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The General Principle of Interaction (GPI) is a materialistic philosophical concept formulated as an attempt to generalize the Einsteinian concept of curved spacetime in order to explain all types of physical interactions with the spacetime (vacuum) geometry. It assumes that any type of physical interaction is governed by a certain type of geometrical deformations of the spacetime that contains a number of unobservable extra dimensions in addition to the ordinary three spatial dimensions and the time dimension. It is expected that the eight-dimensional (8D) extension of the Einstein-Cartan theory will be able to describe the elementary particles as certain wave-like vacuum deformations of the “extended” 8D spacetime. This differential geometry-based theory may be highly complex and hasn’t been yet fully described mathematically.

The Einsteinian understanding of interaction is the core philosophical feature of the theory of General Relativity (GR) that explains gravity as a geometric property of spacetime (as space and time are combined according to the theory). According to the Einsteinian understanding of interaction, matter curves spacetime, which defines the path of an object in the gravitational field. Albert Einstein had made some attempts to interconnect his concept of gravitation with the concept of electromagnetic field and possibly unify the two fundamental forces. Unfortunately, none of those attempts to build a unified classical field theory was successful. It seems very likely that the four-dimensional spacetime cannot induce any force other than gravity. Then, what kind of spacetime deformations would govern other interactions like electromagnetism and nuclear forces? The GPI assumes that the spacetime actually contains more than four ordinary dimensions we sense. It is possible that the “full” spacetime contains certain “unseen” extra dimensions that we cannot test in principle. The geometry of these extra dimensions may be useful to explain forces other than gravity. In 1921, Theodor Kaluza proposed the description for such an extended five-dimensional (5D) spacetime containing an “unseen” fifth dimension that supposedly helps to explain electromagnetism. In 1926, Oskar Klein proposed that the fifth dimension is compactified. Since then, all physical theories extending the GR by introducing a 5D spacetime (even with a noncompact fifth dimension) are called Kaluza-Klein (KK) models. Although Einstein was fond of the Kaluza's idea and tried to implement it in his theoretical works, he was unable to find a successful theory that unifies gravity with electromagnetism in its quantum description. The Einstein's KK models had remained classical and not led to a viable theory of particle interactions that would replace quantum electrodynamics.

Unfortunately, neither Einstein nor others assumed that the electromagnetic field might be actually originated in the fifth dimension and primarily defined by its geometry, not by the four-dimensional geometry. On the contrary, Einstein had accepted Kaluza’s “cylinder condition” stating that physics does not depend on the extra coordinate. Avoiding this fatal flaw, the GPI stipulates that particles’ interactions actually occur in the undetectable subspaces of the “full” spacetime: the “electromagnetic” (fifth, noncompact) dimension and the “nuclear” subspace (additional three dimensions, compactified). Thus, gravity and other fundamental forces can be described via vacuum deformations of the three different “parts” of space, which are bound to one time dimension. This concept makes possible to describe the elementary particles as extra-dimensional wave-like spacetime deformations with integer wavelengths (i.e. quantized naturally). Due to the unobservable nature of the “electromagnetic” and “nuclear” dimensions, the relevant theory will require not classical, but quantum field methods (i.e. complex-valued operators) to describe particle interactions. This would allow in principle to find a unique background-independent unified field theory that would combine (at least in general) the achievements of quantum theories of the Standard Model with the Einsteinian understanding of interaction as in the GR, additionally having a number of advantages over the modern quantum field unification approaches.