It is expected that the full unification is achievable within a quantum field theory “beyond the SM” (Standard Model). An alternative approach is the Kaluza-Klein (KK) extension of the General Relativity (GR) with extra dimensions. However, there is a third possibility that no unification is achievable due to the specific fractal structure of the spacetime and the unique position of the observer situated inside the ordinary (gravitational) subspace and outside the compact extra dimensions, the geometry of which governs particle interactions. The Fractal spacetime concept (FSC) is proposed in order to support the General principle of interaction (GPI), which postulates that all the nature’s forces with no exceptions are governed by the spacetime geometry. The FSC postulates that the spacetime includes three separate subspaces (in addition to the time dimension): the three-dimensional ordinary subspace, the atomic-sized fifth dimension sufficient to explain the electromagnetism, and the set of three nuclear-sized dimensions sufficient to explain the nuclear forces. The spacetime has a simple fractal structure: each of the three subspaces presumably has a spherical shape with the sizes decreased tremendously from one subspace to another. The size differences are responsible for the separation of the subspaces and gradually increased action powers of the three fundamental fields: gravitational, electroweak and strong fields. The present letter shows that the SM equations actually describe the extradimensional spacetime deformations approximated as the gauge quantum fields. With the geometrical approach, the SM can be simplified, as only four types of elementary spacetime deformations (extradimensional waves) are needed: electron, positron, uuu, and ūūū quark triplets. All other elementary particles including photons and gluons are binding states or/and wave polarization modes of the above-mentioned waves. The neutrinos, the weak bosons, and the Higg’s particle are avoided. All particles’ interactions are governed by the positive or negative extradimensional curvatures and the spin-related torsion induced in the nuclear or electromagnetic subspace by the color or electric charges (respectively). The particles’ gravitational interactions are governed by the charge-induced deformations of the ordinary subspace described by the Higg’s field. With the FSC, the GPI explains the geometry-based unified nature of all known interactions. However, a single unified field theory is not possible in principle due to the observational difference between the large geometry of the ordinary subspace and the compact geometry of the extra dimensions. Thus, in general, the FSC supports both the GR and the SM. In special cases, however, it will require quantum field descriptions of gravitational interactions.