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arXiv:1902.08997gr-qc

A Noether Theorem for discrete Covariant Mechanics

Fabio D'Ambrosio

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

Abstract

Noether's theorem is an elegant and powerful tool of classical mechanics, but it is of little to no consequence in discrete theories. Here we define and explore a discrete approach to covariant mechanics and show that within this framework a discrete version of Noether's theorem, completely analogous to the well-known continuum version with all its ramifications, remains valid. We also discuss why more traditional approaches to discretized mechanics violate certain conservation laws by construction.

arXiv comments
11 pages, 2 figures
Journal reference
DOI
Subjects
gr-qcGeneral Relativity and Quantum Cosmology hep-latHigh Energy Physics, Lattice

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Linked by 1 identifiable commenter in 4 comments across 4 threads, from Feb 2023 to Oct 2024.

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Discussed in comments4 threads

  1. Thought experiments that fray the fabric of space-time 1 comment

    • This is a common belief and true of many discrete models because they violate symmetries, but that is not true of all discrete models: A Noether Theorem for discrete Covariant Mechanics, https://arxiv.org/abs/1902.08997

      naaskingView on HNParent context

  2. A physicist who bets that gravity can’t be quantized 1 comment

    • I think naive approaches to digital physics have been inadequate, but newer works have made good progress on important questions. Arguably one of the biggest tools in the physicists' toolbox are symmetries, and there's now a good account for those: A Noether Theorem for discrete…

      naaskingView on HNParent context

  3. Towards quantum computers that are robust to errors 1 comment

    • Nobody knows of any certain reasons to not scale, but there's plenty of speculation. Someone else posted about Gil Kalai in this subthread, so he's one high profile person that has documented his skepticism on quantum computing and explained his reasons. For my part, I don't…

      naaskingView on HNParent context

  4. Norton's Dome 1 comment

    • > As far as we know, time and space are continuous. Our models are continuous. The map is not the territory. > Various aspects of quantum field theories would not work in a discretized universe. If you're referring to symmetries, that's not true [1]. Discretized theories have…

      naaskingView on HNParent context

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