Why No Physical Universe Can Exist Without Constraint: A Structural Theorem

Key Points

• This theorem explores the role of constraints in establishing meaningful physical structures and dynamics in a universe.
• Developed a model-independent theorem
• Analyzed the relationship between automorphism groups and symmetric groups
• Explored implications of symmetry reduction on physical observables
• Demonstrates that nontrivial structures and dynamics arise from symmetry constraints
• Establishes that the absence of constraints leads to a non-physical universe
• Finds a necessary and sufficient condition for physical meaningfulness