Final answer:
The most difficult aspect for Sheldon's theory to manage would be falsifiability, as it must be able to make testable predictions that can potentially be proven wrong, adhering to the scientific method.
Step-by-step explanation:
The most challenging aspect of good scientific research for Sheldon's theory to manage would likely be falsifiability. Falsifiability refers to the ability of a theory to be proven wrong, the hallmark of the scientific method. A theory that explains everything is at risk of not being testable because there's no scenario it can't explain. This presents a paradox because a good scientific theory should make predictions that can be tested and potentially proven wrong. Without falsifiability, it becomes difficult to separate scientific fact from philosophical assertions.
Scientific research thrives on theories that not only explain known phenomena but can also predict unknown phenomena which can then be tested. In instances like string theory and other approaches toward a "Theory of Everything", researchers strive to create a framework that is both inclusive of existing observations and capable of making verifiable predictions. This is why any unified theory like Sheldon's must be approached cautiously, ensuring that it adheres to the fundamental tenets of scientific inquiry, including falsifiability.
As we advance in our understanding of physics, testing these theories, such as through observations made by high-energy accelerators or probing the early universe, will be crucial. These tests could potentially prove or disprove theoretical predictions, thus strengthening the fabric of scientific knowledge.