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Siblings:History/traditions: Physics

507 found
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  1. Origin of Life as a Probabilistic Event in the Universe.Dimitri Marques Abramov & Carlos Alberto Mourão-Junior - manuscript
    By means of a probabilistic mathematical model, we bring into discussion the origin of life as a stochastic process. We consider only the chance of information emergence in the proteome and genome under the ideal thermodynamic and chemical conditions. For a more realistic model, we used, as a parameter, the information amount in N. equitans genome, the simplest known nowadays, as the equivalent to the first living cell that could have emerged in primitive Earth. We estimated the probability of information (...)
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  2. Dark Origins: Departure From an Ex-Nihilo Big Bang.Onyemaechi Ahanotu - manuscript
    With the growing body of research on Black Holes, it is becoming increasingly apparent that these celestial objects may have a stronger part to play in the universe than previously thought, shaping galaxies and influencing star formation. In this manuscript, I take these findings a step further, proposing a new set of boundary conditions to both the early and late Universe, extrapolating from thermodynamics. I propose that the Universe will collapse into a massive black hole and that the Big Bang (...)
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  3. Homo Deceptus: How Language Creates its Own Reality.Bruce Bokor - manuscript
    Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...)
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  4. A Categorical Model of the Elementary Process Theory Incorporating Special Relativity.Marcoen J. T. F. Cabbolet - manuscript
    The purpose of this paper is to show that the Elementary Process Theory (EPT) agrees with the knowledge of the physical world obtained from the successful predictions of Special Relativity (SR). For that matter, a recently developed method is applied: a categorical model of the EPT that incorporates SR is fully specified. Ultimate constituents of the universe of the EPT are modeled as point-particles, gamma-rays, or time-like strings, all represented by integrable hyperreal functions on Minkowski space. This proves that the (...)
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  5. Taming the Delayed Choice Quantum Eraser.Johannes Fankhauser - manuscript
    In this paper I discuss the delayed choice quantum eraser experiment by giving a straightforward account in standard quantum mechanics. At first glance, the experiment suggests that measurements on one part of an entangled photon pair can be employed to control whether the measurement outcome of the other part of the photon pair produces interference fringes at a screen after being sent through a double slit. Significantly, the choice whether there is interference or not can be made long after the (...)
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  6. Fidelity and Mistaken Identity for Symplectic Quantum States.Andreas Henriksson - manuscript
    The distinguishability between pairs of quantum states, as measured by quantum fidelity, is formulated on phase space. The fidelity is physically interpreted as the probability that the pair are mistaken for each other upon an measurement. The mathematical representation is based on the concept of symplectic capacity in symplectic topology. The fidelity is the absolute square of the complex-valued overlap between the symplectic capacities of the pair of states. The symplectic capacity for a given state, onto any conjugate plane of (...)
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  7. Classical Distinguishability and the Gibbs-Liouville Theorem.Andreas Henriksson - manuscript
    It is shown that the theory of classical mechanics can be built from the concept of distinguishability between pairs of classical states. The non-ignorant observer can, with infinite precision, distinguish between arbitrary pairs. Either they are identical, or they are distinct. The distinguishability is postulated to be conserved in time for closed systems. The mathematical representation of this postulate is shown to be given by the Gibbs-Liouville theorem. Alternative statements of this theorem are given. In particular, Hamilton's principle is derived (...)
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  8. History of Science Enters Through the Back Door.Nahum Kipnis - manuscript
    The author argues for a greater involvement of professional historians of science into teaching science to improve the historical component of science. Yet, however much some teachers like history they find no room in the curriculum for a history of science course. The solution is in make the history of science a useful tool for teaching physics. The author shares his experience of using historical experiments carried out by students in a lab setting. Playing scientists not only improved understanding of (...)
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  9. A Live Wire : Machismo of a Distant Surface.Marvin E. Kirsh - manuscript
    The scientific study of socio-cultural phenomenon requires a translocation of topics elaborated from the social perspective of the individual to a rationally ordered rendition of processes suitable for comprehension from a scientific perspective. Scholarly curiosity seeded from exposure in the natural setting to economic, political, socio-cultural, evolutionary, processes dictates that study of the self, should be a science with a necessary place in the body of world literatures; yet it has proven difficult to find a perspective to contain discussions of (...)
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  10. A Methodological Note on Proving Agreement Between the Elementary Process Theory and Modern Interaction Theories.Cabbolet Marcoen - manuscript
    The Elementary Process Theory (EPT) is a collection of seven elementary process-physical principles that describe the individual processes by which interactions have to take place for repulsive gravity to exist. One of the two main problems of the EPT is that there is no proof that the four fundamental interactions (gravitational, electromagnetic, strong, and weak) as we know them can take place in the elementary processes described by the EPT. This paper sets forth the method by which it can be (...)
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  11. The Ineffable Now in Physics.Paul Merriam - manuscript
    While physicists know how to use quantum mechanics, there is no consensus on what quantum mechanics is a mechanics of. The aim of this paper is to introduce the beginning of what might turn out to be an interpretation of quantum mechanics—one that leaves all calculated probabilities intact. The basic idea is that quantum mechanics describes the objective world, but there must be added to it ineffable variables, one of which is the temporal 'now'. Ineffable variables are not 'hidden variables'.
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  12. Termodinamica: Legi, Concepte, Sisteme, Stări.Sfetcu Nicolae - manuscript
    Termodinamica se ocupă cu studiul energiei, a conversiilor sale între diferite forme, cum ar fi căldura, și capacitatea energiei de a produce lucru mecanic. Ea este strâns legată de mecanica statistică, din care pot fi derivate multe relații termodinamice. Se poate argumenta că termodinamica a fost greșit denumită astfel întrucât aceasta nu se referă de fapt la rate de schimbare ca atare și, prin urmare, ar fi fost probabil mai corect ca domeniul să se denumească termostatica. Termodinamica se referă la (...)
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  13. Tests de la gravité quantique.Sfetcu Nicolae - manuscript
    Le test primordial de toute théorie quantique de la gravité est la reproduction des succès de la relativité générale. Cela implique de reconstruire la géométrie locale à partir des observables non locaux. De plus, la gravité quantique devrait probablement prédire la topologie à grande échelle de l'Univers, qui pourrait bientôt être mesurable , et les phénomènes à l'échelle de Planck. Il existe déjà une prédiction liée à la gravité quantique: l'existence et le spectre du rayonnement Hawking du trou noir, une (...)
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  14. Unification de la gravité avec les autres forces fondamentales.Sfetcu Nicolae - manuscript
    Plusieurs théories unificatrices ont été proposées. Une grande unification implique l'existence d'une force électronucléaire. La dernière étape de l'unification nécessiterait une théorie qui inclue à la fois la mécanique quantique et la gravité par la relativité générale (« la théorie finale »). Après 1990, certains physiciens considèrent que la théorie M à 11 dimensions, souvent identifiée à l'une des cinq théories des supercordes perturbateurs, ou parfois à la supergravité à supersymétrie maximale supersymétrique à 11 dimensions, est la théorie finale. L'idée (...)
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  15. Gravité et cosmologie.Sfetcu Nicolae - manuscript
    En cosmologie, la métaphysique implique un large éventail de questions au-delà des preuves empiriques, utilisant parfois l'inférence spéculative. L'analyse épistémologique en cosmologie aide à modéliser l'évaluation. L'étude philosophique offre un cadre général pour interpréter des inférences qui vont au-delà de la science. En cosmologie, il existe des principes ontologiques qui aident à classer les modèles selon leurs caractéristiques, à concevoir la réalité cosmique dans une description plus transparente, et nous permettent de résoudre des équations mathématiques en tant que constructions centrales (...)
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  16. Tests cosmologiques gravitationnels: l'univers en expansion.Sfetcu Nicolae - manuscript
    Les modèles cosmologiques actuels sont construits sur la base de la relativité générale. Les solutions des équations spécifiques, Friedmann-Lemaître-Robertson-Walker, permettent de modéliser l'évolution de l'univers à partir du Big Bang . Certains paramètres de l'univers ont été établis par des observations. Sur la base de ces données et d'autres données d'observation, les modèles peuvent être testés . Les observations sur la vitesse d'expansion de l'univers permettent d'estimer la quantité totale de matière, dont certaines théories prédisent que 90% sont de la (...)
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  17. Tests and Anomalies of Post-Newtonian Gravitational Theories.Nicolae Sfetcu - manuscript
    Usually, the "laboratory" of gravitational tests was the celestial bodies, the astrophysical systems. But such tests are disturbed by non-gravitational effects. The most used such "laboratory" was the solar system. Recently, scientists have focused on observing binary pulsars for the verification of gravitational theories, by observing the variations of the orbital period, thus providing indirect evidence for the emission of gravitational radiation. But the experimenter cannot "arrange the lab" according to his needs, nor trigger certain events when he needs them. (...)
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  18. Tests et anomalies des théories de la gravité post-newtoniennes.Nicolae Sfetcu - manuscript
    Dans la première édition du Principia, Newton considérait que des expériences avec le pendule lui permettraient de déchiffrer les différents types de force de résistance et leur variation avec la vitesse. Habituellement, le « laboratoire » des tests gravitationnels était les corps célestes, les systèmes astrophysiques. Mais ces tests sont perturbés par des effets non gravitationnels. Le « laboratoire » le plus utilisé était le système solaire. Récemment, les scientifiques se sont concentrés sur l'observation des pulsars binaires pour la vérification (...)
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  19. Le modèle atomique de Bohr, un exemple de programme de recherche.Nicolae Sfetcu - manuscript
    Le modèle atomique de Bohr a été l'un des exemples les plus brillants de la méthodologie des programmes de recherche d'Imre Lakatos. Les grandes lignes du programme de recherche de Bohr (Bohr 1913) peuvent être caractérisées par : 1. Le problème initial ; 2. Ses heuristiques négatives et positives ; 3. Les problèmes qu'il a tenté de résoudre au cours du développement ; 4. Son point de dégénérescence (point de saturation) et, enfin, 5. Le programme par lequel il a été (...)
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  20. Unificarea gravitației cu celalalte forțe fundamentale.Nicolae Sfetcu - manuscript
    Au fost propuse mai multe teorii unificatoare. Marea unificare presupune existența unei forțe electronucleare. Ultimul pas în unificare ar necesita o teorie care să includă atât mecanica cuantică cât și gravitația prin relativitatea generală (”teoria finală”). După 1990, unii fizicieni consideră că teoria M 11-dimensională, identificată adesea cu una dintre cele cinci teorii ale supercorzilor perturbative, sau uneori cu supergravitația maximal-supersimetrică 11-dimensională, este teoria finală. DOI: 10.13140/RG.2.2.23549.92642.
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  21. Prolifération des théories post-newtoniennes.Nicolae Sfetcu - manuscript
    Les théoriciens ont formulé un ensemble de critères fondamentaux que toute théorie de la gravité devrait satisfaire, deux purement théoriques et deux fondés sur des preuves expérimentales. Ainsi, une théorie doit être : complet (capable d'analyser à partir des « premiers principes » le résultat de toute expérience d'intérêt), auto-cohérent (sa prédiction pour le résultat de chaque expérience doit être unique), relativiste (à la limite où la gravité est négligée par rapport à d'autres interactions physiques, les lois non gravitationnelles de (...)
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  22. Prolifération des théories post-einsteiniennes - Formalisme paramétrisé post-newtonien (PPN).Nicolae Sfetcu - manuscript
    Immédiatement après l'élaboration et le succès de la relativité générale, des théories alternatives pour la gravité ont commencé à apparaître. En développant ces théories, de nombreuses stratégies différentes (heuristiques positives) ont été essayées, en ajoutant de nouvelles hypothèses à la RG, en utilisant un espace-temps pour lequel l'univers est statique, des hypothèses qui éliminent les singularités gravitationnelles, etc. Pour l'évaluation des modèles de gravité, plusieurs séries de tests ont été proposées. Le formalisme paramétrisé post-newtonien (PPN) détaille les paramètres qui différencient (...)
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  23. Classic Gravitational Tests of Post-Einsteinian Theories.Nicolae Sfetcu - manuscript
    Albert Einstein proposed three tests of general relativity, later named the classic tests of general relativity, in 1916: the precession of the perihelion of Mercury's orbit, sun light deflection, and the gravitational redshift of the light. For gravitational testing, the indirect effects of gravity are always used, usually particles that are influenced by gravity. In the presence of gravity, the particles move along curved geodesic lines. The sources of gravity that cause the curvature of spacetime are material bodies, depending on (...)
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  24. Proliferation of Post-Newtonian, Non-Relativistic Theories.Nicolae Sfetcu - manuscript
    Theoreticians have formulated a set of fundamental criteria that any theory of gravity should satisfy, two purely theoretical and two that are based on experimental evidence. Thus, a theory must be complete (capable of analyzing from the "first principles" the result of any experiment of interest), self-consistent (its prediction for the outcome of each experiment must be unique), relativistic (at the limit when gravity is neglected compared to other physical interactions, non-gravitational laws of physics must be reduced to special relativity (...)
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  25. Gravity and Gravitational Tests.Nicolae Sfetcu - manuscript
    Theories in science in general, and in physics in particular, are confirmed (temporarily) by experiments that verify the assertions and predictions of theories, thus laying the groundwork for scientific knowledge. Francis Bacon was the first to support the concept of a crucial experiment, which can decide the validity of a hypothesis or theory. Later, Newton argued that scientific theories are directly induced by experimental results and observations, excluding untested hypotheses. DOI: 10.13140/RG.2.2.33549.08167.
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  26. Gravité et tests gravitationnels.Nicolae Sfetcu - manuscript
    Les théories scientifiques en général, en physique en particulier, sont confirmées (temporairement) par des expériences vérifiant les affirmations et les prédictions des théories, jetant ainsi les bases de la connaissance scientifique. Francis Bacon a été le premier à soutenir le concept d'une expérience cruciale, qui peut décider la validité d'une hypothèse ou d'une théorie. Plus tard, Newton a soutenu que les théories scientifiques sont directement induites par les résultats expérimentaux et les observations, excluant les hypothèses non vérifiées. DOI: 10.13140/RG.2.2.34744.70403 .
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  27. Strong Field Gravitational Tests.Nicolae Sfetcu - manuscript
    When the density of the body becomes large enough, general relativity predicts the formation of a black hole. The neutron stars of about 1.4 solar masses and the black holes are the final stage for the evolution of the massive stars. Usually a black hole in a galaxy has played an important role in its formation and related cosmic structures. Such bodies provide an efficient mechanism for the emission of electromagnetic radiation and the formation of microquasars. Accretion can lead to (...)
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  28. Gravitational Singularities.Nicolae Sfetcu - manuscript
    Gravitational singularities in general relativity are spacetime locations where the gravitational field becomes infinite. Scalar invariant curves of spacetime include a measure of matter density. Some physicists and philosophers believe that because the density of matter tends to become infinite in singularity, spacetime laws are no longer valid there. A gravitational singularity almost universally accepted in astrophysics and cosmology as the earliest state of the universe, is the Big Bang. In this case also, the known laws of physics are no (...)
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  29. Nature's Information and Harmonic Proportion.Michael A. Sherbon - manuscript
    The history of science is polarized by debates over Plato and Aristotle’s holism versus the atomism of Democritus and others. This includes the complementarity of continuous and discrete, one and the many, waves and particles, and analog or digital views of reality. The three-fold method of the Pythagorean paradigm of unity, duality, and harmony enables the calculation of fundamental physical constants required by the forces of nature in the formation of matter; thereby demonstrating Plato’s archetypal viewpoint.
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  30. Constants of Nature From the Dynamics of Time.Michael A. Sherbon - manuscript
    An archetypal model for the constants of nature is found from the ancient geometry of the the Cosmological Circle and is related to Plato's cosmology, with its dynamics and harmonics of time cycles. The inverse fine-structure constant and the proton-electron mass ratio are calculated, connecting fundamental mathematical constants of geometry with the latest theoretical and experimental values of these physical constants. Continuing in the tradition of George Gamow's suggestion, "Since the works of Sir Arthur Eddington, it has become customary to (...)
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  31. Pythagorean Geometry and Fundamental Constants.Michael A. Sherbon - manuscript
    The Cosmological Circle from ancient geometry, with its right triangles, and the ratios of the Pythagorean Table are found to be harmonically related to the fundamental physical constants. After a brief history of harmonic mathematics, harmonic values are calculated for the speed of light constant, gravitational constant, Planck's constant, and the inverse fine-structure constant. We then calculate the harmonic of electron mass and proton mass, showing the related Pythagorean/Cosmological Circle harmonics; and speculate on geometry and symmetry.
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  32. Classical Quintessence and the Cosmological Constant.Michael A. Sherbon - manuscript
    From the cosmology of classical quintessence and the Cosmological Circle of ancient geometry, quintessence is calculated as the primary fundamental physical constant. The role of the fine-structure constant in quantum electrodynamics is briefly discussed and the same value for inverse alpha, the inverse fine-structure constant found in previous work, is confirmed. Then the cosmological constant is calculated, confirming a recent theoretical prediction related to the fine-structure constant and the cosmological constant.
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  33. Extra-Temporal Causality.Stephen I. Ternyik - manuscript
    The physical properties of time point to extra-temporal causality; this research abtract compiles the key findings.
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  34. Extra-Temporal Causality/Hebrew Version.Stephen I. Ternyik - manuscript
    The physical properties of time point to extra-temporal causality; this research abstract compiles the key findings in Hebrew.
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  35. On the Notion of Existence.Piotr Witas - manuscript
    I argue that a slight shift in our understanding of the notion of existence is needed in order to cope with the problem of external world and the problem of mind and body. As a consequence of it being taught by "givenness" of the subjective mind, and despite its applicability in objective contexts, it should be considered a "tool" akin to qualia, rather than pertaining to a "true", objective reality. In plain language, one's supposed relation with their surroundings is known (...)
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  36. Generalizing "Charge Without Charge" to Obtain Classical Analogs of Short-Range Interactions.Mark Sharlow - 2007
    Several decades ago, Wheeler and Misner presented a model of electric charge based on the topological trapping of electric field lines in wormholes. In this paper, which does not argue for or against the "charge without charge" concept, I describe some generalizations of this model which might serve as topological analogs of color charges and electroweak charges.
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  37. Why Is There Something, Rather Than Nothing?Sean M. Carroll - forthcoming - In Eleanor Knox & Alastair Wilson (eds.), Routledge Companion to the Philosophy of Physics.
    It seems natural to ask why the universe exists at all. Modern physics suggests that the universe can exist all by itself as a self-contained system, without anything external to create or sustain it. But there might not be an absolute answer to why it exists. I argue that any attempt to account for the existence of something rather than nothing must ultimately bottom out in a set of brute facts; the universe simply is, without ultimate cause or explanation.
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  38. Time and Physical Geometry. A Formalization of Putnam’s Proof.Jan Czerniawski - forthcoming - Logic and Logical Philosophy:1.
    Putnam’s proof that time flow is incompatible with Relativity is underestimated, mostly due to Stein’s interpretation of the notion of reality in it as a two-term relation. This interpretation makes it vulnerable to easy criticism and makes various ways of escaping its conclusion possible. An alternative approach is proposed, resulting in a formalization which seems closer to Putnam’s intentions where reality is interpreted as a non-relational property. Although it makes the proof immune to all standard strategies of blocking the proof, (...)
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  39. Explaining Experience In Nature: The Foundations Of Logic And Apprehension.Steven Ericsson-Zenith - forthcoming - Institute for Advanced Science & Engineering.
    At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...)
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  40. Introduction to the Neoclassical Interpretation: Quantum Steampunk.Shiva Meucci - forthcoming - Cosmos and History: The Journal of Natural and Social Philosophy.
    In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based “Hydrodynamic” treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for (...)
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  41. Probabilistic Analysis of the Oseberg GBS Foundation Against Failure in Cyclic Loading.K. Ronold, H. O. Madsen & Thore Egeland - forthcoming - Veritas – Revista de Filosofia da Pucrs.
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  42. OUT OF TIME - Predicting the Science of Future Centuries and Millennia.Rodney Bartlett - 2021 - Beau Bassin-Rose Hill, Mauritius: LAP (LAMBERT Academic Publishing).
    This book is my gift to Albert Einstein on the occasion of his 142nd birthday - and is also a gift to everybody in the world he helped to shape! -/- My book adopts the view that the universe is infinite and eternal - but scientifically created. This paradox of creating eternity depends on the advanced electronics developed by future humanity. Those humans will develop time travel, plus programs that use "imaginary" time and infinite numbers like pi. They'll also become (...)
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  43. How to Witness the Christian Faith in an Age of Immense Scientific Advancements.Moorad Alexanian - 2020 - God and Nature.
    We discuss the intellectual preparation necessary for a Christian student to reconcile his/her Christian faith with science. -/- .
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  44. Other Matters: Karen Barad’s Two Materialisms and the Science of Undecidability.Jonathan Basile - 2020 - Angelaki 25 (5):3-18.
    Karen Barad’s Meeting the Universe Halfway relies on mutually incompatible grounding gestures, one of which describes the relationality of an always already material-discursive reality, while the other seeks to ground this relation one-sidedly in matter. These two materialisms derive from the gesture she borrows from the New Materialist (and other related) fields, which posits her work as an advance over the history of “representationalism” and “social constructivism.” In turn, this one-sided materialism produces a skewed reading of the quantum mechanical phenomena (...)
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  45. What Is Life: An Informational Model of the Living Structures.Florin Gaiseanu - 2020 - Biochemistry and Molecular Biology 5 (2):18-28.
    Schröedinger’s question “what is life?” was a real challenge for the scientific community and this still remains as an opened question, because in spite of the important advances in various scientific branches like philosophy, biology, chemistry and physics,, each of them assesses life from its particular point of view to explain the life’ characteristic features, so not a coherent and well structured general model of life was reported. In this paper life is approached from informational perspective, starting from earlier Draganeacu's (...)
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  46. Resenha do livro "Variational Approach to Gravity Field Theories - From Newton to Einstein and Beyond".Alessio Gava - 2020 - Revista Brasileira de Ensino de Física 42.
    This is a critical review of the book Variational Approach to Gravity Field Theories - From Newton to Einstein and Beyond (2017), written by the Italian astrophysicist Alberto Vecchiato. In his work, Vecchiato shows that physics, as we know it, can be built up from simple mathematical models that become more complex step by step by gradually introducing new principles. The reader is invited to follow the steps that lead from classical physics to relativity and to understand how this happens (...)
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  47. Coronavirus Vaccine — Where We Are Now.Flora Graham - 2020 - Nature 582 (7811):1-4.
    Catch up on the status of the more than 135 vaccines in development against the SARS-CoV-2 virus, ponder the biology and physics of free will and learn how scientists helped win the battle over evolution in US classrooms.
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  48. The Termination Risks of Simulation Science.Preston Greene - 2020 - Erkenntnis 85 (2):489-509.
    Historically, the hypothesis that our world is a computer simulation has struck many as just another improbable-but-possible “skeptical hypothesis” about the nature of reality. Recently, however, the simulation hypothesis has received significant attention from philosophers, physicists, and the popular press. This is due to the discovery of an epistemic dependency: If we believe that our civilization will one day run many simulations concerning its ancestry, then we should believe that we are probably in an ancestor simulation right now. This essay (...)
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  49. Pathological Illustrations Between the Sixteenth and Nineteenth Centuries.Raffaele Pisano - 2020 - Metascience 29 (1):99-101.
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  50. Historical Foundations of Physics & Applied Technology as Dynamic Frameworks in Pre-Service STEM.Raffaele Pisano, Philippe Vincent, Kosta Dolenc & Mateja Ploj Virtič - 2020 - Foundations of Science 1 (1):1-30.
    In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...)
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