k.karaca@utwente.nl

Koray Karaca

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The Higher Dimensional Unification Program in Physics 
 
By: Koray Karaca 
 
In this paper, I aim to call attention to the higher dimensional unification program (HDUP) in physics that 
culminated in a class of higher dimensional space-time theories—aka Kaluza-Klein (KK) theories—aiming 
to unify gravity with gaugefields in a higher dimensional Riemannian space-time. Despite the 
immenseness of the physics literature on the topic on higher dimensional unification, unfortunately 
except a limited number of sources, such as Weingard 1988, Vizgin 1994, Cao 1997 and van Dongen 
2002, the literature of history and philosophy of science is very sparse with regard to the issue of higher 
dimensional unification. In the present work, I adopt a methodology that is both philosophical and 
historical. My historical analysis traces the emergence and development of HDUP as a research program. 
It also complements my philosophical analysis by showing how the methodology of theory construction 
in HDUP has evolved and changed over the years. I divide the history of HDUP into two distinct, but 
related, periods. What I call the classical period concerns the five-dimensional KK theory constructed by 
the joint efforts of Theodor Kaluza (1921)and Oskar Klein(1926)in the twenties to unify gravity with 
electromagnetism in a five-dimensional Riemannian space-time. And, what I call the modern period of 
HDUP spans the late seventies to the early eighties and concerns modern KK theories—namely, higher 
dimensional supergravity and superstring theories—which are still considered by the majority of the 
physics community to be the best hope for a complete unified theory of all physical interactions 
including gravity.  
 
My philosophical analysis aims to reveal different conceptions of unity that have operated in the history 
of HDUP. In the first part of my analysis, I examine the conception of unity underlying the five-
dimensional KK theory. I argue that the unity achieved in this theory is structural in the sense that 
electromagnetic and gravitational fields, which were previously represented under different 
mathematical representations respectively in Maxwell’s theory of electromagnetism (EMT) and 
Einstein’s theory of general relativity (GTR), were united under the same mathematical representation. 
However, I argue, the structural unity in the representation of fields did not produce any ontological 
unity regarding the fields as well as the relation between them. Nevertheless, I argue, even though the 
unity in the five-dimensional KK theory failed to yield a common understanding of gravitational and 
electromagnetic fields, in modern parlance, it can be said to have offered an understanding of U(1) 
gauge symmetry of EMT as a geometrical symmetry of space-time around the coordinate associated 
with the fifth dimension. 
 
I also compare and contrast the structural unity achieved in the five-dimensional KK theory to the unity 
in Einstein’s special theory of relativity (STR). I also characterize the unity in STR as structural in the 
sense of being achieved at the level of the mathematical representation of electric and magnetic fields. 
However, I argue, the structural unity operates differently in these two historical cases. In the case of 
STR, the mathematical representation of the electromagnetic field is irreducible; i.e., it cannot be 
reduced further to the separate representations of electric and magnetic fields. However, in the case of 
the five-dimensional KK theory, the combined mathematical representation of gravity and 
electromagnetic fields in the five-dimensional space-time is further reducible to the distinct irreducible 
representations offered by GTR and EMT in the four-dimensional space-time. Based upon this result, I 
conclude that the structural unity in the five-dimensional KK theory is weaker than the structural unity in 
Einstein’s STR. 
 
My analysis of the modern period of HDUP is guided by my analysis of the historical link between the 
classical and the modern periods of HDUP. First, I explore how the five-dimensional KK theory re-
entered the practice of current physics in the seventies after having stayed dormant for almost half a 
century. To this end, I discuss the historical reasons behind physicists’ changing attitudes towards the 
issue of higher dimensional unification in general, and towards KK theory in particular. I argue that the 
revival of KK theory in the seventies was largely fueled by the confluence of two factors: First, the desire 
to incorporate gravity into the gauge-theory program—which had unified fundamental force fields 
except gravity—led the relevant physics community to adopt a new conception of unity that aimed to 
unify nuclear force fields with gravity. Second, in the sixties it was realized by the joint efforts of 
physicists such as DeWitt 1964, Kerner 1968 and Trautman 1970 that with the addition of more spatial 
dimensions the mathematical formalism of the five-dimensional KK theory—which was originally used to 
unify gravity and electromagnetic fields—could be extended as to include also the mathematical 
representations of nuclear force fields—namely, weak and strong force fields. This in turn led the 
physics community to extend and use the mathematical formalism of the five-dimensional KK theory to 
implement their new conception of unity.  
 
Lastly, I examine the way the unity was achieved in higher dimensional supergravity and superstring 
theories. Here again in this case, I argue that the unity obtained is a kind of structural unity, i.e., unity in 
the mathematical representation of all fundamental force fields, rather than anontological unity. I also 
examine the theoretical structures of higher dimensional supergravity and superstring theories. I 
identify two key features that are common to these theories as follows: The unification of the 
representations of fields by means of enlarging the dimensionality of space, and the treatment of 
different internal symmetries associated with nuclear interactions as gauge symmetries. I also note that 
while the former feature is reminiscent of the way structural unity was obtained in the five-dimensional 
KK theory, the latter feature follows from the basic tenet of gauge-theory program. Based on this result, 
I reach the conclusion that the synthesis of higher dimensional unification with gauge symmetry 
formalism is constitutive to the theoretical structures of higher dimensional supergravity and 
superstring theories. 
 


The Higher Dimensional Unification Program in Physics

https://scholarworks.iu.edu/dspace/bitstream/2022/26137/1/The%20Higher%20Dimensional%20Unification%20Program%20in%20Physics.pdf

The Higher Dimensional Unification Program in Physics

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