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 became the Incredible Shrinking Mother the year they started junior high. If our relationship today depended on physical clout, I would have about the same influence with them that the republic of Liechtenstein has on world politics.”
—Mary Kay Blakely (20th century)
“Thus far women have been the mere echoes of men. Our laws and constitutions, our creeds and codes, and the customs of social life are all of masculine origin. The true woman is as yet a dream of the future. A just government, a humane religion, a pure social life await her coming.”
—Elizabeth Cady Stanton (1815–1902)
“A nation’s domestic and foreign policies and actions should be derived from the same standards of ethics, honesty and morality which are characteristic of the individual citizens of the nation.”
—Jimmy Carter (James Earl Carter, Jr.)
“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)
“It is not impossible, of course, after such an administration as Roosevelt’s and after the change in method that I could not but adapt in view of my different way of looking at things, that questions should arise as to whether I should go back on the principles of the Roosevelt administration.... I have a government of limited power under a Constitution, and we have got to work out our problems on the basis of law. Now, if that is reactionary, then I am a reactionary.”
—William Howard Taft (1857–1930)