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I make a Quinean case that Quine’s ontological relativity marked a wrong turn in his philosophy, that his fundamental commitments point toward the classical view of ontology that was worked out in most detail in his Word and Object (1960). This removes the impetus toward (a version of) structuralism in his later philosophy.
Chapter Six examines the trajectory of physical-psychical scientists in the early twentieth century. By 1900 the network of physical-psychical scientists was weaker because many had died or were too old or busy to commitment themselves to new experimental enquiries. Those strongly committed to psychical research tended to explore connections between physics and psychics via writing rather than new experiments. The writing of Lodge, Barrett, Kingsland and others explored the connections between psychical research and modern developments in physics and religion. Many thought that Lodge’s connections went too far while others did not think the connections went far enough. Among those who sought to transcend Lodge were professional and amateur radio enthusiasts, and psychical researchers, and a younger generation of psychical researchers who believed relativity and quantum theories was more effective than older, mainly ether-based physics, at rendering psychical effects plausible.
The conclusion examines the legacy of physical-psychical scientists. By the 1940s even the most sympathetic physical-psychical scientists were ambivalent at best about the ‘psychical’ achievements of Crookes, Lodge and other veteran physical-psychical scientists. From the 1940s until the 1960s very few of the connections between physics and psychics involved the modern physics of relativity and quantum theories; the 1970s, however, saw a rejuvenation of interest in these possibilities, which became a major focus of the new field of ‘paraphysics’ whose theories and practices continue to cause controversy. I argue that the protagonists of this book would have recognised many of the problems faced by practitioners of paraphysics but repudiated these practitioners’ perceptions that Victorian physics was materialistic, rigid and closed to psychical significance.
The use of Grassmann variables to give a semi-classical description of quantum variables with a finite spectrum introduced by Berezin is described. Then pseudo-classical Lagrangians for the description of spin, of the electric charge, of the sign of the energy of a particle are described. This approach regularizes the divergences of the self-energies: (1) its quantization gives finite results; (2) a suitable mean gives the underlying finite classical theory.
In the chosen family of Einstein space-times one can give an ADM formulation of tetrad gravity and of its first-class constraints, so that fermions can be described in this framework. There are 16 configuration variables, 16 momenta, and 14 first-class constraints. Then one can define a new canonical basis adapted to 10 of the 14 constraints (not to the super-Hamiltonian and super-momentum ones) with a Shanmugadhasan canonical transformation. This allows identifying two pairs of canonical variables describing the tidal effects (the gravitational waves after linearization). However, they are not Dirac observables.
There is a description of the 3+1 approach allowing definition of global non-inertial frames in Minkowski space-time. One gives a time-like observer and a nice foliation with 3-spaces (namely a clock synchronization convention). Then one introduces Lorentz scalar radar 4-coordinates: the time is an increasing function of the proper time of the observer and the 3-coordinates live in the instantaneous 3-spaces. The connection of the radar coordinates with the standard ones defines the four embedding functions describing the foliation with 3-spaces. Then there is the definition of parametrized Minkowski theories for every kind of matter admitting a Lagrangian description. The new Lagrangian is a function of the matter and of the embedding, but is singular so that the embedding variables are gauge variables. As a consequence, the transition from a non-inertial frame to either an inertial or non-inertial frame is a gauge transformation not changing the physics but only the inertial forces.
After a description of inertial and non-inertial frames in the Galilei space-time of non-relativistic Newtonian physics with a discussion of inertial forces, there is metrological definition of what is time and space in special relativity. Then there is a review of the standard 1+3 approach for the “local” description of non-inertial frames and of its limitations.
The following family of Einstein space-times allows the use of the 3+1 approach: (1) globally hyperbolic (this allows the ADM Hamiltonian formulation); (2) asymptotically Minkowskian at spatial infinity (all the 3-spaces approach parallel space-like hyper-planes); (3) without super-translations (at spatial infinity there is the asymptotic ADM Poincaré algebra needed for particle physics). It turns out that the asymptotic ADM Poincaré 4-momentum is orthogonal to the asymptotic hyper-planes. Therefore, the 3+1 approach allows describing the Hamiltonian formulation of metric gravity and of its first-class constraints in the family of the non-inertial rest-frames.
In this chapter there is the description of fields and fluids in the rest-frame instant form of dynamics with the definition of their Wigner-covariant degrees of freedom inside the Wigner 3-spaces after the decoupling of the external center of mass. This is done for the Klein–Gordon, electromagnetic, Dirac, and Yang–Mills fields. In the case of the electromagnetic field there is the identification of the Wigner-covariant Dirac observables. This procedure can be applied also to Yang–Mills fields, but to get the Dirac observables one needs the knowledge of an explicit solution of the Gauss’s law constraints. Then there is the description of relativistic fluids in this framework. In particular a definition of the relativistic micro-canonical ensemble in the Wigner 3-spaces is given and it is shown which equations have to be solved to get a consistent relativistic statistical mechanics.
The post-Minkowskian limit of ADM tetrad gravity in the 3-orthogonal gauges of the non-inertial rest-frames is defined with particles and the electromagnetic field as matter. Then, the post-Newtonian expansion of the post-Minkowskian linearization is studied. For binaries, the results are compatible with the standard one in harmonic gauges. However, there is the new result that a non-local version of the inertial gauge variable York time may explain many of the experimental data giving rise to the existence of dark matter, which would be reduced to a relativistic inertial effect to be treated by means of relativistic celestial metrology.
Given an isolated system of either free or interacting particles and the associated realization of the ten conserved Poincaré generators its total conserved time-like 4-momentum defines its inertial rest-frame as the 3+1 splitting whose space-like 3-spaces (named Wigner 3-spaces) are orthogonal to it and whose inertial observer is the Fokker–Pryce 4-center of inertia. There is a discussion of the problem of the relativistic center of mass based on the fact that the 4-center functions “only” of the Poincaré generators of the isolated system are the following three non-local quantities: the non-canonical covariant Fokker–Pryce 4-center of inertia, the canonical non-covariant Newton–Wigner 4-center of mass and the non-canonical non-covariant Mőller 4-center of energy. At the Hamiltonian level one is able to express the canonical world-lines of the particles and their momenta in terms of the Jacobi variables of the external Newton–Wigner center of mass (a non-local non-covariant non-measurable quantity) and of Wigner-covariant relative 3-coordinates and 3-momenta inside the Wigner 3-spaces. This solves the problem of the elimination of relative times in relativistic bound states and to formulate a consistent Wigner-covariant relativistic quantum mechanics of point particles. The non-relativistic limit gives the Hamilton–Jacobi description of the system after the separation of Newtonian center of mass. Finally there is the definition of the non-inertial rest-frames whose 3-spaces are orthogonal to the total 4-momentum of the isolated system at spatial infinity.
The present study compared both linguistic and non-linguistic representations of motion events in Korean–English sequential bilinguals sampled at varying proficiency levels (N = 80) against each other and against those of Korean and English monolinguals (N = 15 each). The bilinguals' L2 descriptions of motion events showed that their encoding patterns were influenced by both the first language (L1) and second language (L2) and also displayed unique behaviors that were not found in either monolingual norm. The non-verbal results on a triads-matching task demonstrated that bilinguals' categorization patterns followed L1-based patterns rather than L2-based patterns. The extent to which these bilinguals employed L2 encoding patterns in their motion event descriptions was largely modulated by L2 proficiency, whereas length of immersion experience in an L2-speaking country emerged as the only predictor of their non-verbal categorization patterns. These findings suggest that the bilinguals' verbal behavior seems more susceptible to change than their non-verbal behavior.
Here we review special relativity. We define the Lorentz group and Lorentz transformations; then the kinematics of special relativity, defining arbitrary tensors and various common ones; then the relativistic Lorentz force law, for the kinematics of special relativity. We define a relativistically covariant Lagrangian and invariant action for a particle and extend that to a coupling between a current and an electromagnetic gauge field.
We define general relativity. We first consider intrinsically curved spaces and the notion of metric. Einstein's theory of general relativity is defined, based on the two physical assumptions, that gravity is geometry, and that matter sources gravity, and leading to general coordinate invariance and the equivalence principle. Kinematics, specifically tensors, Christoffel symbol and covariant derivatives, is defined. The motion of a free particle in a gravitational field is calculated.
The aim of this work is to provide new information about the history of astronomical science and the efforts of the people that have enriched our discipline, often coming from anonymity. Here we compile the attempts made in our country to prove the theory of General Relativity through experiments that, as they were without success, fell into oblivion.
This paper addresses the relationships between Arthur S. Eddington, former director of the Cambridge Observatory (1914-1944), with the International Astronomical Union. It is demonstrated that the Union was related to every major moment in Eddington’s scientific career. New historical elements are brought forward, in the last section of the paper, to demonstrate Eddington’s action in favour of German colleagues during the Second World War.
We review the early history of the general theory of relativity and its subsequent decline to the backwaters of physics and astronomy. We describe the renaissance of the theory during the 1960s and the renewed effort to subject it to experimental tests using laboratory experiments, the solar system, binary pulsars, and finally in 2015, gravitational waves. We then discuss future directions for experimental tests in the strong-field and dynamical regimes.
We discuss a range of metric theories of gravity and their post-Newtonian limits. We begin with a general recipe for calculating the post-Newtonian limit in generic metric theories, and then turn to specific theories. Included are general relativity, scalar-tensor theories, vector-tensor theories (including Einstein-Aether and Khronometric theories), tensor-vector-scalar theories (including TeVeS), quadratic gravity theories (including Chern-Simons theory), and massive gravity theories. We also review the fate of theories of gravity that were featured in the first edition of this book, but that are no longer considered viable or interesting, including Whitehead’s theory and Rosen’s bimetric theory.