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Finite-State Classical Mechanics

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Reversible Computation (RC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11106))

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Abstract

Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don’t allow information to be erased, and easily accommodate other structural properties of microscopic physics, such as finite distinct state and locality of interaction. In an ideal quantum realization of a reversible lattice dynamics, finite classical rates of state-change at lattice sites determine average energies and momenta. This is very different than traditional continuous models of classical dynamics, where the number of distinct states is infinite, the rate of change between distinct states is infinite, and energies and momenta are not tied to rates of distinct state change. Here we discuss a family of classical mechanical models that have the informational and energetic realism of reversible lattice dynamics, while retaining the continuity and mathematical framework of classical mechanics. These models may help to clarify the informational foundations of mechanics.

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Acknowledgements

I thank Ed Fredkin and Tom Toffoli for pioneering and inspiring these ideas, and Gerald Sussman for many wonderful discussions.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Norman Margolus

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  1. Norman Margolus
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Correspondence to Norman Margolus .

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Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. University of Leicester, Leicester, United Kingdom

    Irek Ulidowski

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Margolus, N. (2018). Finite-State Classical Mechanics. In: Kari, J., Ulidowski, I. (eds) Reversible Computation. RC 2018. Lecture Notes in Computer Science(), vol 11106. Springer, Cham. https://doi.org/10.1007/978-3-319-99498-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-99498-7_3

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-99498-7

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