It is nearly impossible to open a textbook on Newtonian mechanics without encountering the concept of inertial frames: the frames that are privileged by the theory’s dynamics. In this paper, I argue that extant definitions of inertial frames are unsatisfactory. I criticise two common definitions of inertial frames: law-based definitions, according to which inertial frames are simply those in which the laws are true, and structure-based definitions, according to which inertial frames are those that are (...) ‘adapted’ to spatiotemporal structure. I then offer a new, symmetry-based definition of inertial frames. This definition offers a non-conventional way of specifying the dynamically privileged frames. The result clarifies the foundations of Newtonian mechanics and accounts for the empirical success of coordinate-dependent formulations of it. (shrink)

It is suggested that the mathematically abstract coordinate frames of reference commonly visualized to be centered at the celestial bodies have real counterparts in the shape of well-defined rigid spatial resonant singularities of infinite extension, which accommodate the matter waves from the superimposition of which the body residing at the coordinate origin results. A universally valid inertial reference frame system is proposed. Qualitative explanations are offered for the inertial and gravitational forces, their observed proportionality, and for the occurrence (...) of second-order gravitational effects in the vicinity of massive bodies. The universal redshift is assumed to result from a closure condition of the eigenspaces introduced. (shrink)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws. I raise two objections to this inertial functionalism. First, it depends on a prior assumption about which coordinate systems defined in a theory are reference frames, and hence on assumptions about which geometric structures are spatiotemporal. This makes Knox’s account circular. Second, her account is vulnerable to several counterexamples, giving the wrong result when applied to topological quantum field (...) theories and parity- and time-asymmetric theories. I advance an alternative account on which our spacetime concept is a cluster concept. On this view, the notion of metaphysical fundamentality may feature in the cluster, in which case spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws. I raise two objections to this inertial functionalism. First, it depends on a prior assumption about which coordinate systems defined in a theory are reference frames, and hence on assumptions about which geometric structures are spatiotemporal. This makes Knox’s account circular. Second, her account is vulnerable to several counterexamples, giving the wrong result when applied to topological quantum field (...) theories and parity- and time-asymmetric theories. I advance an alternative account on which our spacetime concept is a cluster concept. On this view, the notion of metaphysical fundamentality may feature in the cluster, in which case spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, (...) each non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories. (shrink)

The experimental (apparent) space-time transformations connect coordinates altered by length contraction and clock retardation. When clocks are synchronized by means of light signals (Einstein–Poincaré procedure) or by slow clock transport, the experimental space-time. transformations assume the mathematical form of the “Extended space-time transformations”.(4) These reduce to the Lorentz–Poincaré transformations when one of the frames they connect is the fundamental inertial frame. If the synchronization procedure were perfect, the experimental space-time transformations would assume the form of Selleri’s inertial (...) transformations.(5) The real space-time transformations are those which are disclosed when the systematic measurement distortions are corrected. (shrink)

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: the interpretation of the weak equivalence principle and the relationship between gravity and inertia; the connection between gravitational redshift results and spacetime curvature; and the Einstein equivalence principle and the ability to ``transform away" gravity in local inertial coordinate systems.

A class of theories which satisfy the Relativity Principle has been overlooked. The kinematics for these theories is derived by relaxing the 'boost isotropy' symmetry normally invoked, and the role the dynamical fields play in determining the inertial coordinate systems is emphasised, leading to a criticism of Friedman's (1983) practice of identifying them via the absolute objects of a spacetime theory alone. Some theories complete with 'boost anisotropic' dynamics are given.

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure (...) in a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

With the interaction interpretation, the Lorentz transformation of a system arises with selection from a superposition of its states in an observation-interaction. Integration of momentum states of a mass over all possible velocities gives the rest-mass energy. Static electrical and magnetic fields are not found to form such a superposition and are to be taken as irreducible elements. The external superposition consists of those states that are reached only by change of state of motion, whereas the internal superposition contains all (...) the states available to an observer in a single inertial coordinate system. The conjecture is advanced that states of superposition may only be those related by space-time transformations (Lorentz transformations plus space inversion and charge conjugation). The continuum of external and internal superpositions is examined for various masses, and an argument for the unity of the super-positions is presented. (shrink)

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach (...) the Lorentz transformation is a 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications. (shrink)

Nonstandard synchronizations of inertial observers in special relativity and synchronizations with respect to a uniformly rotating observer are investigated in a setting which avoids coordinates and transformation rules and so removes some misunderstandings.

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations (...) in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields (...) of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity in some sense relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in (...) a space-time coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time (...) coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

Reichenbach, Grünbaum, and others have argued that special relativity is based on arbitrary conventions concerning clock synchronizations. Here we present a mathematical framework which shows that this conventionality is almost equivalent to the arbitrariness in the choice of coordinates in an inertial system. Since preferred systems of coordinates can uniquely be defined by means of the Lorentz invariance of physical laws irrespective of the properties of light signals, a special clock synchronization—Einstein's standard synchrony—is selected by this principle. (...) No further restrictions conerning light signal synchronization, as proposed, e.g., by Ellis and Bowman, are required in order to refute conventionalism in special relativity. (shrink)

Interest has been recently devoted to historical and philosophical aspects about fractional calculus and its adoption as additional mathematical tool in different physics areas as well as in other scientific applications. However, potential application of FC towards relativity is still lacking. In relativity theory, Lorentz transformation of time and position coordinates plays a major role while the corresponding outcomes still defy our ‘common sense’. As some problems in physics can be solved by following different mathematical routes leading to the (...) same result, the present paper suggests an alternative method to relativity. Instead of converting time and position data from different inertial reference frames through Lorentz transformation, it is here envisaged to numerically adjust relativistic results with the help of FC. Bearing in mind well established postulates from relativity, we intend to fill up this gap by addressing and discussing the main arguments in favour of the prospective use of FC as emergent and alternative tool applied to relativity. (shrink)

The Lorentz transformation relates the Einstein-defined measures, associated with two inertial frames, of the space and time coordinates of a body or event. From such information relative velocities and accelerations may be deduced, and their appropriate transformations derived. All other transformations of special relativity are derived from the Lorentz transformation and hence depend on the coordinate measures related by the transformation. In particular, the transformation of forces depends on that for accelerations; hence it may not be appropriately applicable (...) to equilibrium phenomena involving null-acceleration. It is suggested that this is the root of the apparent paradox which arises when the conventional force transformation is applied to the consideration of a right-angled lever in equilibrium in its proper inertial frame. It is shown that this paradox is resolved by the employment of a nonconventional but appropriate special relativistic transformation for forces not associated with corresponding accelerations. (shrink)

Protophysics and Special Theory of Relativity. First, a proposal for a constructive foundation of the Special Theory of Relativity by M. Buth is criticized and confronted with an alternative proposal by the author. The main idea is to solve the problem of transforming coordinates between inertial systems in terms of the General Theory of Measurement. Regarding transformations of co-ordinates as transformations of thecorresponding “functions of measurement” these functions have to meet two demands. 1. To identify measured values which (...) are related to different inertial systems and measuring procedures as the same magnitude, the ratio scale of length and duration has to be defined with respect to the whole class of inertial systems. 2. Using the concept of a certain physical magnitude, propositions about measuring devices are made which are invariant with respect to measuring procedures. As aconsequence every transformation between functions of measurement has to be an equivalence relation. The first demand leads to linearity, the second one reduces the set of permissible transformations between inertial systems to the alternative of Galilei- and Lorentz-transformation. The (im)possibility of putting an absolute simultaneity into practice decides between these transformations. (shrink)

The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based (...) on wave-particle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory. (shrink)

The structure of the Lorentz transformation depends intimately on the conventional operations for measurement of lengths (L) and time intervals (T). The prescription for length measurement leads to justifiable utilization of Euclidean geometry over finite values of the coordinates. Then T-values can be regarded as ratios of length measurements within a suitably defined clock. In certain cases the synchronization process should be supplemented by measurements providing position certification. The Lorentz transformation emerges from three specific symmetry statements, assured by the (...) nature of the L and T operations: (1) one-one correspondence of finite values of the coordinates of two inertial frames, (2) frame reciprocity, and (3) spatial isotropy. (Light signaling is not needed in this derivation. Afterward, it is assumed that light is indeed an agent moving with the common speed revealed by the transformation.) When rest masses have been determined in the conventional fashion, the conservation of momentum and of energy follow from the kinematics—a result due to Einstein. (shrink)

It is argued that, under the assumption that the strong principle of equivalence holds, the theoretical realization of the Mach principle (in the version of the Mach-Einstein doctrine) and of the principle of general relativity are alternative programs. That means only the former or the latter can be realized—at least as long as only field equations of second order are considered. To demonstrate this we discuss two sufficiently wide classes of theories (Einstein-Grossmann and Einstein-Mayer theories, respectively) both embracing Einstein's theory (...) of general relativity (GRT). GRT is shown to be just that “degenerate case” of the two classes which satisfies the principle of general relativity but not the Mach-Einstein doctrine; in all the other cases one finds an opposite situation.These considerations lead to an interesting “complementarity” between general relativity and Mach-Einstein doctine. In GRT, via Einstein's equations, the covariant and Lorentz-invariant Riemann-Einstein structure of the space-time defines the dynamics of matter: The symmetric matter tensor Ttk is given by variation of the Lorentz-invariant scalar densityL mat, and the dynamical equations satisfied by Tik result as a consequence of the Bianchi identities valid for the left-hand side of Einstein's equations. Otherwise, in all other cases, i.e., for the “Mach-Einstein theories” here under consideration, the matter determines the coordinate or reference systems via gravity. In Einstein-Grossmann theories using a holonomic representation of the space-time structure, the coordinates are determined up to affine (i.e. linear) transformations, and in Einstein-Mayer theories based on an anholonomic representation the reference systems (the tetrads) are specified up to global Lorentz transformations. The corresponding conditions on the coordinate and reference systems result from the postulate that the gravitational field is compatible with the strong equivalence of inertial and gravitational masses. (shrink)

I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein’s historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space–time has (...) a discrete spectrum, relative to classical observers in space–time. This description is covariant with respect to coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics. (shrink)

The disk that rotates in an inertial frame in special relativity has long been analysed by assuming a Lorentz contraction of its peripheral elements in that frame, which has produced widely varying views in the literature. We show that this assumption is unnecessary for a disk that corresponds to the simplest form of rotation in special relativity. After constructing such a disk and showing that observers at rest on it do not constitute a true rotating frame, we choose a (...) “master” observer and calculate a set of disk coordinates and spacetime metric pertinent to that observer. We use this formalism to resolve the “circular twin paradox”, then calculate the speed of light sent around the periphery as measured by the master observer, to show that this speed is a function of sent-direction and disk angle traversed. This result is consistent with the Sagnac Effect, but constitutes a finer analysis of that effect, which is normally expressed using an average speed for a full trip of the periphery. We also use the formalism to give a resolution of “Selleri’s paradox”. (shrink)

One of the most debated problems in the foundations of the special relativity theory is the role of conventionality. A common belief is that the Lorentz transformation is correct but the Galilean transformation is wrong. It is another common belief that the Galilean transformation is incompatible with Maxwell equations. However, the “principle of general covariance” in general relativity makes any spacetime coordinate transformation equally valid. This includes the Galilean transformation as well. This renders a new paradox. This new paradox is (...) resolved with the argument that the Galilean transformation is equivalent to the Lorentz transformation. The resolution of this new paradox also provides the most straightforward resolution of an older paradox which is due to Selleri in. I also present a consistent electrodynamics formulation including Maxwell equations and electromagnetic wave equations under the Galilean transformation, in the exact form for any high speed, rather than in low speed approximation. Electrodynamics in rotating reference frames is rarely addressed in textbooks. The presented formulation of electrodynamics under the Galilean transformation even works well in rotating frames if we replace the constant velocity v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {v}$$\end{document} with v=ω×r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {v}=\varvec{\omega }\times \mathbf {r}$$\end{document}. This provides a practical tool for applications of electrodynamics in rotating frames. When electrodynamics is concerned, between two inertial reference frames, both Galilean and Lorentz transformations are equally valid, but the Lorentz transformation is more convenient. In rotating frames, although the Galilean electrodynamics does not seem convenient, it could be the most convenient formulation compared with other transformations, due to the intrinsic complex nature of the problem. (shrink)

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...) dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the (...) ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors EHv and BHv and the abstract tensors, the 4-vectors Ea and Ba. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D bf E and B and their ST. (shrink)

The Möbius transformation (MT) was analyzed as a coordinate transformation in the Minkowski form. The transformation function contains three separate light cones. The Weyl spheres were interpreted as basic constituents of local light cones. These cones are related to the denominators of the MT and its inverse, and their apexes define an axis with the top of the global light cone as the centerpoint. That axis represents the local part of the world-line of a moving frame of reference. On the (...) world-line, the scale factor of the MT is proportional to the ratio of the radii of the initial Weyl sphere and the equivalent transformed one. The projection centers, defining the transformation of the world-line, were determined graphically. There are two types of such MT's. Inner transformations have their projetion centers on the axes of the frame at rest, outer transformations on the axes of the “observed” moving frame. The signature of x 0 2 −r2 is conserved during inner transformations. All possible directions of the world-line of an inertial frame form a timelike “mass cone” around the time axis of the frame at rest. The mass cone and the related spacelike “phase cone” may be seen as projections of a lightlike central motion on the surface of a Weyl sphere. Conformal transformations leave both the mass cone and the phase cone invariant: the MT locally, and the Lorentz transformation globally. The moving frame of any lightlike particle rotates by π/2 radians, thus exchanging the time axis with one of the space axes. The measurable mass of such a particle is considered to be zero because only the central plane of the particle is space-oriented. The real mass is invariant. To test this hypothesis, the two γ-quanta produced by the electron pair annihilation should be led to a recollision, for recreating the initial electron-position pair. (shrink)

Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach, which we call the “true transformations (TT) relativity.” In this approach a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor (when no basis has been introduced) or equivalently by a coordinate-based geometric quantity comprising both components and a basis (when some basis has been introduced). This invariant approach is compared with the usual covariant approach, which mainly deals with the (...) basis components of tensors in a specific, i.e., Einstein's coordinatization of the chosen inertial frame of reference. The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from “3+1” space and time, e.g., the synchronously determined spatial length. This formulation is called the “apparent transformations (AT) relativity.” It is shown that the principal difference between these approaches arises from the difference in the concept of sameness of a physical quantity for different observers. This difference is investigated considering the spacetime length in the “TT relativity” and spatial and temporal distances in the “AT relativity.” It is also found that the usual transformations of the three-vectors (3-vectors) of the electric and magnetic fields E and B are the AT. Furthermore it is proved that the Maxwell equations with the electromagnetic field tensor Fab and the usual Maxwell equations with E and B are not equivalent, and that the Maxwell equations with E and B do not remain unchanged in form when the Lorentz transformations of the ordinary derivative operators and the AT of E and B are used. The Maxwell equations with Fab are written in terms of the 4-vectors of the electric Ea and magnetic Ba fields. The covariant Majorana electromagnetic field 4-vector Ψa is constructed by means of 4-vectors Ea and Ba and the covariant Majorana formulation of electrodynamics is presented. A Dirac like relativistic wave equation for the free photon is obtained. (shrink)

A relative tensor calculus is formulated for expressing equations of mathematical physics. A tensor time derivative operator ▽ b a is defined which operates on tensors λia...ib. Equations are written in a rigid, flat, inertial or other coordinate system a, altered to relative tensor notation, and are thereby expressed in general flowing coordinate systems or materials b, c, d, .... Mirror tensor expressions for ▽ b a λic...id and ▽ b a λic...id exist in a relative geometry G if (...) and only if a rigid coordinate system a exists in G, where ▽ b a λic = λ ,0c ic + λkev ckc aic + λ kc ic v b ckc , ▽jcλic = λ ,jc ic + λkcΓ jc kc ie , and v b aic is the velocity of b relative to a with components in c. These operators are convenient in theoretical analyses and can be incorporated into machine programs for the numerical solution of physical problems. (shrink)

We produce language forms via their relations in coordinate systems: languages. That is virtual language relativity. Languages are related to phenomena and work in the real life of communities. That is real language relativity. We use languages via symbolic behaviors, living in human communities. Relativism collapses at the level of successful exchange of experience between humans belonging to distant cultures. Relativism is a stance of not recognizing the real relatedness of all languages to one and the same human form and (...) world. Absolutism (Universalism) is a stance of not recognizing relativity as definiteness, that is, the virtual interrelatedness of all languages. Languages are shaped by human life processes. We follow the path from “local languages,” which are analogous to ‘inertial systems’, (this represents ‘virtual relativity,’ which is analogous to special relativity in physics) to living people talking about one shared sensual world (this represents ‘real relativity’). (shrink)

Using the Weyl-type canonical coordinates, an integration of Einstein's field equations in the cylindrosymmetric case considered by Kurşunoğlu is reexamined. It is made clear that the resulting metric is not describing the spacetime in a rotating frame, but in astatic cylindrical elastic medium. The conclusion of Kurşunoğlu that “for an observer on a rotating disk there is no way of escape from a curved spacetime” is therefore not valid. The metric in an empty rotating frame is found as a (...) solution of Einstein's field equations, and is not orthogonal. It is shown that the corresponding orthogonal solution represents spacetime in an inertial frame expressed in cylindrical coordinates. Introducing a noncoordinate basis, the metric in a rotating frame is given the static form of Kurşunoğlu's solution. The essential role played by the nonvanishing structure coefficients in this case is made clear. (shrink)

Einstein's gravitational field equations in empty space outside a massive plane with infinite extension give a class of solutions describing a field with flat spacetime giving neutral, freely moving particles an acceleration. This points to the necessity of defining the concept “gravitational field” not simply by the nonvanishing of the Riemann curvature tensor, but by the nonvanishing of certain elements of the Christoffel symbols, called the physical elements, or the nonvanishing of the Riemann curvature tensor. The tidal component of a (...) gravitational field is associated with a nonvanishing Riemann tensor, while the nontidal components are associated with nonvanishing physical elements of the Christoffel symbols. Spacetime in a nontidal gravitational field is flat. Such a field may be separated into a homogeneous and a rotational component. In order to exhibit the physical significance of these components in relation to their transformation properties, coordinate transformations inside a given reference frame are discussed. The mentioned solutions of Einstein's field equations lead to a metric identical to that obtained as a result of a transformation from an inertial frame to a uniformly accelerated frame. The validity of the strong principle of equivalence in extended regions for nontidal gravitational fields is made clear. An exact calculation of the weight of an extended body in a uniform gravitational field, from a global point of view, gives the result that its weight is independent of the position of the scale on the body. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least (...) one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

After recalling the rigorous mathematical representations in Relativity Theory (RT) of (i) observers, (ii) reference frames fields, (iii) their classifications, (iv) naturally adapted coordinate systems (nacs) to a given reference frame, (v) synchronization procedure and some other key concepts, we analyze three problems concerning experiments on rotating frames which even now (after almost a century after the birth of RT) are sources of misunderstandings and misconceptions. The first problem, which serves to illustrate the power of rigorous mathematical methods in RT, (...) is the explanation of the Sagnac effect (SE). This presentation is opportune because recently there have appeared many non sequitur claims in the literature stating that the SE cannot be explained by SRT, even disproving this theory or claiming that the explanation of the effect requires a new theory of electrodynamics. The second example has to do with the measurement of the one-way velocity of light in rotating reference frames, a problem about which many wrong statements appear in recent literature. The third problem has to do with claims that only Lorentz-like type transformations can be used between the nacs associated with a reference frame mathematically modeling of a rotating platform and the nacs associated with a inertial frame (the laboratory). We show that these claims are equivocal. (shrink)

For much of this century it was widely assumed in philosophical circles that the relational doctrine of space, time, and motion had finally been established beyond the point of reasonable controversy. In large part this was due to a widespread perception that the theory of relativity is itself a relational theory. Indeed, some of Einstein’s own pronouncements foster this impression. For example, in his definitive formulation of general relativity of 1916, he argued the need for a generalization of the principle (...) of special relativity in order to eliminate the “factitious” causal role he saw inertial frames playing in classical mechanics and special relativity. ‘The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion’. Einstein claimed this requirement is fulfilled by satisfaction of the Principle of General Covariance—that the equations expressing the laws of nature remain valid under arbitrary coordinate substitutions. This, he says, ‘takes away from space and time the last remnant of physical objectivity.’. (shrink)

In effort to investigate how quantum physics might modify Einstein's Theory of Relativity at speeds v→c, the relationship between space-time coordinates of different reference frames is revisited by introducing only one new parameter xo, a fundamental constant for the quantization of space. The starting point is three criteria: (a) real space-time data are conditioned by standard quantum effects on measurements; (b) since currently used apparatus are only capable of probing the aggregate behavior of these quanta the relevant model is (...) one which maximizes the Entropy subject to certain defining constraints; and (c) the constraints simply involve fixed ensemble averages in the case of an inertial frame, or boundary conditions on running averages in the case of an accelerated frame. In this context it is found that both the Lorentz transformation and a simple scheme for the quantization of space-time which resembles identically Planck's photon picture of radiation are a direct consequence of the Principle of Relativity. Non-inertial behavior corresponds to local Entropy maxima, obtainable by solution of a diffusion equation which gives gradually varying ensemble averages across space-time, as demonstrated by the example of a profile which connects a central region of highly agitated quanta with an asymptotic ambient environment—the outcome is the Schwarzschild metric of General Relativity. Apart from the above, a new feature emerges from the theory: the space-time data of an observer, when referred to the frame of his moving partner, are subject to extra quantum fluctuations which increase indefinitely in severity as v→c, with the Lorentz transformation providing only the mean data values. Thus for fast moving bodies like cosmic rays or matter at the horizon of a black hole, physical processes which affect them may not always be perceived by us to occur at the expected length or time scales. (shrink)

When applied to a dipole source subjected to acceleration which is violent and long lasting (“extreme acceleration”), Maxwell's equations predict radiative power which augments Larmor's classical radiation formula by a nontrivial amount. The physical assumptions behind this result are made possible by the kinematics of a system of geometrical clocks whose tickings are controlled by cavities which are expanding inertially. For the purpose of measuring the radiation from such a source we take advantage of the physical validity of a spacetime (...) coordinate framework (“inertially expanding frame”) based on such clocks. They are compatible and commensurable with the accelerated clocks of the accelerated source. By contrast, a common Lorentz frame with its mutually static clocks won't do: It lacks that commensurability. Inertially expanding clocks give a physicist a window into the frame of a source with extreme acceleration, and thus can locate that source and measure radiation from it without being subjected to such acceleration himself. The conclusion is that inertially expanding reference frames reveal qualitatively distinct aspects of nature which would not be accessible if inertial frames were the only admissible frames. (shrink)

This thesis explores the syntax and semantics of coordinate structures on the basis of three-dimensional syntactic structures. In particular it gives an analysis of sentences of the sort 'a man came and a woman left who knew each other well' on the basis of implicit coordination of NPs, made available within three-dimensionional syntactic structures..

I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to ``explain'' inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of ``explain'' is rather different from what one might have expected. This sense of (...) explanation is connected with a view of theories---I call it the ``puzzleball view''---on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions. (shrink)

Coordination is the presumption that distinct representations have the same referential content. Philosophers have discussed ways in which the presence of coordination might bear on the metasemantic determination of content. One test case for exploring the relationship between coordination and content is the phenomenon of conflation — the situation in which representations are about distinct things but are nevertheless coordinated. In this paper, I use observations about conflation to develop an anaphoric metasemantics for some representations in which coordination plays an (...) integral role. I also develop some novel remarks on the problem of misrepresentation. (shrink)

A salient feature of de Broglie-Bohm quantum theory is that particles have determinate positions at all times and in all physical contexts. Hence, the trajectory of a particle is a well-defined concept. One then may expect that the closely related notion of inertial trajectory is also unproblematically defined. I show that this expectation is not met. I provide a framework that deploys six different ways in which dBB theory can be interpreted, and I state that only in the canonical (...) interpretation the concept of inertial trajectory is the customary one. However, in this interpretation the description of the dynamical interaction between the pilot-wave and the particles, which is crucial to distinguish inertial from non-inertial trajectories, is affected by serious difficulties, so other readings of the theory intend to avoid them. I show that in the alternative interpretations the concept at issue gets either drastically altered, or plainly undefined. I also spell out further conceptual difficulties that are associated to the redefinitions of inertial trajectories, or to the absence of the concept. (shrink)

Frege's picture of attitude states and attitude reports requires a notion of content that is shareable between agents, yet more fine-grained than reference. Kripke challenged this picture by giving a case on which the expressions that resist substitution in an attitude report share a candidate notion of fine-grained content. A consensus view developed which accepted Kripke's general moral and replaced the Fregean picture with an account of attitude reporting on which states are distinguished in conversation by their (private) representational properties. (...) I begin in support of the consensus by showing how a sort of de facto coordination on mental symbols is possible, even for unsophisticated agents. But I go on to argue that whenever conditions are ripe for de facto coordination on symbols, there is an inter-subjective relation that supports a fine-grained notion of content resistant to Kripke's challenge. The consensus view corresponds to a Kripke-resistant strain of the Fregean picture. (shrink)

A shared narrative in the literature on the evolution of cooperation maintains that social _learning_ evolves early to allow for the transmission of cumulative culture. Social _norms_, whilst present at the outset, only rise to prominence later on, mainly to stabilise cooperation against the threat of defection. In contrast, I argue that once we consider insights from social epistemology, an expansion of this narrative presents itself: An interesting kind of social norm — an epistemic coordination norm — was operative in (...) early and important instances of specialised social learning. I show how there’s a need for such norms in two key social learning strategies and explain how this need is constituted. In assessor-teaching (e.g. Castro et al., 2019b, 2021), epistemic coordination norms allow agents to coordinate around the _content_ of social learning, i.e., what is to be known and how this is to be done. These norms also allow agents to coordinate around the form of cultural learning in what’s sometimes called strategic social learning (Laland, 2004; Hoppitt & Laland, 2013; Heyes, 2018, Chap. 5) and elsewhere. Broadly speaking, this concerns how cultural learning is organised within the social group. The upshot is that the evolution of social learning and social norms are intertwined in important and underappreciated ways from early on. The above matters as it informs our views about the evolution of social norms more generally. Truly _social_ norms emerged to coordinate a plurality of complex behaviours and interactions, amongst them specialised social learning. I substantiate this view by contrasting it with Jonathan Birch’s views on the evolution of norms. What results is a general but cohesive narrative on the early evolution of social norms. (shrink)