Rigidly Rotating Disk Revisited

Abstract

In a very interesting article entitled ‘Einstein and the Rigidly Rotating Disk’, (1980) has traced the 0genesis of the general theory of relativity based on the concept of a curved spacetime. As he remarks, the rigidly rotating disk’ seems to provide a “missing link” in the chain of reasoning that led him (Einstein) to the crucial idea that a nonflat metric was needed for a relativistic treatment of the gravitational field’. The chain of reasoning begins essentially with space and time being combined into spacetime as a consequence of the special theory of relativity After that, equivalence principle connecting gravitation to accelerated frames was the first step towards the formulation of the general theory of relativity Now comes the rigidly rotating disk as the “missing link”. The inertial force, namely the centrifugal force, experienced by observers fixed on the rotating disk is identified as equivalent to a gravitational field. Einstein showed that these observers find the ratio of the circumference to the radius of a circle around the axis of rotation to be greater than 2π. This immediately leads to the conclusion that the geometry associated with the rotating disk is non-Euclidean. In other words, the presence of gravitation leads, in analogy with the Gaussian theory of surfaces, to a metrical theory of four dimensional curved spacetime. The general theory of relativity is born and the inertial forces lie dormant under the cover of curved spacetime. Although all gravitational phenomena are considered using general spacetime metrics that are solutions to the Einstein field equations, the basic concepts arising in the case of the rigidly rotating disk are still important. Some of these concepts can be formulated precisely and fruitfully in the case of stationary, axisymmetric Spacetimes.