Quantization causes waves: smooth finitely computable functions are affine


报告题目Quantization causes waves: smooth finitely computable functions are affine


报告人V. Anashin 教授 (莫斯科大学数学系)






摘要:  Every automaton (a letter-to-letter transducer) over a p-symbol alphabet performs a mapping  of infinite words to infinite words. This mapping can be considered as a function (the automaton function) defined on (and valued in) the set of all p-adic integers.We can consider a sort of a graph (a plot) of the automaton function in the unit real square or (which is even more natural) on the unit real torus.It is shown that if the automaton is finite then necessarily every smooth (of class C^2) curve in the plot is a torus winding. The winding can naturally be associated to a standard expression of a de Broglie wave (the matter wave). As every automaton can be considered as a concrete manifestation of the causality law,the result gives some mathematical reasoning why quantum systems are adequately described in terms of  wave functions: Waves emerge inevitably just as a consequence of causality and of quantization (and wider, of the discreteness of matter at Plank's length level). From this view the result can be considered as a contribution to the informational interpretation of quantum theory. Also, the result has applications to (and the problem was motivated by) cryptography and to computable functions.






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