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

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

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

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

SUMO-2 promotes mRNA translation by enhancing interaction between eIF4E and eIF4G

Small ubiquitin-like modifier (SUMO) proteins regulate many important eukaryotic cellular processes through reversible covalent conjugation to target proteins. In addition to its many well-known biological consequences, like subcellular translocation of protein, subnuclear structure formation, and modulation of transcriptional activity, we show here that SUMO-2 also plays a role in mRNA translation. SUMO-2 promoted formation of the active eukaryotic initiation factor 4F (eIF4F) complex by enhancing interaction between Eukaryotic Initiation Factor 4E (eIF4E) and Eukaryotic Initiation Factor 4G (eIF4G), and induced translation of a subset of proteins, such as cyclinD1 and c-myc, which essential for cell proliferation and apoptosis. As expected, overexpression of SUMO-2 can partially cancel out the disrupting effect of 4EGI-1, a small molecule inhibitor of eIF4E/eIF4G interaction, on formation of the eIF4F complex, translation of the cap-dependent protein, cell proliferation and apoptosis. On the other hand, SUMO-2 knockdown via shRNA partially impaired cap-dependent translation and cell proliferation and promoted apoptosis. These results collectively suggest that SUMO-2 conjugation plays a crucial regulatory role in protein synthesis. Thus, this report might contribute to the basic understanding of mammalian protein translation and sheds some new light on the role of SUMO in this process. © 2014 Chen et al

Trapped lipopolysaccharide and LptD intermediates reveal lipopolysaccharide translocation steps across the Escherichia coli outer membrane

Lipopolysaccharide (LPS) is a main component of the outer membrane of Gram-negative bacteria, which is essential for the vitality of most Gram-negative bacteria and plays a critical role for drug resistance. LptD/E complex forms a N-terminal LPS transport slide, a hydrophobic intramembrane hole and the hydrophilic channel of the barrel, for LPS transport, lipid A insertion and core oligosaccharide and O-antigen polysaccharide translocation, respectively. However, there is no direct evidence to confirm that LptD/E transports LPS from the periplasm to the external leaflet of the outer membrane. By replacing LptD residues with an unnatural amino acid p-benzoyl-L-phenyalanine (pBPA) and UV-photo-cross-linking in E.coli, the translocon and LPS intermediates were obtained at the N-terminal domain, the intramembrane hole, the lumenal gate, the lumen of LptD channel, and the extracellular loop 1 and 4, providing the first direct evidence and “snapshots” to reveal LPS translocation steps across the outer membrane

Experimental observation of the optical spin-orbit torque

Spin polarized carriers electrically injected into a magnet from an external polarizer can exert a spin transfer torque (STT) on the magnetization. The phe- nomenon belongs to the area of spintronics research focusing on manipulating magnetic moments by electric fields and is the basis of the emerging technologies for scalable magnetoresistive random access memories. In our previous work we have reported experimental observation of the optical counterpart of STT in which a circularly polarized pump laser pulse acts as the external polarizer, allowing to study and utilize the phenomenon on several orders of magnitude shorter timescales than in the electric current induced STT. Recently it has been theoretically proposed and experimentally demonstrated that in the absence of an external polarizer, carriers in a magnet under applied electric field can develop a non-equilibrium spin polarization due to the relativistic spin-orbit coupling, resulting in a current induced spin-orbit torque (SOT) acting on the magnetization. In this paper we report the observation of the optical counterpart of SOT. At picosecond time-scales, we detect excitations of magnetization of a ferromagnetic semiconductor (Ga,Mn)As which are independent of the polarization of the pump laser pulses and are induced by non-equilibrium spin-orbit coupled photo-holes.Comment: 4 figure, supplementary information. arXiv admin note: text overlap with arXiv:1101.104

Cosmic Flows on 100 Mpc/h Scales: Standardized Minimum Variance Bulk Flow, Shear and Octupole Moments

The low order moments, such as the bulk flow and shear, of the large scale peculiar velocity field are sensitive probes of the matter density fluctuations on very large scales. In practice, however, peculiar velocity surveys are usually sparse and noisy, which can lead to the aliasing of small scale power into what is meant to be a probe of the largest scales. Previously, we developed an optimal ``minimum variance'' (MV) weighting scheme, designed to overcome this problem by minimizing the difference between the measured bulk flow (BF) and that which would be measured by an ideal survey. Here we extend this MV analysis to include the shear and octupole moments, which are designed to have almost no correlations between them so that they are virtually orthogonal. We apply this MV analysis to a compilation of all major peculiar velocity surveys, consisting of 4536 measurements. Our estimate of the BF on scales of ~ 100 Mpc/h has a magnitude of |v|= 416 +/- 78 km/s towards Galactic l = 282 degree +/- 11 degree and b = 6 degree +/- 6 degree. This result is in disagreement with LCDM with WMAP5 cosmological parameters at a high confidence level, but is in good agreement with our previous MV result without an orthogonality constraint, showing that the shear and octupole moments did not contaminate the previous BF measurement. The shear and octupole moments are consistent with WMAP5 power spectrum, although the measurement noise is larger for these moments than for the BF. The relatively low shear moments suggest that the sources responsible for the BF are at large distances.Comment: 13 Pages, 7 figures, 4 tables. Some changes to reflect the published versio

Longitudinal analyses of the DNA methylome in deployed military servicemen identify susceptibility loci for post-traumatic stress disorder

In order to determine the impact of the epigenetic response to traumatic stress on post-traumatic stress disorder (PTSD), this study examined longitudinal changes of genome-wide blood DNA methylation profiles in relation to the development of PTSD symptoms in two prospective military cohorts (one discovery and one replication data set). In the first cohort consisting of male Dutch military servicemen (n=93), the emergence of PTSD symptoms over a deployment period to a combat zone was significantly associated with alterations in DNA methylation levels at 17 genomic positions and 12 genomic regions. Evidence for mediation of the relation between combat trauma and PTSD symptoms by longitudinal changes in DNA methylation was observed at several positions and regions. Bioinformatic analyses of the reported associations identified significant enrichment in several pathways relevant for symptoms of PTSD. Targeted analyses of the significant findings from the discovery sample in an independent prospective cohort of male US marines (n=98) replicated the observed relation between decreases in DNA methylation levels and PTSD symptoms at genomic regions in ZFP57, RNF39 and HIST1H2APS2. Together, our study pinpoints three novel genomic regions where longitudinal decreases in DNA methylation across the period of exposure to combat trauma marks susceptibility for PTSD