Topology Atlas || Conferences
Logic in Hungary, 2005
August 5-10, 2005
Janos Bolyai Mathematical Society
A. Hajnal, J. Suranyi (honorary chair) H. Andreka, I. Juhasz, P. Komjath, I. Nemeti (co-chair) G. Sagi (secretary) L. Csirmaz, M. Ferenczi, M. Redei, I. Sain, L. Soukup (member)
The effects of gravitation on clocks, proved in axiomatic relativity
Judit X. Madarász
Alfréd Rényi Institute of Mathematics, Budapest
Coauthors: Gergely Székely
One of the main themes of, say, black hole physics is that gravity causes
time to run slow: clocks closer to the black hole run slower than ones far
away. This kind of effect is called in popular language "time warp", while
the official name is gravitational time dilation (or gravitational red
shift). Using Einstein's equivalence principle ("gravity"="acceleration"),
we seek to develop a rather simple axiomatization of the theory Th of
accelerated observers such that, in Th , the gravitational time dilation
effect becomes provable. Our aim is to keep the theory Th as simple,
streamlined, and transparent as possible, e.g. we make efforts to remain
within the framework of first order logic. One of the purposes with this is
to provide a logic based conceptual analysis of the gravitational time
dilation effect of relativity, i.e. we seek a logical explanation for why
this effect is there. In other words, we seek to find a minimal number of
axioms which are "responsible" for this effect.
Indeed, we will present a streamlined, purely kinematical axiom system which
proves the gravitational time dilation effect in such a way that none of the
axioms can be omitted. In some sense, our research project is analogous with
what is known as "reverse mathematics" in the foundations of mathematics
(seeking which theorems depend on what axioms of set theory). In our work we
build on the first order logic based analysis of special relativity theories
in  and .
 Madarász, J.X., Németi, I. and Székely, G.: Twin paradox and the
logical foundation of special relativity-theory, Foundations of Physics, to
 Andréka, H., Madarász, J.X., Németi, I.: Logical axiomatizations of
space-time. Samples from the literature. In: János Bolyai Memorial Volume,
Kluwer, to appear.
Date received: June 1, 2005
Copyright © 2005 by the author(s).
The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas.
Document # caqb-41.