{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "noether", "title": "Noether: Invariant Variational Problems", "summary": "Structural relations between continuous symmetries, conservation laws and variational equations.", "boundary": "The first and second theorems and their boundary conditions require separate treatment. Translation does not earn credit for discovering the original theorem.", "area": "Mathematical physics", "topic": "Physics", "year": 1918, "lane": "HUMAN", "result": "THEOREM", "package_id": "noether", "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "humans": [ "Emmy Noether" ], "authors_complete": true, "human_role_note": "Listed source contributors; individual labor shares are not measured", "agents": [], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "noether-source", "title": "Noether (1918), M. A. Tavel translation, arXiv:physics/0503066", "url": "https://arxiv.org/abs/physics/0503066" } ], "geography": { "country_codes": [ "DE" ], "location_basis": "Documented research locations or paper affiliations for this contribution. Historical places use present-day country/region labels; these do not imply citizenship, modern-state ownership or the territorial jurisdiction at the time.", "source_url": "https://emmy-noether.net/Goettingen-1915-bis-1919/Habilitation/", "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION", "reviewed_on": "2026-09-26", "nationality_inferred": false, "sources": [ { "title": "Attribution source", "url": "https://emmy-noether.net/Goettingen-1915-bis-1919/Habilitation/" }, { "title": "Attribution source", "url": "https://gdz.sub.uni-goettingen.de/id/PPN252457811_1918?tify=%7B%22view%22%3A%22info%22%2C%22pages%22%3A%5B241%5D%7D" } ], "coverage_status": "COMPLETE", "country_labels": { "DE": "Germany" } }, "points": "300000", "published_grade": { "id": "noether", "entry_id": "noether", "band": "S", "modifier": null, "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "what_changed": "Structural relations between continuous symmetries, conservation laws and variational equations.", "scope": "The variational symmetry-conservation correspondence under the hypotheses of the 1918 work.", "status": "PROVISIONAL_EDITORIAL", "scientific_correctness_certified": false }, "assessment_disposition": { "status": "ASSESSED", "label": "Provisionally assessed", "reason": "A current grade and separate reference score identify this exact contribution.", "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": null, "published_at": "2026-09-11T00:00:00Z", "publisher": { "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33", "role": "WRS_EDITORIAL_PUBLICATION" }, "record": { "contributors": [ { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Emmy Noether", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Noether (1918), M. A. Tavel translation, arXiv:physics/0503066", "url": "https://arxiv.org/abs/physics/0503066" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Noether (1918), M. A. Tavel translation, arXiv:physics/0503066", "url": "https://arxiv.org/abs/physics/0503066" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "The first and second theorems and their boundary conditions require separate treatment. Translation does not earn credit for discovering the original theorem.", "domain": "数学物理" }, "sources": [ { "citation": "Noether (1918), M. A. Tavel translation, arXiv:physics/0503066", "url": "https://arxiv.org/abs/physics/0503066" } ], "statement": "# Noether: Invariant Variational Problems\n\n## The question\n\nWhy do so many physical models have conserved quantities such as energy or momentum? It is tempting to memorize these as unrelated rules. Noether's work connects continuous symmetries of a variational problem with relations satisfied by its equations. A symmetry here means a mathematically specified transformation that preserves the relevant structure, not merely a picture that looks balanced to the eye.\n\n## The idea\n\nA variational formulation starts with a quantity whose stationary behavior determines equations of motion. Under the appropriate hypotheses, continuous transformation groups yield conservation relations; the treatment of infinite groups also yields differential identities. The original work is broader than one classroom slogan. Its conclusions depend on the variational setting and on the kind of group being considered, so a symmetry claim must be stated precisely before using a conservation conclusion.\n\n## Why it matters\n\nThis is a reusable relationship between the form of a model and the consequences it must satisfy. Instead of discovering every conservation law from scratch, a researcher can inspect a suitable symmetry. WRS's S grade concerns that structural contribution. It does not claim that every process conserves every quantity, or that a mathematical symmetry by itself proves a proposed physical theory matches the world.\n\n## A teaching example\n\nImagine describing a simple idealized experiment today and again tomorrow. If the model has no explicit preference for the starting time, that is a candidate time-translation symmetry. Now imagine adding a motor whose forcing changes according to a prescribed schedule. The clock matters to the setup, so you cannot reuse the same symmetry argument without accounting for the forcing. This thought experiment helps you ask what is actually preserved. It is not a proof of a theorem, and a real apparatus may exchange energy with parts omitted from the model.\n\n## Scope and a useful next step\n\nThe linked arXiv document is Tavel's English translation of the 1918 work, with its own revision history. Begin with the theorem statements in Section 1 before reading their proofs. A useful small task is to take one worked model, specify its variational quantity and transformation, and identify the missing hypothesis if a claimed conservation law fails. Preserve the model's boundaries and external interactions rather than treating the word symmetry as sufficient evidence.\n\n## Scientific scope\n\nThe first and second theorems and their boundary conditions require separate treatment. Translation does not earn credit for discovering the original theorem.\n\n## Sources for this explanation\n\n- [Noether (1918), M. A. Tavel translation, arXiv:physics/0503066](https://arxiv.org/abs/physics/0503066): Identified original contribution source. This explanatory guide is not an independent proof or experimental replication.\n", "summary": "Structural relations between continuous symmetries, conservation laws and variational equations.", "title": "Noether: Invariant Variational Problems" }, "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "source_ref": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:08150b5b41e8f527c9c4a08d3f945f90c9c6454702a26e280cfc3920d955a89d" }, "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "noether", "entry_id": "noether", "revision": 1, "title": "Noether: Invariant Variational Problems", "context": "Mathematical physics", "track": "Scoped historical scientific contribution", "band": "S", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-09-14", "evidence_cutoff": "2026-09-14", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Structural relations between continuous symmetries, conservation laws and variational equations.", "scope": "The variational symmetry-conservation correspondence under the hypotheses of the 1918 work.", "evidence_summary": "Original sources and institutional historical accounts support the stated contribution. The reading boundary is recorded at each source; this assessment is not an independent scientific verification.", "references": [ { "title": "Noether (1918), M. A. Tavel translation, arXiv:physics/0503066", "url": "https://arxiv.org/abs/physics/0503066", "locator": "Retained catalogue source review: Bibliography and stated result; no full proof audit" } ], "roles": [ { "who": "Emmy Noether", "credit": "SCIENCE", "did": "Named source contributor to this scoped work; individual labor shares are not measured." } ], "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "300000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "noether", "sections": [ { "title": "The question", "text": "Why do so many physical models have conserved quantities such as energy or momentum? It is tempting to memorize these as unrelated rules. Noether's work connects continuous symmetries of a variational problem with relations satisfied by its equations. A symmetry here means a mathematically specified transformation that preserves the relevant structure, not merely a picture that looks balanced to the eye." }, { "title": "The idea", "text": "A variational formulation starts with a quantity whose stationary behavior determines equations of motion. Under the appropriate hypotheses, continuous transformation groups yield conservation relations; the treatment of infinite groups also yields differential identities. The original work is broader than one classroom slogan. Its conclusions depend on the variational setting and on the kind of group being considered, so a symmetry claim must be stated precisely before using a conservation conclusion." }, { "title": "Why it matters", "text": "This is a reusable relationship between the form of a model and the consequences it must satisfy. Instead of discovering every conservation law from scratch, a researcher can inspect a suitable symmetry. WRS's S grade concerns that structural contribution. It does not claim that every process conserves every quantity, or that a mathematical symmetry by itself proves a proposed physical theory matches the world." }, { "title": "A teaching example", "text": "Imagine describing a simple idealized experiment today and again tomorrow. If the model has no explicit preference for the starting time, that is a candidate time-translation symmetry. Now imagine adding a motor whose forcing changes according to a prescribed schedule. The clock matters to the setup, so you cannot reuse the same symmetry argument without accounting for the forcing. This thought experiment helps you ask what is actually preserved. It is not a proof of a theorem, and a real apparatus may exchange energy with parts omitted from the model." }, { "title": "Scope and a useful next step", "text": "The linked arXiv document is Tavel's English translation of the 1918 work, with its own revision history. Begin with the theorem statements in Section 1 before reading their proofs. A useful small task is to take one worked model, specify its variational quantity and transformation, and identify the missing hypothesis if a claimed conservation law fails. Preserve the model's boundaries and external interactions rather than treating the word symmetry as sufficient evidence." } ], "target": { "record_id": "urn:uuid:744889c6-26e6-4031-a082-ec77bb0e9116", "version": 1, "content_hash": "sha256:a26f2162aeb9de8ba6ffe5d95a099026fa4241d7695234f85a503690c355ef7f" }, "references": [ { "title": "Noether (1918), M. A. Tavel translation, arXiv:physics/0503066", "url": "https://arxiv.org/abs/physics/0503066", "locator": "Identified original contribution source. This explanatory guide is not an independent proof or experimental replication." } ] }, "reading_status": "EXPLANATORY_GUIDE" }