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Local Energy Fluctuations and Global Conservation in Closed Quantum Measurement: An Exact Unitary Analysis of Many-Worlds Interpretation

Muhammad Ghazi Al Gifari

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.23537.03689

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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.
We revisit Einstein’s 1927 thought experiment on electron diffraction, using a single-electron source and an opaque hemispheric detector array, now achievable with modern sensors (~0.1 ns). In this fully enclosed system, where no signals escape the hemisphere, we provide a direct empirical comparison of the Many-Worlds Interpretation (MWI) and the Branched Hilbert Subspace Interpretation (BHSI). Both maintain unitarity without invoking wavefunction collapse, as in the Copenhagen Interpretation (CI), but differ ontologically: MWI proposes irreversible global branching into parallel worlds, while BHSI describes local, potentially reversible branching into decohered subspaces. In this setup, all quantum events (branching, engagement, disengagement, and relocation) occur entirely within the local system, and the Born rule, naturally emerging through branch weights, can be observed in detector statistics. To explore branching dynamics more thoroughly, we suggest an enhanced dual-layer experimental setup with an inner transparent detector. Because the electron’s transit time between layers (~0.12 ns) is shorter than the average response times of the inner sensors (~1 ns), this allows a crucial test of measurement timing and potential anomalies (“delayed” or “uncommitted” choice?). Our analysis challenges the notion that unitarity necessitates parallel worlds, instead advocating for a simpler view: local, unitary branching without collapse or global splitting.