Why Does Theoretical Physics Fail to Explain and Predict Earthquake Occurrence?

1. The multidimensional character of seismicity: time, space, and earthquake focal mechanism need to be modeled. The latter is a symmetric second-rank tensor of a special kind. 2. The intrinsic randomness of earthquake occurrence, necessitating the use of stochastic point processes and appropriate complex statistical techniques. 3. The scale-invariant or fractal properties of earthquake processes; the theory of random stable or heavy-tailed variables is significantly more difficult than that of Gaussian variables and is only now being developed. Earthquake process theory should be capable of being renormalized. 4. 4. Statistical distributions of earthquake sizes, earthquake temporal interactions, spatial patterns and focal mechanisms are largely universal. The values of major parameters are similar for earthquakes in various tectonic zones. The universality of these distributions will enable a better foundation for earthquake process theory. 5. The quality of current earthquake data statistical analysis is low. Since little or no study of random and systematic errors is performed, most published statistical results are artifacts. 6. During earthquake rupture propagation, focal mechanisms sometimes undergo large 3-D rotations. These rotations require non-commutative algebra (e.g., quaternions and gauge theory) for accurate models of earthquake occurrence. 7. These phenomenological and theoretical difficulties are not limited to earthquakes: any fracture of brittle materials, tensile or shear, would encounter similar problems.