Empirical constraints on vacuum decay in the stringy landscape

It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of ``parallel universes'' is a necessary consequence of the string-landscape dynamics and might well allow us to ``survive'' vacuum decay. As a consequence our stringy vacuum's lifetime is empirically unconstrained and could be very short. Based on this counter-intuitive insight I propose a novel type of laboratory experiment that searches for an apparent violation of the quantum-mechanical Born rule by gravitational effects on vacuum decay. If the lifetime of our vacuum should turn out to be shorter than 6 x 10^{-13} seconds such an experiment is sufficiently sensitive to determine its value with state-of-the-art equipment.Comment: 13 pages, 2 figures, proposes a laboratory experimen

Computing with Classical Real Numbers

There are two incompatible Coq libraries that have a theory of the real numbers; the Coq standard library gives an axiomatic treatment of classical real numbers, while the CoRN library from Nijmegen defines constructively valid real numbers. Unfortunately, this means results about one structure cannot easily be used in the other structure. We present a way interfacing these two libraries by showing that their real number structures are isomorphic assuming the classical axioms already present in the standard library reals. This allows us to use O'Connor's decision procedure for solving ground inequalities present in CoRN to solve inequalities about the reals from the Coq standard library, and it allows theorems from the Coq standard library to apply to problem about the CoRN reals

Philosophical Implications of Inflationary Cosmology

Recent developments in cosmology indicate that every history having a nonzero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like our own, as well as infinitely many civilizations that differ from our own in any way permitted by physical laws. We explore the implications of this conclusion for ethical theory and for the doomsday argument. In the infinite universe, we find that the doomsday argument applies only to effects which change the average lifetime of all civilizations, and not those which affect our civilization alone.Comment: 25 pages; v2: revised version to appear in British Journal for the Philosophy of Scienc