Physical Laws Derived From Symmetry Principles
Many fundamental physical laws are mathematical consequences of various symmetries of space, time, or other aspects of nature. Specifically, Noether's theorem connects some conservation laws to certain symmetries. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different than any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose-Einstein condensation for bosons. The rotational symmetry between time and space coordinate axes (when one is taken as imaginary, another as real) results in Lorentz transformations which in turn result in special relativity theory. Symmetry between inertial and gravitational mass results in general relativity.
The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space.
One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions.
Read more about this topic: Physical Law
Famous quotes containing the words physical, laws, derived, symmetry and/or principles:
“... life is moral responsibility. Life is several other things, we do not deny. It is beauty, it is joy, it is tragedy, it is comedy, it is psychical and physical pleasure, it is the interplay of a thousand rude or delicate motions and emotions, it is the grimmest and the merriest motley of phantasmagoria that could appeal to the gravest or the maddest brush ever put to palette; but it is steadily and sturdily and always moral responsibility.”
—Elizabeth Stuart Phelps (1844–1911)
“In time of war the laws are silent.”
—Marcus Tullius Cicero (106–43 B.C.)
“All moral discipline, all moral perfection derived from the soul of literature.”
—Thomas Mann (1875–1955)
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)
“Magic is akin to science in that it always has a definite aim intimately associated with human instincts, needs, and pursuits. The magic art is directed towards the attainment of practical aims. Like other arts and crafts, it is also governed by a theory, by a system of principles which dictate the manner in which the act has to be performed in order to be effective.”
—Bronislaw Malinowski (1984–1942)