The uncertainty relation for an assembly of Planck-type oscillators. A possible GR-quantum mechanics connection

It is shown that an assembly of Planck-type oscillators may be described by a continuous group with three parameters. In such a case, the uncertainty relation may be obtained by the application of a theorem on the invariant functions, when a simultaneous action of two isomorphic groups is involved. The groupʹs parameters are interpreted by means of a variational principle, as field amplitudes of a stationary metric, while the groupʹs invariant function is interpreted as the square root of a wave function satisfying a Schrödinger-type equation.