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:
“I have no purpose to introduce political and social equality between the white and black races. There is a physical difference between the two, which, in my judgement, will probably for ever forbid their living together upon the footing of perfect equality; and inasmuch as it becomes a necessity that there must be a difference, I ... am in favour of the race to which I belong having the superior position.”
—Abraham Lincoln (1809–1865)
“Nature and Nature’s laws lay hid in night;
God said Let Newton be! and all was light.”
—Alexander Pope (1688–1744)
“The sceptics assert, though absurdly, that the origin of all religious worship was derived from the utility of inanimate objects, as the sun and moon, to the support and well-being of mankind.”
—David Hume (1711–1776)
“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)
“My country is bleeding, my people are perishing around me. But I feel as a South Carolinian, I am bound to tell the North, go on! go on! Never falter, never abandon the principles which you have adopted.”
—Angelina Grimké (1805–1879)