The fact that the nuclear and Electromagnetic theories all rely on the Gauge Invariance principle, and that the latter in turn is closely related to General Covariance has raised the hope that perhaps these are pieces of the same theory. The differences could arise due to specific limiting conditions and if only we know how to transcend these, there would be a single theory with a unique symmetry principle and requiring only one coupling constant. Specifically, it is proposed that at extremely high energies of interaction, or equivalently, under explorations of space-time regions at a super-microscope scale, the limiting conditions disappear.
The earliest attempts along these lines were those of T. Kaluza and O. Klein. In sec. 3.3, the notion of space was proposed to be expanded by attachment of a copy of the gauge function space at every point. This latter space happened to be a circle. Kaluza and Klein proposed that this circle actually constitutes an extra - fifth - dimension of space-time but with two important differences. Firstly, this dimension is not open or unending like the ordinary dimensions. It is closed up to make a circle. Secondly, the scale of distances on this circle is so tiny that in all the experiments so far, we do not perceive any ``motion'' into this dimension. Thus this dimension is elevated to the same status as the usual dimensions and endowed with a distance scale, something not proposed for the auxiliary dimension. The remarkable fact was that the observed gauge invariance could now be derived as a residual effect of the full fledged 5-dimensional General Covariance in the limit that the fifth dimension was small and closed.
The Kaluza-Klein proposal can be generalised to include the gauge function spaces of the nuclear forces. Then all one would need is General Covariance on a space-time of some large number of dimensions, eleven according to one proposal. These ideas however do not work because there are some fundamental facts predicted from them which conflict with observations. Alternatively one has to modify the idea in some complicated and inelegant way.
Through the 1970's and 1980's, several deep and elegant proposals have been made for unification, but I shall mention only two more in support of a point to be made in the concluding section. One is the Grand Unification proposal of Georgi and Glashow. Here Gravity is not included. It is proposed that the space of the nuclear gauge functions is 24-dimensional and that only one coupling constant is sufficient to explain all the observed gauge forces. The theory failed because the proton did not display the required miniscule extent of instability towards decay into lighter particles. A more ambitious and far reaching proposal are the Superstring theories. These exploit intricate symmetries of two dimensional spaces to explain all the observed forces, including Gravity. It also has the potential to explain certain other things physicists never expected to be able to explain. This includes the dimensionality of the space-time we live in. It also unifies Gravity and nuclear forces elegantly. Superstring theories are yet being explored. The absence in them of any verifiable predictions makes their relevance of Physics all the harder to explain.