Whereas SR2 defines energy and its dynamics as the intrinsic, independent source from which spacetime emerges, its mathematical framework remains classical. Yet if energy dictates how time flows and space contracts, then we have a much better mathematical framework to work with; a framework perfectly aligned with quantum theory: Hamiltonian mechanics.

In traditional physics, the Hamiltonian generates dynamics within a fixed spacetime background. But what if the Hamiltonian can also define how emergent spacetime itself adapts to energy dynamics? More importantly, what if it can serve both as the source of quantum evolution AND relativistic effects?

Welcome to Hamiltonian Relativity.

This isn't just mathematical elegance—it's a conceptual breakthrough. Where conventional approaches treat spacetime and energy as separate entities requiring complex bridging, Hamiltonian Relativity reveals them as fundamentally united. Time intervals, spatial distances, and momentum emerge as quantum observables that adapt to energy eigenstates, not as independent coordinates requiring transformation.

This mathematical unification places quantum theory and special relativity on equal footing. Instead of juggling separate frameworks for quantum mechanics and relativity, we discover a single formalism where both domains emerge naturally from the same energy foundation. The Hamiltonian doesn't just describe how quantum systems evolve—it defines an adapting flat spacetime in which that evolution occurs. Quantum mechanics no longer defines time as a fixed parameter against which a quantum state evolves, but as a dynamic observable adapting to a system's energy.

This approach creates something unprecedented: a seamless bridge between the probabilistic world of quantum mechanics and the geometric certainties of relativity. Energy eigenvalues determine both quantum states and flat spacetime geometry, unifying these seemingly incompatible descriptions of nature.

The implications extend far beyond mathematical convenience. Hamiltonian Relativity positions energy as fundamental and independent, with spacetime properties—time intervals, spatial distances, momentum—emerging as quantum observables that adapt to the energy eigenstates of observed reference frames. This perspective simplifies the mathematical structure of relativity while offering a revolutionary physical interpretation of space, time, and their relationship to energy, laying the foundation for the complete unification explored in the Unified Wave Equation.

The details of Hamiltonian Relativity can be found in Part I of E-Theory available as a preprint on ai.viXra.org: https://ai.vixra.org/abs/2505.0179

Additionally, we provide an E-Theory Interactive Companion, an advanced AI agent available for students and senior researches interested in the finer details of Hamiltonian Relativity.