Heim Quantum Theory is an attempt to unify quantum theory and general relativity, based on the work of the German physicist Berkhard Heim. Heim Theory is also used to refer to various theories which extend or generalize Heim's work, such as those put forth by his long-time collaborator Walter Dröscher.
Heim Theory is a quantized form of General Relativity and proposes a quantized spacetime similar to Loop Quantum Gravity. All fundamental forces are described geometrically in higher-dimensional spaces in the same way that gravity is explained by General Relativity, but all additional dimensions above the four classical dimensions of space & time are considered to be purely mathematical abstractions with no real physical interpretation.
Unlike most of string theory, Heim Theory makes several directly testable predictions. In its original version, Heim Theory used six dimensions, which allowed the derivation of formulae for calculating the masses of elementary particles. This is perhaps the most important part of Heim Theory currently, as it is the most easily tested and no other current theory of elementary particles is capable of making such predictions. Currently, the predicted particle masses are all within the range of experimental error for observed particle masses, and have improved with better measurements of the value of G, one of the four parameters used in the particle mass calculations.
Dröscher's 8-dimensional extension reproduces the group structure of the standard model of particle physics and reproduces all of the known fundamental interactions(electromagnetism, weak nuclear force, strong nuclear force, and gravity). However, it also predicts two additional as-yet-unobserved fundamental interactions and their carrier particles (the gravitophoton and the repulsive vacuum or quintessence particle). The first new interaction, mediated by gravitophotons, allows the transformation of electromagnetic radiation into a gravity-like field. An experiment has been proposed to test this, involving a rapidly spinning torus of insulating material suspended in a high-intensity radial magnetic field. If Heim Theory is correct, this should result in a Heim-Lorentz Force, analogous to the Lorentz Force but acting on all matter, not just charged particles. The major obstacle to this experiment is generating sufficiently powerful magnetic fields, but Sandia National Laboratories' Z machine may be up to the job. The second new interaction may explain the origin of dark energy.
A final 12-dimensional version of Heim Theory uses the extra four dimensions to describe probability state space.
If proven correct, Heim Quantum Theory would cause a revolution in current physics, most notably in the area of propulsion, due to the extra two predicted fundamental interactions. The predicted gravitophoton field could potentially be used to construct a Gravitophoton Field Propulsion engine, a type of space drive powered by extracting energy from the quantum vacuum, as described in "Heim Quantum Theory for Space Propulsion Physics" (Walter Dröscher and Jochem Häuser, 2005).
Update: It seems that the biggest peice of evidence supporting Heim Theory, the correct prediction of particle masses, may not be all that great after all. Apparently, Berkhard Heim input the particle masses into the theory directly, just as the Standard Model does--they just happened to be sufficiently well hidden among other universal constants that nobody noticed for a while.