3 research outputs found
Algebrai logika; relativitáselmélet logikai struktúrájának vizsgálata = Algebraic logic; investigating the logical structure of relativity theory
Gödel, Einstein Ă©s Tarski hagyományait kĂvánjuk folytatni, elmĂ©lyĂtve a Gödel-Einstein egyĂĽttműködĂ©s eredmĂ©nyeit is, Ă©s folytatva Tarski tudományegyesĂtĂ©si programmját. Ismert, hogy a logika Ă©s a matematika modern megalapozása Gödel Ă©s Tarski ĂşttörĹ‘ munkásságára vezethetĹ‘ vissza. KevĂ©sbbĂ© ismert, hogy Gödel 1948-tĂłl majdnem Ă©lete vĂ©gĂ©ig Einsteinnel szorosan egyĂĽttműködve relativitáselmĂ©leten dolgozott, ahol ugyanolyan meghökkentĹ‘ Ăşj horizontokat tárt fel mint logikában, Ă©s hogy Gödel relativitáselmĂ©leti gondolatai folytatásakĂ©nt foghatĂł fel a forgĂł fekete lyukak mai elmĂ©lete. Ezen elĹ‘zmĂ©nyek folytatása a jelen projektum, mely Tarskival Ă©s munkatársaival valĂł szemĂ©lyes egyĂĽttműködĂ©s (pl. közös könyv) keretĂ©ben kezdĹ‘dött. Az alapgondolat a logika, algebra, geometria, tĂ©ridĹ‘elmĂ©let Ă©s relativitáselmĂ©let egysĂ©gben valĂł művelĂ©se. EredmĂ©nyeinkbĹ‘l egy pĂ©lda: Nagy, lassan forgĂł fekete lyukakrĂłl bizonyĂtottuk, hogy a belsejĂ©ben lĂ©trejövĹ‘ un. zárt idĹ‘szerű görbe (idĹ‘hurok) lĂ©trejöttĂ©re vonatkozĂł szokásos irodalmi magyarázatok tĂ©vesek. Nem az un. drag effect (mozgĂł anyag magával vonszolja a tĂ©ridĹ‘t) okozza a zárt görbĂ©ket, hanem egy egĂ©szen más jellegű hatás: a fĂ©nykĂşpok kinyĂlása a forgással ellentĂ©tes irányban. Az eredmĂ©ny a General Relativity and Gravitation cĂmű folyĂłiratban jelenik meg. | The reported project intends to continue traditions of Gödel, Einstein and Tarski continuing the spirit of the Gödel-Einstein collaboration and pursuing Tarski's programme for unifying science. Modern logic and meta-mathematics was created (basically) by Gödel and Tarski. It is less well known that beginning with 1948 Gödel spent much time with Einstein and worked on relativity theory. Of course, he remained a logician in spirit. Gödel obtained fundamental breakthroughs in relativity like his ones in logic and foundations. The theory of general relativistic spacetimes not admitting a global Time was initiated by Gödel, and came to full blossom during the renaissance of black hole physics during the last 25 years. The present project was originally started in personal cooperation with Tarski and his collaborators. The idea is to study logic, algebra, geometry, spacetime theory and relativity in a strong unity. A sample result of ours: We proved about big, slowly rotating black holes that the usual explanation in the literature of why such black holes contain a closed timelike curve (CTC) is flawed. Namely, it is not the gravitational frame dragging effect which creates CTCs, instead, there is a completely different kind of effect in action there: light cones open up in the direction opposite to that of the rotation of the source and this goes on to such an extreme extent that CTCs are created. Our paper on this appears in the journal General Relativity and Gravitation