The Higher Dimensional Unification Program in Physics

Kaluza-Klein-space

A review of Historical and Conceptual Foundations of the Higher Dimensional Unification Program in Physics, by Koray Karaca.

In this dissertation, Koray Karaca provides an analysis of the “Higher Dimensional Unification Program” (HDUP) in twentieth-century theoretical physics. The HDUP is identified as a pattern of theory-building pursued by physicists in which they postulate the existence of dimensions of space-time beyond the familiar three dimensions of space and one of time. This additional theoretical structure allowed physicists to attempt to unify mathematical descriptions of the fundamental forces of nature. The HDUP proceeded in two phases: first, a five-dimensional theory, in which Einstein’s theory of gravity was unified with theories of electromagnetism, was elucidated in the 1920s separately by Theodor Kaluza and Oskar Klein (Kaluza-Klein theories, abbreviated as KK) (Chapter 3); second, in the 1970s and 1980s, “modern KK theories” in 10 and 11 dimensions that aimed to unify gravity with inter-nuclear forces were developed (Chapter 4).

Karaca uses published scientific papers to trace the development of the fundamental ideas and methods in these phases, and holds them up to the light of two philosophical questions: What is the relationship between unification and explanation (Chapters 2 and 5)? And what does it mean for a scientific theory to be “ad hoc” (Chapters 6 and 7)? The question of the relationship between explanation and unification is explored by reference to the work of Philip Kitcher and Margaret Morrison, especially the former’s “Explanatory Unification” (Philosophy of Science 48 (1981), pp.507-531) and the latter’s Unifying Scientific Theories: Physical Concepts and Mathematical Structures (Cambridge: Cambridge University Press, 2000). Karaca develops the question of what an “ad hoc” theory is through an analysis of the work of a number of philosophers. In both discussions, Karaca also includes the scientists’ views on these questions. Karaca concludes that HDUP theories fail to be explanatory on Kitcher’s model of explanation, and that HDUP theories, though “ad hoc” in a way meaningful to physicists, do not fit comfortably within extant philosophical work on “ad hoc”-ness.

How might physicists’ attempts to unify different theories be understood as helping to develop scientific explanations? It is not unreasonable to assume that the goal of science is to produce explanations. Then all this unifying would be in the service of explaining. Karaca applies Philip Kitcher’s analysis of “explanatory unification”, which is based in a “syntactic” view of scientific theories (roughly, those that view scientific theories as sets of sentences). According to Karaca, Kitcher thinks that “successful unification brings about a reduction in the number of types of facts that are taken to be fundamental to natural phenomena, and that this is essential to the scientific understanding of nature” (p.10). Central to Kitcher’s account of explanation is the concept of “argument patterns” that can be used to explain many different phenomena, for example, the treatment of a one-body problem in Newtonian mechanics (p.11). Karaca analyzes Margaret Morrison’s contrasting view that this type of unification is not explanatory. According to Morrison, in order to be explanatory a putative explanation must include a physical mechanism. But Karaca finds Morrison’s definition of “mechanism” wanting (pp.14-30). Rather, he prefers Kitcher’s account, partly on its own merits and partly because Karaca sees Kitcher’s account of explanation as capturing the normative aspect of physicists’ own views of explanation, as expressed in the published literature (pp.116-119). One of the most important points of the dissertation comes in section 5.3 where Karaca evaluates the physicists’ Kaluza-Klein (KK) unification scheme according to Kitcher’s account. Karaca finds that “KK theory fails to offer ‘argument patterns’ which Kitcher’s account requires of unification” (p.111).  This  “point[s] to a mismatch between KK unification” and Kitcher’s account (p.112).

If KK unification schemes are not explanatory, perhaps they can be diagnosed as being “ad hoc”? The next crucial section of Karaca’s dissertation is a discussion of six twentieth-century philosophical perspectives on what “ad hoc”-ness in a scientific theory might mean (Chapter 6). Karaca covers Karl Popper, Imre Lakatos, Eli Zahar, Kenneth Schaffner, Adolf Grünbaum, and Jarrett Leplin. It is not possible here to detail each account, but some general points can be noted. Karaca finds that “it is almost impossible to reach a complete consensus” among the accounts, resulting in the lack of a “received view” in the field of philosophy of science (p.120). In Chapter 7, Karaca confronts two physical theories with the philosophical positions discussed. The theories are (1) the current theory of the electromagnetic- and weak nuclear-forces and (2) the Kaluza-Klein theories discussed above. Karaca also includes published remarks by physicists on the “ad hoc”-ness of their rivals’ theories. Karaca finds that in both physical theories, the mechanisms — “spontaneous symmetry breaking” and extra dimensions respectively — are proposed “without empirical justification” (p.164). On this basis he finds that they are “ad hoc” in the same sense. However, this is not the same sense as the philosophers’ analysis of what “ad hoc”-ness is, thus opening up a new avenue for philosophical critique (p.165).

This dissertation marks a great and unique contribution to historically-attuned philosophy of science, and the humanistic analysis of important, technically sophisticated, areas of twentieth-century physics.

Aaron Sidney Wright
Institute for the History and Philosophy of Science and Technology
University of Toronto
aaron.wright@mail.utoronto.ca

Dissertation Information

Indiana University. 2010. 191pp. Primary Advisor: Jordi Cat.

 

Image: “Kaluza-Klein Space” by Professor Brad Dowden, California State University, Sacramento.

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