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:
“Whenever reality reinforces a child’s fantasied dangers, the child will have more difficulty in overcoming them...So, while parents may not regard a spanking as a physical attack or an assault on a child’s body, the child may regard it as such, and experience it as a confirmation of his fears that grown-ups under certain circumstances can really hurt you.”
—Selma H. Fraiberg (20th century)
“His talk was like a spring, which runs
With rapid change from rocks to roses:
It slipped from politics to puns,
It passed from Mahomet to Moses;
Beginning with the laws which keep
The planets in their radiant courses,
And ending with some precept deep
For dressing eels, or shoeing horses.”
—Winthrop Mackworth Praed (1802–1839)
“There is, it seems to us,
At best, only a limited value
In the knowledge derived from experience....”
—T.S. (Thomas Stearns)
“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)
“The principles of the good society call for a concern with an order of being—which cannot be proved existentially to the sense organs—where it matters supremely that the human person is inviolable, that reason shall regulate the will, that truth shall prevail over error.”
—Walter Lippmann (1889–1974)