LOGICAL FOUNDATIONS OF PHYSICS. PART I. ZENO’S DICHOTOMY PARADOX,SUPERTASKS AND THE FAILURE OF CLASSICAL INFINITARY REASONING

Several variants of Zeno’s dichotomy paradox are considered, with the objective of exploring the logical foundations of physics. It is shown that Zeno’s dichotomy paradox leads to contradictions at the metamathematical (as opposed to formal) level in the basic classical infinitary reasoning that is routinely used in theoretical physics. Both Newtonian mechanics and special relativity theory suffer from these metamathematical inconsistencies, which occur essentially because the classical refutation of the dichotomy paradox requires supertasks to be completed. In previous papers, Non-Aristotelian Finitary Logic (NAFL) was proposed as a logical foundation for some of the basic principles of quantum mechanics, such as, quantum superposition and entanglement. We outline how the finitistic and paraconsistent reasoning used in NAFL helps in resolving the metamathematical inconsistencies that arise from the dichotomy paradox

Characterization of Proton Production and Consumption Associated with Microbial Metabolism

BACKGROUND: Production or consumption of protons in growth medium during microbial metabolism plays an important role in determining the pH of the environment. Such pH changes resulting from microbial metabolism may influence the geochemical speciation of many elements in subsurface environments. Protons produced or consumed during microbial growth were measured by determining the amount of acid or base added in a 5 L batch bioreactor equipped with pH control for different species including Escherichia coli, Geobacter sulfurreducens, and Geobacter metallireducens. RESULTS: An in silico model was used to predict the proton secretion or consumption rates and the results were compared with the data. The data was found to confirm predictions of proton consumption during aerobic growth of E. coli with acetate as the carbon source. However, in contrast to proton consumption observed during aerobic growth of E. coli with acetate, proton secretion was observed during growth of Geobacter species with acetate as the donor and Fe(III) as the extracellular electron acceptor. CONCLUSIONS: In this study, we have also shown that the final pH of the medium can be either acidic or basic depending on the choice of the electron acceptor for the same electron donor. In all cases, the in silico model could predict qualitatively the proton production/consumption rates obtained from the experimental data. Therefore, measurements of pH equivalents generated or consumed during growth can help characterize the microbial physiology further and can be valuable for optimizing practical applications such as microbial fuel cells, where growth associated pH changes can limit current generation rates

Evidence for a large population of shocked interstellar clouds

A 21 cm absorption measurement over a long path length free of the effects of differential galactic rotation indicates the existence of two distinct cloud populations in the plane. One of them consisting of cold, dense clouds has been well studied before. The newly found hot clouds appear to be at least five times more numerous. They have a spin temperature of ˜ 300 K, an rms velocity of ˜ 35 km/s-1, twice the total mass, and hundred times the kinetic energy of the cold clouds. Over long path lengths, the hot clouds have NH/kpc ˜ 2 × 1021/cm-2 kpc-1, and are estimated to have individual column densities ≤ 1020/cm-2. We propose that they are shocked clouds found only within supernova bubbles and that the cold clouds are found in the regions in-between old remnants, immersed in an intercloud medium. We conclude that the solar neighborhood must be located between old supernova remnants rather than within one

Pulsar activity and the morphology of supernova remnants

We use the recently introduced concept of a 'window' of magnetic field strengths in which pulsars can be active to explain the variation in morphology of supernova remnants. The striking difference between shell-type and filled-type remnants is attributed to differences in he magnetic field strengths of the neutron stars left by the respective Supernovae. Field strengths of a value permitting pulsar activity result in particle production and Crab-like centrally concentrated remnants. Other field values lead to strong magnetic dipole radiation and consequent shell formation (e.g. Cas A). Several apparent inconsistencies concerning pulsar-supernova associations appear to find a logical explanation on the basis of this hypothesis

LOGICAL FOUNDATIONS OF PHYSICS. PART I. ZENO’S DICHOTOMY PARADOX,SUPERTASKS AND THE FAILURE OF CLASSICAL INFINITARY REASONING

Several variants of Zeno’s dichotomy paradox are considered, with the objective of exploring the logical foundations of physics. It is shown that Zeno’s dichotomy paradox leads to contradictions at the metamathematical (as opposed to formal) level in the basic classical infinitary reasoning that is routinely used in theoretical physics. Both Newtonian mechanics and special relativity theory suffer from these metamathematical inconsistencies, which occur essentially because the classical refutation of the dichotomy paradox requires supertasks to be completed. In previous papers, Non-Aristotelian Finitary Logic (NAFL) was proposed as a logical foundation for some of the basic principles of quantum mechanics, such as, quantum superposition and entanglement. We outline how the finitistic and paraconsistent reasoning used in NAFL helps in resolving the metamathematical inconsistencies that arise from the dichotomy paradox