The existence of higher-dimensional objects beyond energy/matter, as described by theories such as String Theory, is primarily based on theoretical and mathematical arguments rather than direct experimental evidence. Here are some lines of reasoning and indirect evidence that support the concept of higher-dimensional objects:
Mathematical Consistency: String Theory and other theories that propose extra dimensions, such as Supergravity and M-theory, offer mathematically consistent frameworks for unifying gravity with the other fundamental forces. These theories require the existence of extra dimensions to achieve this mathematical consistency.
Resolution of Theoretical Problems: The inclusion of extra dimensions in String Theory helps resolve certain theoretical challenges, such as the ultraviolet divergences in quantum field theory and the inconsistencies between General Relativity and Quantum Mechanics. These extra dimensions provide a framework for reconciling these fundamental theories.
Kaluza-Klein Theory: The Kaluza-Klein theory, a precursor to String Theory, introduced the concept of compactified extra dimensions. It demonstrated that by assuming the existence of extra dimensions, it was possible to unify electromagnetism with gravity in a 5-dimensional framework. This provided an early indication that extra dimensions could play a role in fundamental physics.
Black Hole Thermodynamics: Studies in black hole physics and thermodynamics have suggested connections between black holes and higher-dimensional objects. For example, the Bekenstein-Hawking entropy formula, which relates the entropy of a black hole to its surface area, has analogies with the statistical mechanics of higher-dimensional objects.
Dualities and Symmetries: String Theory exhibits various dualities and symmetries, such as T-duality and S-duality, which relate different string theories or gauge theories in different dimensions. These dualities provide evidence for the interplay between different dimensional descriptions and suggest a deep connection between different physical systems.
It's important to note that direct experimental confirmation of extra dimensions or higher-dimensional objects has not yet been achieved. Due to the extremely small size of these dimensions, they are currently beyond the reach of current experimental techniques. As such, the evidence for higher-dimensional objects primarily comes from their theoretical consistency, mathematical elegance, and their ability to address existing theoretical problems in fundamental physics.