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Studies in logic and the foundations of mathematics

The Mathematical Meaning of Operationalism in Quantum Mechanics

Irving E. Segal

Published Jan 1, 1959• 48 citations
Publisher
DOI
10.1016/s0049-237x(09)70039-4

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A short philosophical and speculative essay proposing that quantum mechanics (QM) and algorithmic information theory (AIT) are actually equivalent, or reciprocal, means or operations of describing nature. An understanding of this relationship could provide a means to solve complex problems via a formal correspondence between continuous mathematics and discrete mathematics. Subjective attributes are noted between the operations and compared for their similarities as a first step to motivate additional technical research toward a formal and fundamental theorem of the relationship.
Quantum computation and quantum information is an emerging cross-disciplinary research field and includes some subjects,such as physics,computer sciences,mathematics and information sciences and so on.By employing quantum information theory,we present an adaptive mean filter program based on quantum mechanics.In the proposed mean filter,the moved window image pixels are denoted by quantum superposition states.With the action of measurement operators generated by the characteristics of pixels on the image window to adjust the weights of the mean operator window,then the filter based on quantum mechanics is proposed.Computer simulation shows that the proposed mean filter is more effective than the traditional one.