ELFT HÍRADÓ

["Laszlo E. Szabo" <leszabo AT ludens.elte.hu>]

Az előző hírdetésben Hraskó Péter előadásának dátumát elírtam. Elnézést 
kérek! Természetesen 25-én lesz.
_______________________________


Department of History and Philosophy of Science
Eotvos University
Budapest, Pazmany P. setany 1/A

PHILOSOPHY OF SCIENCE COLLOQUIUM
(http://hps.elte.hu/seminar)
________________________________________________

February program


 18 February 4:00 PM 6th floor 6.54

Gábor Etesi* **  (lecturer) and István Németi**
*  Yukawa Institute, Kyoto University, Japan
**Alfréd Rényi Institute of Mathematics, Budapest

General relativistic- (and/or quantum-) computability; computing
non-Turing-computable functions in Malament-Hogarth spacetimes

It used to be a (meta) theorem of mathematical logic that
mankind will never know that ZFC (which forms the foundation
of mathematics) is consistent, assuming it is. We will argue
that this meta-theorem is gone, it is no more provable.
We will report on (convergent) results of various research
groups at various parts of the world coming, independently,
to the same conclusion which is, roughly, that Turing computability
may not (after all) be the final limit of the capabilities
of artificial computing devices. Some of the above mentioned
researchers are e.g. Hogarth (Cambridge), Malament, Earman,
ourselves, Kieu (Australia), F. Tipler, to mention only
a few.

We investigate the Church--Kalmár--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.
(We note that the goal of ``computing the uncomputable''
is distincly more modest than executing so called supertasks.
Indeed, we do not claim possibility of the second.)

A paper advocating carefully and it detail the view we adopt
here -- that developments in the background physical theory
can influence profoundly the fundamentals of the theories
of computability and logic -- appeared in Bull. Symbolic
Logic Vol. 6 No 3 (2000), pp.265-283 by Deutsch et al. Our
paper on this subject is available on the following internet
address:
[http://ipsapp008.lwwonline.com/ips/frames/menu.asp?J=4779&S=36698&M=40800#]
A further useful reference is Hogarth, M.: ``Predictability,
Computability, and Spacetime'', pp.1-123, available from
[mh10026 AT cam.ac.uk].

 25 February 4:00 PM 6th floor 6.54

Péter Hraskó
Janus Pannonius University, Pécs

Mit mond a kvantumelmélet az alagúteffektus időtartamáról?
(What does quantum theory say about the duration of tunneling?)

A kvantumelmélet az alagúteffektus valószínűségét pontosan
megjósolja, de nem ad egyértelmű előírást az alagutazás
időtartamának a kiszámítására. Az utóbbi időben lehetővé
vált a probléma kísérleti vizsgálata fotonokkal, mert sikerült
olyan fóliát előállítani, amely foton-barrierként viselkedik.
Ez a fejlemény tette aktualissá az alagutazási idő problémáját,
amely összefügg a spontán állapotredukció kérdésével és
a kvantumelmélet alapjait érinti. A kérdéskörbe a R. Y.
Chiao, [http://ArXiv.org/abs/quant-ph/9811019] összefoglaló
nyújt bevezetést. Az előadás szorosan vett témáját a P.
Hraskó, [http://ArXiv.org/abs/quant-ph/0010056]
cikkben végzett alagutazási-idő számítás alapgondolata képezi.

___________________
The organizer of the seminar: László E. Szabó


--
Laszlo E. Szabo
Department of Theoretical Physics
Department of History and Philosophy of Science
Eotvos University, Budapest
H-1518 Budapest, Pf. 32, Hungary
Phone/Fax: (36-1)372-2924
Home: (36-1) 200-7318
Mobil/SMS: (36) 20-366-1172
http://hps.elte.hu/~leszabo