Lagrangian ubiquity

[AntonioLao]

Unless two gravitating objects come into actual physical contact, Lagrangian points always exist. These are points of zero gravity. On the other hand, the question arise: "Just how close physical contact must be in order to be defined as actual physical contact?" Nevertheless, actual physical contact can be defined if and only if the angular momentum of each object is zero, or if not zero must be in the same direction. On the contrary, if the angular momenta are infinitesimally small but never exactly zero and never pointed in the same direction then Lagrangian points always exist somewhere, sometime, and in every possible location of the spacetime continuum.

In this sense, the existence of Lagrangian points can be interpolated into the infinitesimal regions between quarks. Since quarks are always in local motions, their angular momenta cannot be zero. Since quarks have mass, they are classified as gravitating objects. However, the existence of Lagrangian points among them prevent them from coming into actual physical contact. This is an alternative explanation for the existence of asymptotic freedom, implying that quarks are free as long as their angular momenta are not zero and not pointing in the same direction. The ideal differentiable directions are simply orthogonal directions, providing some unique values for orthonormal basis for every 2-quark or 3-quark configuration. The first is the meson configuration. The second is the baryon configuration. These are respectively analogous to the two-body and three-body problems of Newtonian mechanics. The final analysis of all local and global Langrangian points altogether comprises the existence of the spacetime continuum. Furthermore, these can be used to defined the square of zero-point energies of the quantum vacuum fluctuations.