The invariance of a system defines a conservation law, e.g., if a system is invariant under translations the linear momentum is conserved, if it is invariant under rotation the angular momentum is conserved.
Mr Nozick goes on to unpack the idea of objectivity in terms of invariance under transformations of different kinds, to downgrade the notion of metaphysical necessity, and to suggest an evolutionary function for consciousness and for morals.
Unfortunately, unrestricted invariance claims are rarely true.
We have said much about the relativity of simultaneity but little about the invariance of the speed of light.
Expected utility's partition invariance makes an act's expected utility independent of selection of a partition of states and thereby increases expected utility's explanatory power.
Sobel (1994: Chap. 9) investigates partition invariance.
Noting Weyl's strong association of gauge invariance with relativity theory in Weyl's 1929 paper, Yang (1986) remarks: "Twenty years later, when Mills and I worked on non-Abelian gauge fields, our motivation was completely divorced from general relativity and we did not appreciate that gauge fields and general relativity are somehow related.
Taken together, the attributes shown to belong to what must be amount to a set of perfections: everlasting existence, immutability, the internal invariances of wholeness and uniformity, and the invariance at its extremity of being optimally shaped.
First, a selection S of a subsequence of sequence A belongs to the "domain of invariance" of B, if the probability of B (for all lags) in S is unchanged from the probability of B in A, and if the same holds for any selection S from A with a lag.
This causal relevance can be confirmed by altering any one of these variables (e.g. the density of ion channels in the cell membrane) to generate alterations in the action potential, and by verifying the consistency of the purported invariance between the variables.
