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

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

Zum Stufenaufbau des Parallelenaxioms

Euclid 's parallel postulate is shown to be equivalent to the conjunction of the following two weaker postulates: “Any perpendicular to one side of a right angle intersects any perpendicular to the other side” and “For any acute angle Oxy, the segment PQ — where P is a point on O x , Q a point on O y and PQ ⊥ Oy — grows indefinitely, i. e. can be made longer than any given segment”.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43033/1/22_2005_Article_BF01226859.pd

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

Glycerol monolaurate prevents mucosal SIV transmission

Although there has been great progress in treating human immunodeficiency virus 1 (HIV-1) infection1, preventing transmission has thus far proven an elusive goal. Indeed, recent trials of a candidate vaccine and microbicide have been disappointing, both for want of efficacy and concerns about increased rates of transmission2–4. Nonetheless, studies of vaginal transmission in the simian immunodeficiency virus (SIV)–rhesus macaque (Macacca mulatta) model point to opportunities at the earliest stages of infection in which a vaccine or microbicide might be protective, by limiting the expansion of infected founder populations at the portal of entry5,6. Here we show in this SIV–macaque model, that an outside-in endocervical mucosal signalling system, involving MIP-3α (also known as CCL20), plasmacytoid dendritic cells and CCR5+ cell-attracting chemokines produced by these cells, in combination with the innate immune and inflammatory responses to infection in both cervix and vagina, recruits CD4+ T cells to fuel this obligate expansion. We then show that glycerol monolaurate—a widely used antimicrobial compound7with inhibitory activity against the production of MIP-3α and other proinflammatory cytokines8—can inhibit mucosal signalling and the innate and inflammatory response to HIV-1 and SIV in vitro, and in vivo it can protect rhesus macaques from acute infection despite repeated intra-vaginal exposure to high doses of SIV. This new approach, plausibly linked to interfering with innate host responses that recruit the target cells necessary to establish systemic infection, opens a promising new avenue for the development of effective interventions to blockHIV-1 mucosal transmission

Glycerol monolaurate prevents mucosal SIV transmission

Although there has been great progress in treating human immunodeficiency virus 1 (HIV-1) infection1, preventing transmission has thus far proven an elusive goal. Indeed, recent trials of a candidate vaccine and microbicide have been disappointing, both for want of efficacy and concerns about increased rates of transmission2–4. Nonetheless, studies of vaginal transmission in the simian immunodeficiency virus (SIV)–rhesus macaque (Macacca mulatta) model point to opportunities at the earliest stages of infection in which a vaccine or microbicide might be protective, by limiting the expansion of infected founder populations at the portal of entry5,6. Here we show in this SIV–macaque model, that an outside-in endocervical mucosal signalling system, involving MIP-3α (also known as CCL20), plasmacytoid dendritic cells and CCR5+ cell-attracting chemokines produced by these cells, in combination with the innate immune and inflammatory responses to infection in both cervix and vagina, recruits CD4+ T cells to fuel this obligate expansion. We then show that glycerol monolaurate—a widely used antimicrobial compound7with inhibitory activity against the production of MIP-3α and other proinflammatory cytokines8—can inhibit mucosal signalling and the innate and inflammatory response to HIV-1 and SIV in vitro, and in vivo it can protect rhesus macaques from acute infection despite repeated intra-vaginal exposure to high doses of SIV. This new approach, plausibly linked to interfering with innate host responses that recruit the target cells necessary to establish systemic infection, opens a promising new avenue for the development of effective interventions to blockHIV-1 mucosal transmission