an extended body, and can be put into practice only in exceptional cases by careful work leave of forces on different parts of the body. A rigid body in itself would in fact be in contradiction to special relativity, because in such a the speed of sound would be infinite.

The limits of the Born rigidity were in 1910 by Gustav Herglotz and Fritz Noether demonstrated ( Herglotz -Noether theorem). It has been demonstrated that the movement of the entire Born- rigid body is generally completely determined by the desired motion of one of its points. Exceptions are only possible in special cases according Herglotz, where the world lines of the points have a constant curvature. According to this theorem, a Born- rigid body has only three degrees of freedom. A modern version of the Herglotz - Noether theorem states that the rotational- rigid motion in Minkowski space must be a Killing Movement.

The narrow limits of the Born rigidity, have lead to the Ehrenfest 's paradox, that, while a disc can rotate uniformly on Born- rigid manner, but no accelerated rotation can be subjected without deformations occur. So discs can not be transferred to Born- rigid way from from hibernation in rotation. Another example is the Bell's spaceship paradox in which the two end points of a body have the same acceleration profile, and are accelerated at the same time in an inertial system. Again, the Born rigidity can not be met because of the mitbeschleunigten observer, the distance between the points, so that stresses in the material. General showed Herglotz (1911 ) that a relativistic theory of elasticity can be justified on the assumption that stresses occur when the Born rigidity is violated.