![]() ![]() What we find is that this arises as a general mathematical feature of divergence-free fields (and closed two-forms), which are the appropriate tools to describe a flow that conserves the number of states. This physically motivated understanding of the classical theory can be used to characterize both the physics and the geometry underlying the principle of stationary action. We have found that Lagrangian mechanics is equivalent to three assumptions: determinism/reversibility, independence of degrees of freedom and kinematics/dynamics equivalence 7. We are left to wonder: what exactly is the action and why is it stationary for actual trajectories?Īs part of our larger project Assumptions of Physics, we developed an approach, called Reverse Physics 6, which examines current theories to find a set of starting physical assumptions that are sufficient to rederive them. Moreover, the Lagrangian for a system is not uniquely defined, making the actual value of the action for a path not directly physically significant. First of all, the typical characterization of the Lagrangian as the difference between kinetic and potential energy fails even for simple systems, like a charged particle under a magnetic field. This use of the Correspondence Principle can provide considerable insight into the underlying classical physics embedded in quantal systems.While the principle of stationary action is regarded by many as one of the most important tools in physics, its physical meaning is not completely clear 1, 2, 3, 4, 5. Example \(14.12.1\) showed that there is a close correspondence between classical-mechanics predictions, and quantal predictions, for both the rotational and vibrational collective modes of the nucleus, as well as for the single-particle motion of the nucleons in the nuclear mean field, such as the onset of Coriolis-induced alignment. The nucleus is the epitome of a many-body, strongly-interacting, quantal system. For example, this book has studied the classical-mechanics analogs of the observed behavior for typical quantal systems, such as the vibrational and rotational modes of the molecule, and the vibrational modes of the crystalline lattice. ![]() The Correspondence Principle now is used to project out the analogous classical-mechanics phenomena that underlie the observed properties of quantal systems. Quantum theory now is a well-established field of physics that is equally as fundamental as is classical mechanics. ![]() Bohr’s Correspondence Principle played a pivotal role in the development of the old quantum theory, from it’s inception in 1912, until 1925 when the old quantum theory was superseded by the current matrix and wave mechanics representations of quantum mechanics. Bohr’s Correspondence Principle requires that the predictions of quantum mechanics must reproduce the predictions of classical physics in the limit of large quantum numbers. Similarly, the General Theory of Relativity reduces to Newton’s Law of Gravitation in the limit of weak gravitational fields. ![]() For example, Einstein’s Special Theory of Relativity satisfies the Correspondence Principle since it reduces to classical mechanics for velocities small compared with the velocity of light. The Correspondence Principle implies that any new theory in physics must reduce to preceding theories that have been proven to be valid. ![]()
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