http://arxiv.org/abs/1507.01815
We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized cosmological systems. The construction is based on a particular model of computation, developed by Alan Turing, with cosmic observers (CO), cosmic measures (CM) and cosmic symmetries (CS) described by Turing machines. CO machines always start with a blank tape and CM machines take CO’s Turing number (also known as description number or G{\” o}del number) as input and output the corresponding probability. Similarly, CS machines take CO’s Turing number as input, but output either one if the CO machines are in the same equivalence class or zero otherwise. We argue that CS machines are more fundamental than CM machines and, thus, should be used as building blocks in constructing CM machines. We prove the non-computability of a CS machine which discriminates between two classes of CO machines: mortal that halts in finite time and immortal that runs forever. In context of eternal inflation this result implies that it is impossible to construct CM machines to compute probabilities using cut-off prescriptions or that all of the cut-off measures are non-computable.
V. Vanchurin
Wed, 8 Jul 15
20/42
Comments: 13 pages, 2 figures
