12 research outputs found
Non-Turing computations via Malament-Hogarth space-times
We investigate the Church-Kalm\'ar-Kreisel-Turing Theses concerning
theoretical (necessary) limitations of future computers and of deductive
sciences, in view of recent results of classical general relativity theory.
We argue that (i) there are several distinguished Church-Turing-type Theses
(not only one) and (ii) validity of some of these theses depend on the
background physical theory we choose to use. In particular, if we choose
classical general relativity theory as our background theory, then the above
mentioned limitations (predicted by these Theses) become no more necessary,
hence certain forms of the Church-Turing Thesis cease to be valid (in general
relativity). (For other choices of the background theory the answer might be
different.)
We also look at various ``obstacles'' to computing a non-recursive function
(by relying on relativistic phenomena) published in the literature and show
that they can be avoided (by improving the ``design'' of our future computer).
We also ask ourselves, how all this reflects on the arithmetical hierarchy and
the analytical hierarchy of uncomputable functions.Comment: Final, published version: 25 pages, LaTex with two eps-figures,
journal reference adde
A twist in the geometry of rotating black holes: seeking the cause of acausality
We investigate Kerr-Newman black holes in which a rotating charged
ring-shaped singularity induces a region which contains closed timelike curves
(CTCs). Contrary to popular belief, it turns out that the time orientation of
the CTC is opposite to the direction in which the singularity or the ergosphere
rotates. In this sense, CTCs "counter-rotate" against the rotating black hole.
We have similar results for all spacetimes sufficiently familiar to us in which
rotation induces CTCs. This motivates our conjecture that perhaps this
counter-rotation is not an accidental oddity particular to Kerr-Newman
spacetimes, but instead there may be a general and intuitively comprehensible
reason for this.Comment: 21 pages, 5 figures; replaced to match published version forthcoming
in General Relativity and Gravitatio
First-Order Logic Foundation of Relativity Theories
Motivation and perspective for an exciting new research direction
interconnecting logic, spacetime theory, relativity--including such
revolutionary areas as black hole physics, relativistic computers, new
cosmology--are presented in this paper. We would like to invite the logician
reader to take part in this grand enterprise of the new century. Besides
general perspective and motivation, we present initial results in this
direction.Comment: 25 pages, 4 figure
Economic and organizational problems of developing the grain and meat verticums
Lectures delivered at the scientific-production conference on agricultural economics and farm organizatio