07 August 2022

On Conservation Laws (1950-1999)

"In conventional statistical mechanics the energy plays a preferred role among all dynamical quantities because it is conserved both in the time development of isolated systems and in the interaction of different systems. Since, however, the principles of maximum-entropy inference are independent of any physical properties, it appears that in subjective statistical mechanics all measurable quantities may be treated on the same basis, subject to certain precautions." (Edwin T Jaynes, "Information Theory and Statistical Mechanics" I, 1956)

"It is common knowledge today that in general a symmetry principle (or equivalently an invariance principle) generates a conservation law. For example, the invariance of physical laws under space displacement has as a consequence the conservation of momentum, the invariance under space rotation has as a consequence the conservation of angular momentum." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"Whereas the continuous symmetries always lead to conservation laws in classical mechanics, a discrete symmetry does not. With the introduction of quantum mechanics, however, this difference between the discrete and continuous symmetries disappears. The law of right-left symmetry then leads also to a conservation law: the conservation of parity." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"The law of causality is no longer applied in quantum theory and the law of conservation of matter is no longer true for the elementary particles." (Werner K Heisenberg, "Physics and Philosophy: The revolution in modern science", 1958)

"In the everyday world, energy is always unalterably fixed; the law of energy conservation is a cornerstone of classical physics. But in the quantum microworld, energy can appear and disappear out of nowhere in a spontaneous and unpredictable fashion." (Paul C W Davies, "God and the New Physics", 1983)

"There is a fact, or if you wish, a law governing all natural phenomena that are known to date. There is no known exception to this law - it is exact as far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens." (Richard P Feynman et al, "The Feynman Lectures on Physics" Vol. 1, 1983)

"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures. [...] In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"What is conserved, in modern physics, is not any particular substance or material but only much more abstract entities such as energy, momentum, and electric charge. The permanent aspects of reality are not particular materials or structures but rather the possible forms of structures and the rules for their transformation." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

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