ABSTRACT
In this chapter, the authors examine some of the most common uses of N-Dimensional “spaces” in modern physics practice and identify the care with which their must handle them when conversing with non-specialists about these practices. They discusses the “scare-quotes” around many words that have been borrowed from the language of physical Space and trust that readers will not fall into confusion as a result. N-dimensional space simply refers to a number of independent variables employed to mathematically grapple with a physical system of interest. Indeed, by formalizing non-intuitive mathematical definitions of everyday words, mathematicians have successfully devised variations on non-Euclidean geometry since the nineteenth century. Hilbert space extends the Euclidean Space of our experience to an arbitrary, mathematical vector space where the different dimensions represent independent parameters of a quantum mechanical system. A non-Euclidean property of “straightness” has a mathematical definition divorced from what the word means in the context of Euclidean Space.
