Invariance Quotes

Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don't get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability – which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948. (Steven Weinberg)
One of the things that excited me so much about quantum chromodynamics after the work of Gross and Wilczek and Politzer was that it seemed to provide a rational explanation for what had always been mysterious to me - the fact that there were symmetries, like parity conservation, charge conjugation invariance, and strangeness conservation, that were very good symmetries of the strong and electromagnetic interactions - as far as we knew exact - and yet were not respected by the weak interactions. Why should nature have ... symmetries that are symmetries of part of nature but not other parts of nature? View quote
Steven Weinberg
Like all obsessions, Ballard's novel is occasionally boring and frequently ridiculous. The invariance of its intensity is not something the reviewer can easily suggest. Ballard is quite unlike anyone else; indeed, he seems to address a different - a disused - part of the reader's brain. You finish the book with some bafflement and irritation. But this is only half the experience. You then sit around waiting for the novel to come and haunt you. And it does. View quote
Martin Amis
Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. ...whilst leaving some underlying theme unchanged. ...for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time... the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation... discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be. There were fewer roles for the Deity to play... View quote
John D. Barrow
The conformal invariance of the Yang-Mills equations in four dimensions greatly facilitates the study of the temporal asymptotic behavior of their solutions. View quote
John C. Baez
Ours, according to Leibnitz, is the best of all possible worlds, and the laws of nature can therefore be described in terms of extremal principles. Thus, arising from corresponding variational problems, the differential equations of mechanics have invariance properties relative to certain groups of coordinate transformations. View quote
Carl Ludwig Siegel
The possibility and significance of fractional angular momentum is discussed, and some simple physical realizations of it are mentioned. This leads naturally to consideration of the possibility of fractional quantum statistics, which is seen to be a possibility inherent in the kinematics of 2+1 dimensional quantum mechanics. Both sorts of fractionalization are intimately related to theories, and the classic considerations of Aharonov and Bohm on the significance of the vector potential in quantum mechanics. The meaning and importance of discrete gauge invariance in continuum theories is pointed out. Fractional statistics is shown to have a simple dynamical realization in the dynamics of charge-flux tube composites. Fractional statistics is shown to occur very naturally in the most geometrical quantum field theories in 2+1 dimensions, that is in the nonlinear sigma model and in quantum electrodynamics. View quote
Frank Wilczek