An Exactly Solvable Model of Local Energy Oscillations in Everettian Branching
Abstract
Abstract The apparent local nonconservation of energy within individual branches during Everettian measurement remains a subtle foundational question in quantum mechanics. While the global expectation value of energy is strictly invariant under unitary time evolution, localized observer branches generically experience dynamic energy fluctuations. In this work, we present an exactly solvable two qubit model governed by an excitation exchange Hamiltonian structurally analogous to the Jaynes Cummings interaction. By decomposing the universalwavefunction |Ψ⟩ through structural projection operators, we derive closed form analytical expressions for the energetic trajectories of the emergent branches. We show that the dynamic asymmetry between a static branch and an oscillatory branch arises directly from total excitation number conservation rather than an eigenstate condition. Furthermore, we prove that local energy oscillations are precisely counterbalanced by time dependent shifts in branch probability weights via the resolution of identity, ensuring absolute global energy conservation. A parametric sweep confirms that this exact compensation mechanism persists across all interaction regimes. These results establish a rigorous mathematical demonstration that local energy oscillations in Everettian branching do not signal genuine thermodynamic violations, but emerge naturally as an observational artifact of subsystem confinement within a globally unitary framework.
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