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, proposed by and later named after Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...
, is a concept in special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
. It is one answer to the question of what, in special relativity, corresponds to the rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...
of non-relativistic classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
The defining property of Born rigidity is locally constant distance in the co-moving frame for all points of the body in question. It is a very restrictive sense of rigidity; for example, Ehrenfest paradox
The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity.In its original formulation as presented by Paul Ehrenfest 1909 in the Physikalische Zeitschrift, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry...
states that it is impossible to put a disk into rotation while maintaining its Born rigidity. A similar Bell's spaceship paradox
Bell's spaceship paradox is a thought experiment in special relativity involving accelerated spaceships and strings. The results of this thought experiment are for many people paradoxical. While J. S. Bell's 1976 version of the paradox is the most widely known, it was first designed by E. Dewan and M...
demonstrates that if we have a body at rest and try to move it along its length, then its Born rigidity will be broken.
Several weaker substitutes have been proposed as rigidity conditions.
Note that Born rigidity is a constraint on the motion of an extended body, achieved by careful application of forces to different parts of the body. A body rigid in itself would violate special relativity, as its speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
would be infinite.
The Herglotz-Noether theorem
The Herglotz-Noether theorem in special relativity restricts the possible linear and rotational motions of a Born-rigid object. It states that such a body may only possess a linear acceleration if it is not rotating.-References:...
states that it is impossible to impose a linear acceleration on a rotating Born-rigid object.