The recent detection of gravitational waves by the LIGO team has rightly been hailed as “the crowning achievemen of classical physics”. This detection, which came at the end of a decade-long quest, involved 950 investigators, and cost around one billion US dollars, was the scientific star of the year 2015. What, if any, is the philosophical impact of this scientific breakthrough, which Albert Einstein had anticipated one century earlier? To answer this question we start by examining the central (...) equations of Einstein’s theory of gravitation, also known as general relativity. Subsequently we analyze the special case of a hollow sphere, in an attempt to answer the question of the reality and even materiality of space or, rather, spacetime. As well, the view that gravitation is a manifestation of the curvature of spacetime is discussed, and the reality of gravitational waves is regarded as the coup de grâce to that view. (shrink)

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that—analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge—a gravitational wave must necessarily be nonlinear to transport its own charge—that is, energy-momentum.

Advanced Virgo detector joined advanced LIGO twin detectors on 1st August 2017 in the quest to look for the gravitational waves. The global network of three detectors was operational for 25 days until the LIGO shut down on 25th August 2017. Two gravitational wave events were registered during this period. One of them was the binary black hole merger dubbed as GW170814 and other one is binary neutron star merger referred to as GW170817. Electromagnetic counterpart associated with (...) binary neutron star merger was promptly identified which marks the beginning of multi-messenger astronomy. This article describes these events emphasizing on the crucial role played by the Virgo and focusing on some methodological issues. (shrink)

I discuss the recent claims made by Mario Bunge on the philosophical implications of the discovery of gravitational waves. I think that Bunge is right when he points out that the detection implies the materiality of spacetime, but I reject his identification of spacetime with the gravitational field. I show that Bunge’s analysis of the spacetime inside a hollow sphere is defective, but this in no way affects his main claim.

Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×108 neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by (...) assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate. (shrink)

The LIGO-Virgo Collaboration achieved the first ‘direct detection’ of gravitational waves in 2015, opening a new “window” for observing the universe. Since this first detection (‘GW150914’), dozens of detections have followed, mostly produced by binary black hole mergers. However, the theory-ladenness of the LIGO-Virgo methods for observing these events leads to a potentially-vicious circularity, where general relativistic assumptions may serve to mask phenomena that are inconsistent with general relativity (GR). Under such circumstances, the fact that GR can ‘save (...) the phenomena’ may be an artifact of theory-laden methodology.This paper examines several ways that the LIGO-Virgo observations are used in theory and hypothesis testing, despite this circularity problem. First, despite the threat of vicious circularity, these experiments succeed in testing GR. Indeed, early tests of GR using GW150914 are best understood as a response to the threat of theory-ladenness and circularity. Each test searches for evidence that LIGO-Virgo’s theory-laden methods are biasing their overall conclusions. The failure to find evidence of this places constraints on deviations from the predictions of GR. Second, these observations provide a basis for studying astrophysical and cosmological processes, especially through analyses of populations of events. As gravitational-wave astrophysics transitions into mature science, constraints from early tests of GR provide a scaffolding for these population-based studies. I further characterize this transition in terms of its increasing connectedness to other parts of astrophysics and the prominence of reasoning about selection effects and other systematics in drawing inferences from observations.Overall, this paper analyses the ways that theory and hypothesis testing operate in gravitational-wave astrophysics as it gains maturity. In particular, I show how these tests build on one another in order to mitigate a circularity problem at the heart of the observations. (shrink)

I discuss the recent claims made by Mario Bunge on the philosophical implications of the discovery of gravitational waves. I think that Bunge is right when he points out that the detection implies the materiality of spacetime, but I reject his identification of spacetime with the gravitational field. I show that Bunge’s analysis of the spacetime inside a hollow sphere is defective, but this in no way affects his main claim.

An internationally famous physicist and electrical engineer, the author of this text was a pioneer in the investigation of gravitational waves. Joseph Weber's General Relativity and Gravitational Waves offers a classic treatment of the subject. Appropriate for upper-level undergraduates and graduate students, this text remains ever relevant. Brief but thorough in its introduction to the foundations of general relativity, it also examines the elements of Riemannian geometry and tensor calculus applicable to this field. Approximately a quarter (...) of the contents explores theoretical and experimental aspects of gravitational radiation. The final chapter focuses on selected topics related to general relativity, including the equations of motion, unified field theories, Friedman's solution of the cosmological problem, and the Hamiltonian formulation of general relativity. Exercises. Index. (shrink)

This paper reviews recent applications of the Einstein- Rosen type space-times to some problems of modern cosmology. An extensive overview of inhomogeneous universes filled with gravitational waves, classical fields, and relativistic fluids is given. The dynamics of primordial inhomogeneities, such as gravitational and matter waves and shocks, their interactions, and the global evolution of the models considered, is presented in detail.

In the following paper, I review and critically assess the four standard routes commonly taken to establish that gravitational waves possess energy-momentum: the increase in kinetic energy a GW confers on a ring of test particles, Bondi/Feynman’s Sticky Bead Argument of a GW heating up a detector, nonlinearities within perturbation theory, taken to reflect the fact that gravity contributes to its own source, and the Noether Theorems, linking symmetries and conserved quantities. Each argument is found to either to (...) presuppose controversial assumptions or to be outright spurious. I finally examine the standard interpretation of binary systems, according to which orbital decay is explained in terms of the system’s energy being via GW energy- momentum transport. I contend that a better interpretation, drawing only on the general-relativistic Equations of Motions and the Einstein Equations, is available - and in fact preferable; thereby also an inference to the best explanation for the vindication of GW energy-momentum is blocked. (shrink)

A quantum measurement-like event can produce any of a number of macroscopically distinct results, with corresponding macroscopically distinct gravitational fields, from the same initial state. Hence the probabilistically evolving large-scale structure of space-time is not precisely or even always approximately described by the deterministic Einstein equations.Since the standard treatment of gravitational wave propagation assumes the validity of the Einstein equations, it is questionable whether we should expect all its predictions to be empirically verified. In particular, one might expect (...) the stochasticity of amplified quantum indeterminacy to cause coherent gravitational wave signals to decay faster than standard predictions suggest. This need not imply that the radiated energy flux from gravitational wave sources differs from standard theoretical predictions. An underappreciated bonus of gravitational wave astronomy is that either detecting or failing to detect predicted gravitational wave signals would constrain the form of the semi-classical theory of gravity that we presently lack. (shrink)

"This book is a very impressive achievement. Kennefick skillfully introduces readers to some of the most abstruse yet fascinating concepts in modern physics stemming from Einstein's gravitational theory.

This paper explores the role of physically impossible idealizations in model-based explanation. We do this by examining the explanation of gravitational waves from distant stellar objects using models that contain point-particle idealizations. Like infinite idealizations in thermodynamics, biology and economics, the point-particle idealization in general relativity is physically impossible. What makes this case interesting is that there are two very different kinds of models used for predicting the same gravitational wave phenomena, post-Newtonian models and effective field theory (...) models. The paper contends that post-Newtonian models are explanatory while effective field theory models are not, because only in the former can we eliminate the physically impossible point-particle idealization. This suggests that, in some areas of science at least, models invoking ineliminable infinite idealizations cannot have explanatory power. (shrink)

The gravitational waves from a binary black hole with masses \ can be detected with the Laser Interferometer Space Antenna once their orbital frequency exceeds 10\–10\ Hz. The binary separation at this stage is \R_{\mathrm{g}}\), and the orbital speed is \\). I argue that at this stage, the binary will be producing bright electromagnetic radiation via gas bound to the individual BHs. Both BHs will have their own photospheres in X-ray and possibly also in optical bands. Relativistic Doppler (...) modulations and lensing effects will inevitably imprint periodic variability in the EM light-curve, tracking the phase of the orbital motion, and serving as a template for the GW inspiral waveform. Advanced localization of the source by LISA weeks to months prior to merger will enable a measurement of this EM chirp by wide-field X-ray or optical instruments. A comparison of the phases of the GW and EM chirp signals will help break degeneracies between system parameters, and probe a fractional difference difference \ in the propagation speed of photons and gravitons as low as \. (shrink)

This paper explores the role of physically impossible idealizations in model-based explanation. We do this by examining the explanation of gravitational waves from distant stellar objects using models that contain point-particle idealizations. Like infinite idealizations in thermodynamics, biology and economics, the point-particle idealization in general relativity is physically impossible. What makes this case interesting is that there are two very different kinds of models used for predicting the same gravitational wave phenomena, post-Newtonian models and effective field theory (...) models. The paper contends that post-Newtonian models are explanatory while effective field theory models are not, because only in the former can we eliminate the physically impossible point-particle idealization. This suggests that, in some areas of science at least, models invoking ineliminable infinite idealizations cannot have explanatory power. (shrink)

This paper focuses on the nonlinear self-interaction of gravitational waves and explores its impact on the spectrum of the resulting gravitational wave. While many authors primarily investigate the nonlinear effects within the framework of "gravitational memory," we take a different approach by conducting a comprehensive analysis of harmonic generation. Theoretical analysis indicates that higher harmonics do not possess suitable conditions for energy accumulation. However, our study presents intriguing evidence supporting the concept of "nonlinear gravitational memory": (...) the conversion and accumulation of gravitational wave energy into a persistent metric deformation in the background space (specifically referred here to as zero harmonics). In simpler terms, a wave leaves a lasting imprint on the background space, even after the gravitational pulse subsides. Furthermore, our study estimates the significance of this effect and demonstrates that it should not be disregarded. (shrink)

Gravity’s Ghost is a book about the search for gravitational waves , which are predicted by the general theory of relativity to be ripples in space–time that propagate at the speed of light. The direct detection of GWs, if they exist at all, is exceptionally difficult, because they are theoretically expected to be very weakly coupled to matter. To this date, there is yet no conclusive evidence for the direct detection of GWs. The search for GWs was started (...) by a series of experiments performed by Joseph Weber in the 1960s. The history of the early GW detection experiments, as well as Weber’s claimed detection of GWs, which was eventually discredited, has been examined in great details by Harry Collins .Collins has long advocated a sociological approach to the study of scientific research groups that is premised on the view that in order to understand how scientific knowledge is produced collectively by a group of researchers, it is necessary to engage in the cultu .. (shrink)

How can we make informed decisions about whom to trust given expert disagreement? Can experts on both sides be reasonable in holding conflicting views? Epistemologists have engaged the issue of reasonable expert disagreement generally; here I consider a particular expert dispute in physics, given conflicting accounts from Harry Collins and Allan Franklin, over Joseph Weber’s alleged detection of gravitational waves. Finding common ground between Collins and Franklin, I offer a characterization of the gravity wave dispute as both social (...) and evidential. While experimental evidence alone may not have forced resolution of the dispute, there were also credibility‐based reasons warranting epistemic trust and distrust. Thus we see how social factors can have evidential significance and how expert disagreement can be reasonable. †To contact the author, please write to: Philosophy Dept., Communication Arts Division, College of Lake County, 19351 W. Washington St., Grayslake, IL 60030; e‐mail: [email protected]. (shrink)

In a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It has generally been assumed that there was a conceptual error underlying this fallacious claim. It will be shown, through a detailed study of the extant referee report, that this claim was probably only the result of a calculational error, the accidental use of a pathological coordinate transformation.

An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of (...) these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense. (shrink)

Using the linearized Einstein gravitational field equations and the Maxwell field equations it is shown that the plane of polarization of an electromagnetic wave is rotated by the gravitational field created by the electromagnetic radiation of a ring laser. It is further shown that this gravitational Faraday effect shares many of the properties of the standard electromagnetic Faraday effect. An experimental arrangement is then suggested for the observation of this gravitational Faraday effect induced by the ring (...) laser. (shrink)

The law of gravitation is taken in the formR 44=0, whereR 44 is the time curvature component of the Ricci tensor. Space-time separable equations are developed in spherical coordinates for the nonlinear wave equation determined byR 44=0. One exact solution is examined in detail.

Consequences in physical theory of assuming the general relativistic time transformation for the de Broglie frequencies of matter, v = E/h = mc2/h, are investigated in this paper. Experimentally it is known that electromagnetic waves from a source in a gravitational field are decreased in frequency, in accordance with the Einstein general relativity time transformation. An extension to de Broglie frequencies implies mass decrease in a gravitational field. Such a decrease gives an otherwise missing energy conservation for (...) some processes; also, a physical alteration is then associated with change in gravitational potential. Further, the general relativity time transformation that is the source of gravitational action in the weak field (Newtonian) approximation then has a physical correlate in the proposed gravitational mass loss. Rotational motion and the associated equivalent gravitational-field mass loss are considered; an essential formal difference between metric (gravitational) mass loss and special relativity mass increase is discussed. For a spherical, nonrotating mass collapsed to its Schwarzschild radius the postulated mass loss is found to give a 25% decrease in the mass acting as origin of an external gravitational field. (shrink)

How does the physics community deal with the subsequent work of a scientist whose earlier work has been regarded as incorrect? An interesting case of this involves Joseph Weber whose claim to have observed gravitational waves was rejected by virtually all of the physics community, although Weber himself continued to defend his work until his death in 2000. In the course of this defense Weber made a startling suggestion regarding the scattering of neutrinos. I will summarize the history (...) of gravity waves including the rejection of Weber's claim around 1975, his later work on gravity waves, and examine the reaction of the physics community to his neutrino hypothesis.----------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------. (shrink)

The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim (...) \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$. (shrink)

The generally covariant Lagrangian densityG = ℛ + 2K ℒmatter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg ikand φ of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form Γ kl i = kl i for the coefficients г kl i of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of φ, gik, and (...) the coefficients г kl i . Then the г kl i are determined by the Palatini equations. From these equations and from the symmetry г kl i = г lk i for all matter fields with δℒ/δΓ=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, δℒ/δΓ becomes dependent on the Dirac current, essentially with a coupling factor ∼Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10−81erg cm3. (shrink)

In Roger Boscovich’s Theory of Natural Philosophy, the dynamics of matter is described by the curve of forces, either attractive or repulsive – depending on the distances of the centres of forces. At great distances, the curve of forces is manifested similar to Newton’s gravitation. The gravitation is integrative for the visible universe, but not for the hypothetical multitude of universes that possibly parallelly exist separated by a repulsive force, comparable to the contemporary concept of the dark energy. In the (...) concept of continuous forces in a discontinuous matter, Faraday recognises the idea of a dynamic electromagnetic field, completed by Maxwell, while Einstein later predicted the existence of gravitational waves recently detected. The wave-nature of real space-time matter is found in Boscovich’s model at the small scale of the curve of forces, while the atomic-corpuscular dynamics of classical mechanics is found at the large scale. (shrink)

It’s generally taken to be established that no local hidden-variable theory is possible. That conclusion applies if our world is a _thread_, where a thread is a world where particles follow trajectories, as in Pilot-Wave theory. But if our world is taken to be a _set_ of threads locality can be recovered. Our world can be described by a _many-threads_ theory, as defined by Jeffrey Barrett in the opening quote. Particles don’t follow trajectories because a particle in our world is (...) a set of _elemental_ particles following different trajectories, each in a thread. The “elements” of a superposition are construed as subsets in such a way that a particle in our world only has definite position if all its set-theoretic elements are at corresponding positions in each thread. Wavefunction becomes a 3D density distribution of particles’ subset measures, the stuff of an electron’s “probability cloud”. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles (approximated by Many Interacting Worlds theory). EPR-Bell nonlocality doesn’t apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition. (shrink)

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference (...) between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)

Quantum mechanics teaches that before detection, knowledge of particle position is, at best, probabilistic, and classical trajectories are seen as a feature of the macroscopic world. These comments refer to detected particles, but we are still free to consider the motions generated by the wave equation. Within hydrogen, the Schrodinger equation allows calculation of kinetic energy at any location, and if this is identified as the energy of the wave, then radial momentum, allowing for spherical harmonics, becomes available. The distance (...) across the real zone of radial momentum is found to match semi-integer wavelengths of the adjusted matter wave, consistent with what is expected from a standing wave condition. The approach is extended to include orbital motions, where it is established that the underlying wave, which has direction and wavelength at each location, forms a series of connected trajectories, which are shown to be ellipses orientated at various angles to the equatorial plane. This suggests that wave trajectories, rather than particle trajectories, are still a feature of the hydrogen atom. The finding allows the reason for the coincidence between energy results derived by Sommerfeld’s classical trajectories and the Schrodinger wave equation to be appreciated. The result has implications when the relativistic situation is considered, as Sommerfeld’s correct deduction of the relativistic energy levels of hydrogen well before Dirac derived his wave equation has long been somewhat puzzling. (shrink)

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandoned. Here we propose a nonlinear scalar field theory able (...) to reproduce the PWI for the Schrödinger and Klein–Gordon guiding waves. Our model relies on a relativistic ‘phase harmony’ condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the N particles cases in presence of entanglement and external (classical) electromagnectic fields. (shrink)

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.

In this paper, we investigate non-homogeneous wave equations in fractional space-time domains of space dimension _D_, \(0 and time dimension \(\beta\), \(0. We write the wave equations in terms of potential functions and non-zero source terms. For scalar source terms, the potential functions are also scalar functions, and for vector source terms, the potential functions are vector functions. We derived an expression for the wave to propagate from the source point to the observation point. The study shows that the time (...) for a wave to propagate from the source point to the observation point in a fractional space-time domain could be different from that in an integer order space-time domain. (shrink)

We consider a model of the state evolution of relativistic vector bosons, which includes both the dynamical equations for the particle four-velocity and the equations for the polarization four-vector evolution in the field of a nonlinear plane gravitational wave. In addition to the gravitational minimal coupling, tidal forces linear in curvature tensor are suggested to drive the particle state evolution. The exact solutions of the evolutionary equations are obtained. Birefringence and tidal deviations from the geodesic motion are discussed.

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a “particle wave,” which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle (...) can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity. (shrink)

In the traditional frame of classical electrodynamics, a hydrogen atom would emit electromagnetic waves and thus constantly lose energy, resulting in the fall of the electron on the proton over a finite period of time. The corresponding results were derived under the assumption of the instantaneous interaction between the proton and the electron. In 2004, Raju published a paper where he removed the assumption of the instantaneous interaction and studied the role of a time delay in the classical hydrogen (...) atom. He introduced a model of this effect that can be solved analytically. He calculated the radius rsel of a selected orbit, for which this effect and the radiation reaction force would cancel each other with respect to the tangential acceleration. It turned out that rsel is by an order of magnitude smaller than the Bohr radius. In the present paper we use Raju’s model for the corresponding gravitational situation. In frames of Newton’s gravity, we calculate analytically the radius and the energy Esel of a selected orbit, for which the retardation effect and the radiation reaction force would cancel each other out with respect to the tangential acceleration. Then we compare our outcome with some results of Kaplan’s solution for the two-body gravitational problem based on the Schwarzschild’s field. We show that Esel is very close to the minimum energy of bound states obtained by Kaplan in Einstein’s gravity. We emphasize that the selected orbit from the present paper represents the second only physical situation where the radiation reaction force is zero, but the radiation-caused energy loss is not zero. (shrink)