is change we can count There is no evidence whatsoever for a smooth background of spacetime Bell’s Inequalities have been telling us for a while now that there’s something wrong with Minkowski’s 4D “spacetime”
is not irreversible All our theories are time reversal invariant Classical (Newtonian) Relativistic (Special and General) Standard Model (Quantum Field Theory)
Agent A ∅ Half Link A Half-Edge Entangled (Hidden ENTL Packets) ENTL Circulating ENTL Event ENTL ENTL w x z y EARTH Computing Link • Reversible • No-Copying • Atomic Information Transfer (AIT) Guaranteed in the sense that both sides can “know” if it failed or succeeded Cell Agent A Cell Agent B Half Link A Half Link B Tx/Rx Media
Foundation Groupoid semantics for timeless networks and secure classical key distribution David Reutter Department of Computer Science, University of Oxford david.reutter@cs.ox.ac.uk Jamie Vicary Department of Computer Science, University of Oxford jamie.vicary@cs.ox.ac.uk Abstract—We provide a mathematical foundation for timeless networks, a new paradigm for distributed communication which has recently been proposed. Our approach is based on groubits, generalizations of classical bits arising from groupoids with spe- cial properties. Our techniques give a clean mathematical model for timeless networks, and allow the description and veriﬁcation of a number of interesting protocols, including message routing without timeouts, and information theoretically–secure classical key distribution, under minimal security assumptions. We also build classical-physics implementations of a number of quantum protocols on networks of groubits, including dense coding and teleportation. I. INTRODUCTION A. Overview In this paper we study the foundations of timeless networks, a new paradigm for distributed communication presented re- cently by Borrill [1] and currently under commercial devel- opment by Earth Computing1. We study a mathematically- The read operation destroys a groubit and creates a conven- tional bit, while the write operation destroys a conventional bit and creates a new groubit. Pairs of groubits can also be connected by a link, enabling the Tick operation, where A and B label the two connected nodes, and ⊕ is addition modulo 2: • Tick((AL,AI ),(BL,BI ) =((AL,AI ⊕BL ),(BL,BI ⊕AL )) Intuitively, for each node in the pair, we ﬂip the internal bit just when the other node has logical bit equal to 1. Nodes can belong to multiple links, in general forming a graph topology. B. Assumptions We make some assumptions about these groubit operations. • Atomicity. The operations Init, Swap, Read, Write and Tick are implemented atomically. • Security. A user can never discover any information about the state of a node, except via Read. We emphasize that claims we make about the functionality arxiv.org/abs/1707.00966