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44 45 symmetry in physics invariance and the laws of nature Since the amount of energy in a closed system is invariant, the law of conservation of energy is now seen as a symmetry law. In fact there is a real sense in which the history of physics at least in the modern period might be characterised as a successive uncovering of such universal conservation principles. The great discoveries of Galileo and Newton concerning gravity, for instance, were essentially the recognition of physical laws that deeply affect the material world, and yet are in some sense independent of it. Newtons Law, in postulating a symmetrical force acting on all objects, discovered the invariant quality of gravity, i.e., that it is the same everywhere in the universe. By extending these laws to a moving, even an accelerating observer, Einstein added further symmetries. This was the basis of his theory of General Relativity. Gravity is now recognised as just one of four fundamental forces of nature underlying all natural phenomena. In one of the greatest intellectual achievements of the 20th century the mathematician Emmy Noether established the connection between these dynamic forces and the abstract notion of symmetry. Since the laws of physics apply equally in every part of ordinary space they are regarded as possessing translational symmetry, which, on the most basic level, is a consequence of or equivalent to the law of the Conservation of Momentum. Physical laws do not change over time either, which means that they are symmetric under translations in time, leading to a conservation law, in this case, the Conservation of Energy. In physics, there is now an absolute connection between symmetry and the laws of nature, so that physicists consciously search for invariance in their quest for new conservation laws. Reality, it seems, is threaded through with concealed symmetries. NOETHERS THEOREM For every continuous symmetry of the laws of physics, there must exist a conservation law. For every conservation law, there must exist a continuous symmetry. Emmy Noether, 1915
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