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Logic of spacetime and relativity theory
, 2006
"... 2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics......................... 4 ..."
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Cited by 23 (12 self)
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2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics......................... 4
A logic road from special relativity to general relativity. submitted
, 2010
"... Abstract. We present a streamlined axiom system of special relativity in firstorder logic. From this axiom system we “derive ” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we h ..."
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Cited by 16 (8 self)
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Abstract. We present a streamlined axiom system of special relativity in firstorder logic. From this axiom system we “derive ” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the nonspecialist.
Logical analysis of relativity theories
 FirstOrder Logic Revisited
, 2004
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General relativistic hypercomputing and foundation of mathematics
"... Abstract. Looking at very recent developments in spacetime theory, we can wonder whether these results exhibit features of hypercomputation that traditionally seemed impossible or absurd. Namely, we describe a physical device in relativistic spacetime which can compute a nonTuring computable task, ..."
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Cited by 9 (1 self)
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Abstract. Looking at very recent developments in spacetime theory, we can wonder whether these results exhibit features of hypercomputation that traditionally seemed impossible or absurd. Namely, we describe a physical device in relativistic spacetime which can compute a nonTuring computable task, e.g. which can decide the halting problem of Turing machines or decide whether ZF set theory is consistent (more precisely, can decide the theorems of ZF). Starting from this, we will discuss the impact of recent breakthrough results of relativity theory, black hole physics and cosmology to well established foundational issues of computability theory as well as to logic. We find that the unexpected, revolutionary results in the mentioned branches of science force us to reconsider the status of the physical Church Thesis and to consider it as being seriously challenged. We will outline the consequences of all this for the foundation of mathematics (e.g. to Hilbert’s programme). Observational, empirical evidence will be quoted to show that the statements above do not require any assumption of some physical universe outside of our own one: in our specific physical universe there seem to exist regions of spacetime supporting potential nonTuring computations. Additionally, new “engineering ” ideas will be outlined for solving the socalled blueshift problem of GRcomputing. Connections with related talks at the Physics and Computation meeting, e.g. those of Jerome DurandLose, Mark Hogarth and Martin Ziegler, will be indicated. 1
A logical analysis of the timewarp effect of general relativity,” in preparation
"... Abstract. Several versions of the Gravitational Time Dilation effect of General Relativity are formulated by the use of Einstein’s Equivalence Principle. It is shown that all of them are logical consequence of a firstorder axiom system of Special Relativity extended to accelerated observers. 1. ..."
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Abstract. Several versions of the Gravitational Time Dilation effect of General Relativity are formulated by the use of Einstein’s Equivalence Principle. It is shown that all of them are logical consequence of a firstorder axiom system of Special Relativity extended to accelerated observers. 1.
COMPARING RELATIVISTIC AND NEWTONIAN DYNAMICS IN FIRSTORDER LOGIC
"... In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of firstorder logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom ..."
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Cited by 6 (2 self)
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In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of firstorder logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom
Can general relativistic computers break the Turing barrier?
"... Abstract. Can general relativistic computers break the Turing barrier? Are there final limits to human knowledge? Limitative results versus human creativity (paradigm shifts). Gödel’s logical results in comparison/combination with Gödel’s relativistic results. Can Hilbert’s programme be carried ..."
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Cited by 3 (2 self)
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Abstract. Can general relativistic computers break the Turing barrier? Are there final limits to human knowledge? Limitative results versus human creativity (paradigm shifts). Gödel’s logical results in comparison/combination with Gödel’s relativistic results. Can Hilbert’s programme be carried through after all? 1 Aims, perspective The Physical ChurchTuring Thesis, PhCT, is the conjecture that whatever physical computing device (in the broader sense) or physical thought experiment will be designed by any future civilization, it will always be simulatable by a Turing machine. The PhCT was formulated and generally accepted in the 1930’s. At that time a general consensus was reached declaring PhCT valid, and indeed in the succeeding decades the PhCT was an extremely useful and valuable maxim in elaborating the foundations of theoretical computer science, logic, foundation of mathematics and related areas. But since PhCT is partly a physical conjecture, we emphasize that this consensus of the 1930’s was based on the physical worldview of the 1930’s. Moreover, many thinkers considered PhCT as being based on
Vienna Circle and Logical Analysis of Relativity Theory
, 2009
"... 1 introduction In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain firstorder logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main a ..."
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1 introduction In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain firstorder logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a casestudy showing that the Vienna
Can new physics challenge “old ” computational barriers?
"... Abstract. We discuss the impact of very recent developments of spacetime theory, black hole physics, and cosmology to well established foundational issues of computability theory and logic. Namely, we describe a physical device in relativistic spacetime which can compute a nonTuring computable task ..."
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Abstract. We discuss the impact of very recent developments of spacetime theory, black hole physics, and cosmology to well established foundational issues of computability theory and logic. Namely, we describe a physical device in relativistic spacetime which can compute a nonTuring computable task, e.g. which can decide the halting problem of Turing machines or whether ZF set theory is consistent or not. Connections with foundation of mathematics and foundation of spacetime theory will be discussed. 1