Axioms | |
Orthogonality and Dimensionality | |
关键词: quantum logic; Piron’s representation theorem; foundations of quantum mechanics; | |
DOI : 10.3390/axioms2040477 | |
来源: mdpi | |
【 摘 要 】
In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the cardinality of a maximal collection of mutually orthogonal elements (which, for instance, can be seen as spatial directions). Following this idea, we develop a formalism based on two basic ingredients, namely an orthogonality relation and matroids which are a very generic algebraic structure permitting to define a notion of dimension. Having obtained what we call
【 授权许可】
CC BY
© 2013 by the author; licensee MDPI, Basel, Switzerland.
【 预 览 】
Files | Size | Format | View |
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RO202003190030817ZK.pdf | 178KB | download |