Vienna Circle and Logical Analysis of Relativity Theory

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 first-order 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 case-study showing that the Vienna Circle's (VC) approach to doing science is workable and fruitful when performed with using the insights and tools of mathematical logic acquired since its formation years at the very time of the VC activity. We think that logical positivism was based on the insight and anticipation of what mathematical logic is capable when elaborated to some depth. Logical positivism, in great part represented by VC, influenced and took part in the birth of modern mathematical logic. The members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure

Arc Simulation at Shunt-Reactor Switching in H.V. Circuit Breakers

High energy re-ignitions occur in h.v. circuit breakers, when interrupting shunt-reactor currents. The es-calating high frequency over-voltages, which are proportional to the arcing time, are stressful both to the reactor and the circuit breakers. We simulated the electric, thermal and flow field inside the thermal chamber and determined the reduced electric field distribution. Analysing the simulation results the main factors to improve the shunt-reactor breaking capacity are demonstrated

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 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

Neural Cell Response to Nanostructured Biosensor Surfaces

AbstractIn our work we investigate the interaction of cells and nanotextured surfaces as a model of implanted device surface and living tissue interaction. We developed a maskless nanostructuring method, which can be integrated into our neural biosensor fabrication process. Morphology of the fabricated nanograss was characterised using SEM. The nanorods are 520-800nm in height and their density is 18-70/μm2. Electrochemical impedance spectroscopy and contact angles of different surfaces were measured. The specific surface area is 30 times larger than the reference. The contact-angle can be tuned. The samples will be tested in viability and adhesion assays using neural cell cultures

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Exponential Distribution of Locomotion Activity in Cell Cultures

In vitro velocities of several cell types have been measured using computer controlled video microscopy, which allowed to record the cells' trajectories over several days. On the basis of our large data sets we show that the locomotion activity displays a universal exponential distribution. Thus, motion resulting from complex cellular processes can be well described by an unexpected, but very simple distribution function. A simple phenomenological model based on the interaction of various cellular processes and finite ATP production rate is proposed to explain these experimental results.Comment: 4 pages, 3 figure

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

A Geometrical Characterization of the Twin Paradox and its Variants

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.Comment: 22 pages, 3 figure

Environmental and Toxicological Impacts of Glyphosate with Its Formulating Adjuvant

Environmental and toxicological characteristics of formulated pesticides may substantially differ from those of their active ingredients or other components alone. This phenomenon is demonstrated in the case of the herbicide active ingredient glyphosate. Due to its extensive application, this active ingredient was found in surface and ground water samples collected in Békés Country, Hungary, in the concentration range of 0.54–0.98 ng/ml. The occurrence of glyphosate appeared to be somewhat higher at areas under intensive agriculture, industrial activities and public road services, but the compound was detected at areas under organic (ecological) farming or natural grasslands, indicating environmental mobility. Increased toxicity of the formulated herbicide product Roundup compared to that of glyphosate was observed on the indicator aquatic organism Daphnia magna Straus. Acute LC50 values of Roundup and its formulating adjuvant polyethoxylated tallowamine (POEA) exceeded 20 and 3.1 mg/ml, respectively, while that of glyphosate (as isopropyl salt) was found to be substantially lower (690-900 mg/ml) showing good agreement with literature data. Cytotoxicity of Roundup, POEA and glyphosate has been determined on the neuroectodermal cell line, NE-4C measured both by cell viability test and holographic microscopy. Acute toxicity (LC50) of Roundup, POEA and glyphosate on NE-4C cells was found to be 0.013±0.002%, 0.017±0.009% and 6.46±2.25%, respectively (in equivalents of diluted Roundup solution), corresponding to 0.022±0.003 and 53.1±18.5 mg/ml for POEA and glyphosate, respectively, indicating no statistical difference between Roundup and POEA and 2.5 orders of magnitude difference between these and glyphosate. The same order of cellular toxicity seen in average cell area has been indicated under quantitative cell visualization. The results indicate that toxicity of the formulated herbicide is caused by the formulating agent, but in some parameters toxicological synergy occurs between POEA and glyphosate