{"paper":{"title":"Explanation of the Generalizations of Uncertainty Principle from Coordinate and Momentum Space Periodicity","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Subir Ghosh","submitted_at":"2024-03-25T16:05:05Z","abstract_excerpt":"Generalizations of coordinate $x$-momentum $p_x$ Uncertainty Principle, with $\\Delta x$ and $\\Delta p_x$ dependent terms ($\\Delta$ denoting standard deviation), $$\\Delta x \\Delta p_x\\geq i\\hbar (1+\\alpha\\Delta p_x^2 +\\beta \\Delta x^2)$$ have provided rich dividends as a poor person's approach towards Quantum Gravity, because these can introduce coordinate and momentum scales ($\\alpha,\\beta$ ) that are appealing conceptually. However, these extensions of Uncertainty Principle are purely phenomenological in nature. Apart from the inherent ambiguity in their explicit structures, the introduction "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.16893","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.16893/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}