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The correspondence principle connects the quantum mechanics with the classical mechanics, the relativistic classical mechanics with the Newtonian mechanics, and the theory of general relativity with the theory of special relativity. These examples give us a scenario of constructing a new theory in the grammatical way. That is to say, first we propose a new coordinate system M_{new} whose range includes the range of the old coordinate system M_{old} as a subset, and then we seek the equation for Φ(∈the domain of definition of M_{new}) which reduces to the old theory's equation for Ψ(∈the domain of definition of M_{old}) when M_{new}(Φ) = M_{old}(Ψ), and we adopt it as the equation of the new theory. It reminds me of analytic continuation and Tayler expansion. However, even when such an equation doesn't exist, it does not mean immediately that the new grammar has failed, and we can hope that we find an appropriate equation which is as near to that as possible. Actually, in the case of the transition from the classical mechanics to the existing quantum mechanics, the Schrödinger equation doesn't have more desirable features than the Ehrenfest theorem. This is not a fault of the Schrödinger equation but a fault of the condition proposed above by me. An example of making new equation is seen in Uda Equation @ Theory of Quantum History Entangled in Timelike Direction @ Products.  The content of this article was presented at APS+JPS 2006 Autumn Meeting.  ref. Correspondence principle  Wikipedia 

Author Yuichi Uda, Write start at 2016/04/04/12:18JST, Last edit at 2016/04/04/14:52JST  




