On the number of spatial dimensions

Abstract

[EU] Dimentsio espazialen kopuruaren azterketa ikuspegi ezberdinetatik abiatuz. Alde batetik, dimentsio gehiago eskatzen dituzten teoriak jorratu dira, eta bestetik, printzipio antropikoa erabiliz, egile ezberdinek emandako argudioak bildu dira.

[EN] Most physical theories take the number of spacetime dimensions for granted, they are constructed according to the number of dimensions perceived by us: three spatial ones, and a single time one. The aim of this study is to analyse proposals which question this assumption, either by stating that our universe could have a different number of dimensions, or by arguing that the number in fact agrees with our perception. Bearing in mind that the majority of theories involving a different dimensionality of spacetime refer to the spatial dimensions, these are the ones which will be focused on. Two radically different approaches have been chosen for this purpose. On the one hand, attempts to formulate a unified theory of physics have been considered, which often postulate additional spatial dimensions. This approach has had a significant impact on our understanding of spatial dimensions, and has led to a thorough consideration of extra compact dimensions. On the other hand, the reasoning induced by the anthropic principle will be studied, and its specific application on the number of dimensions. Firstly, unified theories will be discussed in a chapter composed of two sections, the Kaluza-Klein theory will be explained in the former, and string theory, in the latter. The Kaluza-Klein theory postulates an extra spatial dimension, in order to construct a unified theory of electromagnetism and gravitation. As regards to string theory, the focus will be on a single calculation, due to a particularity of the theory under question: the number of spacetime dimensions is not postulated, it is a requirement of the theory. Secondly, regarding the anthropic principle, as forementioned, the actual reasoning it entails is what the chapter will be centred on. Therefore, its historical development will be exposed, that is to say, the precedents from which it arose will be explained, and subsequently, the application of this reasoning on the number of spatial dimensions will be considered.