Double-Slit Interference and Temporal ToposFoundations of Physics
AbstractThe electron double-slit interference is re-examined from the point of view of temporal topos. Temporal topos (or t-topos) is an abstract algebraic (categorical) method using the theory of sheaves. A brief introduction to t-topos is given. When the structural foundation for describing particles is based on t-topos, the particle-wave duality of electron is a natural consequence. A presheaf associated with the electron represents both particle-like and wave-like properties depending upon whether an object in the site (t-site) is specified (particle-like) or not (wave-like). It is shown that the localization of the electron at one of the slits is equivalent to choosing a particular object in the t-site and that the electron behaves as a wave when it passes through a double-slit because there are more than one object in the t-site. Also, the single-slit diffraction is interpreted as a result of the possibility of many different ways of factoring a morphism between two objects.
Citation InformationGoro Kato and Tsunefumi Tanaka. "Double-Slit Interference and Temporal Topos" Foundations of Physics Vol. 36 Iss. 11 (2006) p. 1681 - 1700
Available at: http://works.bepress.com/gkato/7/