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Springer eBooks

Quantum Spacetime

Benjamin F. Dribus

Published Jan 1, 2017• 0 citations
Publisher
DOI
10.1007/978-3-319-50083-6_6

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This paper discusses how the transactional interpretation of quantum mechanics can provide for a natural account of the emergence of spacetime events from a quantum substratum. In this account, spacetime is not a substantive manifold that becomes occupied with events; rather, spacetime itself exists only in virtue of specific actualized events. This implies that spacetime is discrete rather than continuous, and that properties attributed to spacetime based on the notion of a continuum are idealizations that do not apply to the real physical world. It is further noted that the transactional picture of the emergence of spacetime can provide the quantum dynamics that underlie the causal set approach as proposed by Sorkin and others.
In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x0,x1{x}_{0},{x}_{1}x0​,x1​, Bob inputs a bit bbb and outputs xb{x}_{b}xb​. Secure OT requires that Alice and Bob learn nothing about bbb and xb‾{x}_{\overline{b}}xb​, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output xb{x}_{b}xb​ within Rb{R}_{b}Rb​, where R0{R}_{0}R0​ and R1{R}_{1}R1​ are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.