[FOM] Re: Physical Church Thesis

Istvan Nemeti inemeti at axelero.hu
Tue Feb 3 06:16:51 EST 2004

(I) In his Jan 12/16:12:23 FOM posting Jose Felix Costa credits the
general relativistic paper "Non-Turing computations via Malament-Hogarth
spacetimes" to Gabor Etesi. In reality, the authors are

Gabor Etesi and Istvan Nemeti, Mathematical Inst. Hung. Academy of Sci.

The paper is available at http://www.math-inst.hu/Contents.html and has
appeared in Internat. J. Theoretical Physics 41,2 (2002), pp.341-370.

(II) There seems to be a second misunderstanding about this paper.
Namely, the paper does not intend to boldly disprove the physical Church
Thesis (CT for short), instead, it wants to call attention to the more
subtle issue that

CT was formulated and accepted before the elaboration of the full,
modern theory of Kerr black holes, and before the modern version of
global general relativistic world-view was generally accepted (a change
starting around and after the 1960's). The paper argues that what was
obvious in the quasi-Newtonian paradigm (around the time when CT was
formulated) needs re-thinking in the paradigm of the post 1990 general
relativistic world view, cf. e.g. [John Earman's book "Bangs, crunches,
whimpers, and shrieks (Singularities and acausalities in relativistic
spacetimes)", Oxford University Press,1995], and Kip Thorne's and Igor
Novikov's post 1990 works.

I emphasize that our paper does not aim for a bold refutation of CT, but
instead calls attention to certain subtle changes in our understanding
of the physical background/weltanschung which make things that were
obvious in the classical world-view less obvious in the new one. In this
direction cf. also [Mark Hogarth: "Predictability, computability, and
spacetime", PhD Dissertation, University of Cambridge, 2001] and
[Pour-El, M. B. and Richard, J. I.: Computability in analysis and
physics, Springer, 1989], the results of which already indicate that
there are things about the physical CT which are less obvious than one
might think at first sight.

To indicate the historical perspective involved, we note that
Schwarzschild black holes are not sufficient for the kind of
relativistic computers proposed by Etesi&Nemeti, David Malament, and
Hogarth. Further, Kerr black holes became sufficiently "accessible" only
approximately after the 1970's (Boyer & Lindquist did their work on them
in 1967 and astronomical evidence was mounting only beginning with
1968-1975). The Etesi-Nemeti relativistic computers use Kerr black
holes. One of the reasons for this is that Kerr black holes seem to
represent one of the most likely "final" forms of collapsing matter. Our
point is that this kind of perspective was not available at the time
when the physical Church-Turing Thesis was formulated. Therefore it
seems justified to have a fresh look at the matter with the new physical
background/worldview in mind.

Paul Davies writes that the reason for studying whether closed timelike
curves (CTC's) can exist in spacetime is that whatever the answer will
be, it will take us closer to a better understanding of spacetime.
Similarly, studying whether modern physics allows us, in principle, to
design a futuristic device which realizes a non-Turing computable
function can improve our understanding of both (1) computability and
(2)theoretical physics. Of course, the experience of many decades shows
us that "easy solutions" will not work. (Also, constructions which would
work also in Newtonian physics will probably turn out to be flawed.
Deemed this way are e.g. constructions based on, say, infinitely precise

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