Final answer:
A theory decouples from gravity when gravitational interactions can be ignored due to their negligible effects at certain energy scales. This can sometimes be seen in the theory's Lagrangian by the absence of terms related to gravity. String theory aims to unify gravity with quantum mechanics but lacks experimental evidence.
Step-by-step explanation:
When a theory is said to decouple from gravity, it means that it can be studied without taking gravitational interactions into account, which can happen at energy scales where gravity's effects are negligible compared to other forces. In terms of a Lagrangian, which is a mathematical formulation used to describe the dynamics of a physical system, this decoupling can manifest as the absence of terms that involve the gravitational field or graviton exchange.
When examining the mathematical framework of string theory, it is currently the most promising approach to integrate gravity with quantum mechanics into a unified Theory of Everything (TOE). However, due to the high energy scales and small separations involved, definitive experimental evidence for string theory or a fully realized TOE remains elusive. The integration of quantum mechanics and gravity, especially in extreme conditions, is a fundamental goal in physics to achieve a deeper understanding of the universe.