Frameindifferent

Frameindifferent, also written frame-indifferent or frame indifference, is a concept in physics and continuum mechanics describing the invariance of physical laws or constitutive relations under changes of reference frame. It is closely related to the idea of objectivity or material frame indifference (MFI), which demands that material response depends only on intrinsic state and not on the observer’s orientation or motion.

In continuum mechanics, frame indifference requires constitutive equations to be objective. Mathematically, this means that if a deformation gradient F is transformed by a rigid-body rotation Q as F' = QF, then the corresponding stress measure should transform accordingly, typically sigma' = Q sigma Q^T. Consequently, constitutive models are formulated in terms of objective, frame-invariant quantities such as strain invariants or strain energy functions. To maintain frame indifference in rate-form constitutive laws, objective rates (such as the Jaumann rate) are used to prevent non-physical dependence on spin during rigid-body motions.

The principle has broad application across materials science, solid and fluid mechanics, and rheology. It guides the development of material models, ensuring consistent predictions across observers and coordinate systems. Violations or improper implementations of frame indifference can lead to spurious stresses or unphysical results, especially under large rotations or complex loading. While the core idea is widely accepted, discussions continue about its application to active matter or materials with internal structure that may couple to rotation in nontrivial ways.

See also objectivity, material frame indifference, Jaumann rate, invariant theory.