Einstein ended his career attempting to unify the mathematical theories of electromagnetism and general relativity. His effort, while ultimately fruitless, was motivated by the faith that since everything that we observe about nature happens at the same time, there must be one consistent set of equations that demonstrate the feasibility of the universe around us. That theory should be invariant under mathematical transformations. It was the consideration of these transformations that led Einstein to special and general relativity. Strangely, Einstein did not consider these ideas to be "revolutionary": they appeared to him to be a natural extension of the work of others.
However, the idea of mathematical invariance subsequently took a powerful hold over the community of theoretical physicists. The power of mathematical invariance is seductive. It is a healthy constraint on the imaginations of young theorists, particularly as the investment in new physics facilities has blown through decades and billions of dollars.
Along with the frame invariance of relativity, particle theory has adopted a few other principles to guide its search for a "grand unification": a theory that integrates all known physics. We list these below.
Causality - meaning, in effect, that all of the observable behavior of fermions is mediated by gauge fields, which, if massless, move at the speed of light.
Symmetry. The presumption that, deep down inside, all fermions are interchangeable, and all gauge fields are interchangeable. The theory presumes that the spatial dimensions are special types of field, so we have:
- A mathematical foundation in group theory, which explores the dimensionality of mathematical objects, and the nature of the mathematical objects that regulate their transformations.
- Fermions in families of 16.
- 26-dimensional gauge fields, 10 of which correspond to spatial dimensions.
Symmetry breaking - the presumption that the diversity of physics arises because some of the gauge fields have mass.
This is a prejudice that arises solely out of theoretical success in applying group theory to field theory.
There are certain mathematical constraints that were required for a successful unification. These include:
- A particle's charges are constrained to the same position, but oscillate on a one-dimensional topological "string".
- Predictions for energetically suppressed physics - both particles and fields - at least one order of magnitude more complex than the actual observable physics.
Neither of these last two assertions is directly falsifiable.