Causality–Complexity–Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of consequences. First, the usual definitions of randomness depend on a causal structure and turn meaningless. So motivated, we propose an intrinsic, physically motivated measure for the randomness of a string of bits: its length minus its normalized work value, a quantity we closely relate to its Kolmogorov complexity (the length of the shortest program making a universal Turing machine output this string). We test this alternative concept of randomness for the example of non-local correlations, and we end up with a reasoning that leads to similar conclusions as in, but is conceptually more direct than, the probabilistic view since only the outcomes of measurements that can actually all be carried out together are put into relation to each other. In the same context-free spirit, we connect the logical reversibility of an evolution to the second law of thermodynamics and the arrow of time. Refining this, we end up with a speculation on the emergence of a space-time structure on bit strings in terms of data-compressibility relations. Finally, we show that logical consistency, by which we replace the abandoned causality, it strictly weaker a constraint than the latter in the multi-party case.
This text is based on a presentation at the “Workshop on Time in Physics,” organized by Sandra Ranković, Daniela Frauchiger, and Renato Renner at ETH Zurich in Summer 2015.
The authors thank Mateus Araújo, Veronika Baumann, Charles Bédard, Gilles Brassard, Harvey Brown, Caslav Brukner, Harry Buhrman, Matthias Christandl, Sandro Coretti, Fabio Costa, Bora Dakic, Frédéric Dupuis, Paul Erker, Adrien Feix, Jürg Fröhlich, Nicolas Gisin, Esther Hänggi, Arne Hansen, Marcus Huber, Lorenzo Maccone, Alberto Montina, Samuel Ranellucci, Paul Raymond-Robichaud, Louis Salvail, L. Benno Salwey, Andreas Winter, and Magdalena Zych for inspiring discussions, and the Einstein Kaffee as well as the Reitschule Bern for their inspiring atmosphere.—Grazie mille!
The authors thank Claude Crépeau for his kind invitation to present this work, among others, at the 2016 Bellairs Workshop, McGill Research Centre, Barbados.
Our work was supported by the Swiss National Science Foundation (SNF), the National Centre of Competence in Research “Quantum Science and Technology” (QSIT), the COST action on Fundamental Problems in Quantum Physics, and the Hasler Foundation.
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