{"knowledge_schema": {"broad_category": "Physics \u2192 Relativity \u2192 Particle Physics", "refinement": "This problem involves the conservation of momentum and energy in particle collisions, specifically in the context of relativistic particles (electron and positron) annihilating to produce photons.", "specific_scope": "The focus is on determining the angle between the directions of two photons produced from the annihilation of an electron and a positron, taking into account their relativistic speeds and the conservation laws.", "goal": "Calculate the angle between the directions of the two photons produced in the annihilation event."}, "summary": "This problem is rooted in the principles of relativistic physics, specifically the annihilation of an electron and a positron resulting in the production of two photons. The scenario requires applying conservation of momentum and energy to determine the angle between the directions of the emitted photons. Given the Lorentz factors of the particles and the symmetry of the situation, the goal is to find the angle between the two photons, which can be calculated using the properties of their momenta and energies."}