Classical billiards can compute
2025/12/22 by Eva Miranda, Isaac Ramos, Miranda, Eva +1 · 8 voices
Physics and Astronomy · Engineering · #Quantum chaos and dynamical systems #Quantum many-body systems #Control and Stability of Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2512.19156
Abstract
We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems under steep confining potentials. By invoking the undecidability of the halting problem, originally established by Turing, our results show that undecidable trajectories arise in physically natural billiard-type models, including models associated with hard-sphere gases and with collision-chain limits in celestial mechanics.
Citations
Discussions
- Classical billiards can compute (2d billiard systems are Turing complete) [hn, 32 points, 5 comments]
- Since the halting problem is undecidable, this means there are some yes-or-no questions about the eventual future behavior of a point bouncing around in this region of the plane that cannot be settled [bsky, 9 points, 1 comments]
- Happy Holidays! arxiv.org/abs/2512.19156 [bsky, 8 points, 1 comments]
- ok "reduction of [extremely fucked up] billiards to halt checker by way of Turing machine" is WORLD-CLASS academic shitposting arxiv.org/abs/2512.19156 [bsky, 5 points, 0 comments]
- Cool. Classical billiards can compute - but only "for some value of billiard table" I think. arxiv.org/abs/2512.19156 [bsky, 1 points, 0 comments]
- Classical Billiards is turing complete Classical billiards can compute arxiv.org/abs/2512.19156 [bsky, 0 points, 0 comments]
- Classical billiards can compute (2d billiard systems are Turing complete) https:// arxiv.org/abs/2512.19156 # arxiv [mastodon, 0 points, 0 comments]
- Classical billiards can compute (2d billiard systems are Turing complete) https://arxiv.org/abs/2512.19156 (https://news.ycombinator.com/item?id=46363993) [bsky, 0 points, 0 comments]
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