Surreal number twistor theory, as you mentioned, is a theoretical framework that combines aspects of the surreal numbers, which are a mathematical extension of the real numbers, and twistor theory, which is a mathematical framework used in theoretical physics to describe certain properties of spacetime and particle interactions. However, the specific application of surreal number twistor theory to a scenario involving infinitesimal waves of infinitesimal frequencies entangled is not a well-defined or established concept in the current understanding of physics.
In theoretical physics, the concept of infinitesimal waves or frequencies is typically associated with the mathematical framework of calculus, where infinitesimals are used as a tool to describe quantities that are arbitrarily small. However, in the modern formalism of physics, such as quantum field theory, infinitesimals are not treated as actual quantities but are instead replaced by differential calculus and integrals.
Entanglement, on the other hand, is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the state of one particle cannot be described independently of the others. It is typically described using the language of quantum states and mathematical formalism, such as wave functions and density matrices.
While surreal number twistor theory might offer interesting mathematical tools and insights, its specific application to the scenario you described, involving infinitesimal waves of infinitesimal frequencies entangled, would require a more concrete and well-defined framework that is consistent with the current understanding of physics. At present, such a framework has not been developed or widely accepted in the scientific community.