29 research outputs found
A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory
In this paper we present a proof of a mathematical version of the strong
cosmic censor conjecture attributed to Geroch-Horowitz and Penrose but
formulated explicitly by Wald. The proof is based on the existence of
future-inextendible causal curves in causal pasts of events on the future
Cauchy horizon in a non-globally hyperbolic space-time. By examining explicit
non-globally hyperbolic space-times we find that in case of several physically
relevant solutions these future-inextendible curves have in fact infinite
length. This way we recognize a close relationship between asymptotically flat
or anti-de Sitter, physically relevant extendible space-times and the so-called
Malament-Hogarth space-times which play a central role in recent investigations
in the theory of "gravitational computers". This motivates us to exhibit a more
sharp, more geometric formulation of the strong cosmic censor conjecture,
namely "all physically relevant, asymptotically flat or anti-de Sitter but
non-globally hyperbolic space-times are Malament-Hogarth ones".
Our observations may indicate a natural but hidden connection between the
strong cosmic censorship scenario and the Church-Turing thesis revealing an
unexpected conceptual depth beneath both conjectures.Comment: 16pp, LaTeX, no figures. Final published versio
An Explicit Solution to Post’s Problem over the Reals
Abstract. In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post’s Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such intermediate Turing degrees. Then we strengthen the above result and show as well the existence of an uncountable number of incomparable semi-decidable Turing degrees below the real Halting problem in the BSS model. Again, our proof will give concrete such problems representing these different degrees.
Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity
Dynamic reasoning and time pressure: Transition from analytical operations to experiential responses
Time pressure, Decision-making, Judgement, Strategies,