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. The issues that it once helped with are now dealt with by descriptions of a process called decoherence, an intrinsic implication of the quantum theory without any extra philosophical baggage.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. There remain some serious questions about the interpretation of that stage, but the complementarity principle is not really of any use in addressing these questions. The behavior that emerges at large scales involves the apparent disappearance of part of the resulting wave-like state. The electron's (or other small object's) behavior is governed by a wave-like equation at all times. As we've gotten more used to using quantum mechanics, those qualitative descriptions seem less and less relevant. Typically, one is taught that this means that an electron can either be a particle or a wave, depending on the circumstances. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. This crucial point.implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear. Here's what Bohr said about complementarity, borrowed from Wikipedia: It doesn't apply to any of the many experimental set-ups used to violate the Bell Inequalities, which apply to anything even vaguely like classical mechanics. It doesn't apply to superconductivity, magnetism. However, there are certain special cases especially involving mechanical behavior in which it works. However, the question is important and my answers will not be the sort most teachers would like, so here goes.īohr's correspondence principle states that the behavior of large enough quantum things comes very close to obeying the laws of classical physics. This looks suspiciously like a homework assignment.
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