We are a loosely bound group of physicists and astronomers with a common interest in Einstein’s dream of unifying the “low-grade wood” of matter and energy with the “fine marble” of geometry (as he put it in a 1936 article in the Journal of the Franklin Institute). Our approach follows one originally due to Kaluza and Klein, but with important differences. Like Kaluza, we begin with Einstein’s field equations in D > 4 dimensions and assume no higher-dimensional sources (i.e., we do not put in any matter or energy terms “by hand”). Unlike Klein and many others since, we avoid overly restrictive assumptions about the physical units, scale or topology of the extra coordinates. Dimensional reduction then leaves us with the standard field equations of four-dimensional general relativity, along with extra terms arising solely from the geometry of the higher-dimensional manifold. We move these terms to the right-hand side of the field equations; that is, we identify them with matter and energy in the four-dimensional world. Our approach can be summarized mathematically as follows (where A,B = 0,1,2,3, … D):
Space-Time-Matter (STM) theory has important features in common with other geometrically motivated unified-field theories, including those based on strings, branes and large extra dimensions. It is consistent with the classical tests of general relativity in the solar system, as well as cosmological and other experimental data. It also contains a candidate for dark matter in the form of higher-dimensional analogs of black holes known as solitons. The theory is generally covariant in five dimensions, not four, so it must violate four-dimensional conservation laws at some level, and therefore be testable in principle. Experimental and observational constraints discussed so far involve the dynamics of spinning bodies, violations of the equivalence principle, a time-dependent cosmological “constant” and others.