Invariance

Since a cell would be generated through an OOL process, would'nt having to presume the existence of one and the genome in it to refute the contention that a measure of genomic invariance is necessary, not be self-defeating? ❋ Unknown (2006)

This principle of time invariance is enshrined in Noether’s Theorem. ❋ Unknown (2009)

Considered formally, the admission of a coordinate system which is accelerated with respect to the original "inertial" coordinates means the admission of non-linear coordinate transformations, hence a mighty enlargement of the idea of invariance, i.e., the principle of relativity. ❋ Einstein, Albert, 1879-1955 (1950)

In contrast, quantum theory depends on a more fundamental, non-local topological invariance which is well known to be free of metrical constraints. ❋ Nicki Pombier Berger (2009)

They almost always break the Lorentz invariance which is always a huge problem because the Lorentz invariance is one of the key experimentally verified principles underlying modern science (special relativity is crucial in particle physics). ❋ Unknown (2010)

(1953, 149), and: “The feature which suggests reality is always some kind of invariance of a structure independent of the aspect, the projection” (149). ❋ Ladyman, James (2009)

This is applicable for discrete and continuous symmetries (although no time reversal symmetries) that are associated with invariance under unitary transformations. ❋ Unknown (2010)

There is, in fact, a most elegant generalization, in the context of quantum mechanics, which is applicable to all symmetries, discrete and continuous, that are associated with invariance under unitary transformations. [ref] ❋ Unknown (2010)

Put more technically, the state space of an elementary system must not contain any relativistically invariant subspaces, i.e., it must be the state space of an irreducible representation of the relevant invariance group. ❋ Gordon McCabe (2009)

Now suppose that our Lagrangian has a time-independent symmetry (we mean a symmetry as an invariance: something does not change under a set of transformations). ❋ Unknown (2010)

This would prevent our universe from ever reaching an exact state of conformal invariance in the far future. ❋ Gordon McCabe (2009)

The Weyl curvature thereby returns to zero, all particles are massless again, and conformal invariance resumes. ❋ Gordon McCabe (2009)

With conformal invariance both in the remote future and at the Big-Bang origin, we can try to argue that the two situations are physically identical, so the remote future of one phase of the universe becomes the Big Bang of the next. link ❋ Unknown (2008)