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Space Exploration

Browse research papers under Space Exploration.

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The Hamiltonian Constraint A First-Class Constraint and the Limits of the Zero-Energy ArgumentThe scalar Hamiltonian constraint C = 0 in general relatvity is read, in expositons of the canonical formalism, as a statement that the total energy of a closed universe vanishes. From this, popular accounts and some expository treatments infer that the universe could arise as a zero-energy quantum fuctuaton, a creaton from nothing. This paper argues that the inference rests on a category error. The constraint is a frst-class constraint that follows from the difeomorphism invariance of the acton, and its content is a restricton on phase space. The energy of the canonical formulaton sits in a boundary term, which a compact slice without boundary leaves absent, so the standard asymptotc and quasi-local defnitons of gravitatonal energy have nothing to atach to. A physical Hamiltonian can nevertheless arise on such a slice once a mater clock deparametrises the theory, and its value is generically
2026 · OpenAlex