Abstract
After nearly a century of development, the central conceptual and interpretive problems in quantum mechanics still remain unsettled, even in the wake of marked improvements in technology and experimental methodology. Among these now infamous and interrelated problems are: [1] the problem of measurement; [2] quantum nonlocality; [3] the coherent integration of quantum and classical physical theories. In our current project, we demonstrated how all three of these difficulties can be properly understood as aspects of a single problem: the absence in quantum mechanics of a formal means of relating local to global in an extensive continuum. While this problem is most popularly exemplified in the incompatibility of quantum mechanics and the general theory of relativity, we demonstrated that its proper solution lies first in recognizing the centrality of local-global relations in all three of the aforementioned problems; and second, recognizing that the overall genesis of difficulty is the presumption of a fundamentally metrical theory of extension grounded in a set-theoretic structure. While this convention has clearly proven fruitful as a conceptual framework for formal physics, the latter's evolutionary leap in the early 20 th century with the advent of quantum theory and general relativity has rendered explicit its limitations—viz. its vulnerabilities to paradoxes, singularities, and infinites.