On Logical Analysis of Relativity Theories

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.Comment: 19 pages, 1 figure

A logic road from special relativity to general relativity

We present a streamlined axiom system of special relativity in first-order 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 non-specialist

A logic road from special to general relativity

We present a streamlined axiom system of special relativity in first-order 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 non-specialist

Axiomatizing relativistic dynamics without conservation postulates

A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous E=mc^2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated

Faster than light motion does not imply time travel

Seeing the many examples in the literature of causality violations based on faster-than-light (FTL) signals one naturally thinks that FTL motion leads inevitably to the possibility of time travel. We show that this logical inference is invalid by demonstrating a model, based on (3+1)-dimensional Minkowski spacetime, in which FTL motion is permitted (in every direction without any limitation on speed) yet which does not admit time travel. Moreover, the Principle of Relativity is true in this model in the sense that all observers are equivalent. In short, FTL motion does not imply time travel after all

Complexity in the interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime

Interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime is investigated in detail in the paper, with the aim of finding the simplest definitions. Based on ideas scattered in the literature, definitions are given between any two of these binary relations that use 4 variables, i.e., they use only 2 auxiliary variables. All these definitions work over arbitrary Euclidean fields in place of the field of reals, if the dimension n of spacetime is greater than two. If n=2, the definitions work over arbitrary ordered fields except the ones based on lightlike relatedness (where no definition can work by symmetry). None of these relations can be defined from another one using only one auxiliary variable. These definitions use only one universal and one existential quantifiers in a specific order. In some of the cases, we show that the order of these quantifiers can be reversed for the price of using twice as many quantifiers. Except in two cases, we provide existential/universal definitions using 3 auxiliary variables or show that no existential/universal definition exists. There are no existential/universal definitions between any two of these relations using only 2 auxiliary variables. It remains open whether there is an existential (universal) definition of timelike (lightlike) relatedness from spacelike relatedness if n>2. Finally, several other open problems related to the quantifier complexity of the simplest possible definitions are given

Aortastenosis – kihívást jelentő diagnosztikától egy nem mindennapi terápiáig

Az aortastenosis napjainkban egy egyre gyakoribbá váló életminőséget jelentősen limitáló kórkép. Mára mind a betegség diagnosztizálásához, mind a definitív ellátáshoz számos módszer áll rendelkezésre. A 88 éves csökkent ejekciós frakciójú szívelégtelen nőbeteg kórelőzményéből korábbi perkután koronáriaintervenció (PCI) valamint 2021-ben többszöri kardiális dekompenzáció miatti hospitalizáció emelendő ki. Ezek során transthoracalis echokardiográfia (TTE) low-flow low-gradient aortastenosist, ismételt koronarográfia két ág betegséget igazolt. Az aortavitium szignifikanciájának megítélése kapcsán dobutamin stressz-echokardiográfia (DBSE) történt, amely alapján „true severe” aortastenosist véleményeztek, további terápia céljából a beteget intézetünknek referálták. A nem egyértelműen diagnosztikus DBSE miatt CT-vizsgálattal billentyű kalcium score-t, invazív hemodinamikai méréssel Gorlin szerinti aortabillentyű area-meghatározást végeztünk. Az invazív beavatkozással egy ülésben a koronáriabetegség is revaszkularizációra került. Tekintettel a beteg magas életkorára és extrém műtéti kockázatra (STS PROM-score: 14,9% EURO-score: 18,7%) transzkatéteres aortabillentyű-beültetést (TAVI) terveztünk. A CT során leírt aorta ascendenst és descendenst, valmint az aorto-iliacalis átmenetet érintő súlyos kalcifikáció miatt transzapikális behatolás mellett döntöttünk. 2021 decemberében ismételt kardiális dekompenzációt követően a beavatkozást sürgőséggel és sikeresen elvégeztük