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The difficulty of explaining non-local correlations in a fixed causalstructure sheds new light on the old debate on whether space and time are to beseen as fundamental. Refraining from assuming space-time as given a priori hasa number of consequences. First, the usual definitions of randomness depend ona causal structure and turn meaningless. So motivated, we propose an intrinsic,physically motivated measure for the randomness of a string of bits: its lengthminus its normalized work value, a quantity we closely relate to its Kolmogorovcomplexity (the length of the shortest program making a universal Turingmachine output this string). We test this alternative concept of randomness forthe example of non-local correlations, and we end up with a reasoning thatleads to similar conclusions as in, but is conceptually more direct than, theprobabilistic view since only the outcomes of measurements that can actuallyall be carried out together are put into relation to each other. In the samecontext-free spirit, we connect the logical reversibility of an evolution tothe second law of thermodynamics and the arrow of time. Refining this, we endup with a speculation on the emergence of a space-time structure on bit stringsin terms of data-compressibility relations. Finally, we show that logicalconsistency, by which we replace the abandoned causality, it strictly weaker aconstraint than the latter in the multi-party case.

Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?