{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3592363c9ba96d2d334a12d953fd8e9704c4fae2c603cc7add17c4440a66d7ee","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"c1fc35c83e7953678edabe1b2dd143b57025778c94e638b6266580d354281f78","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"grav.problem-of-time.wdw-inner-product","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The Wheeler-DeWitt equation is the quantum version of Einstein's equations for the whole universe. There is no rigorous way to normalize its solutions, so probabilities are not defined.","posed_since":"1967","precise":"For $3+1$ general relativity (vacuum or with a scalar field) quantized canonically, construct a physical inner product on solutions of the Hamiltonian and momentum constraints $H \\Psi = 0, H_{i} \\Psi = 0$, with a complete set of Dirac observables represented as self-adjoint operators, beyond minisuperspace truncations. An answer is a rigorous construction (for example group averaging with proven convergence) or a proof that none exists for a stated operator ordering and regularization.","problem_ref":null,"references":"","settled_by":"A mathematically rigorous construction of the physical Hilbert space for a field-theoretic (not minisuperspace) gravitational model in 3+1 dimensions.","status_note":"","title":"Construct the physical Hilbert space of the Wheeler-DeWitt equation","topic_ref":"266bbe8da17b18c5bdcf2f6e3eb994ed918fe1decf73bbef01ce81ac54cc2474"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"16719346ddf369fe12fc51d8925007c73095f45e1e8e6bb63716f9b00c64706d","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"113a66a3356c29549df7f31e4f7f9dd782a15b7c27226e0f286d900e776330fd","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"lrnLckToctvYrjt1KtYEler-yZXBmu-NU1BIPQPDYOVgSpwJXfrAZ0Jw2l8KIvd5COBgfxDsOiM1lGgZhvIeDA"},"schema":"pubphys.envelope/1"},"record_hash":"16719346ddf369fe12fc51d8925007c73095f45e1e8e6bb63716f9b00c64706d","leaf_index":1496}