The metaphysics of Machian frame-dragging

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding

Unruh effect in a real scalar field with the Higgs type potential on the de Sitter space

It has been predicted that an accelerating electron performs a Brownian motion in the inertial frame. This Brownian motion in the inertial frame has its roots in the interaction with the thermal excitation given by the Unruh effect in the accelerating frame. If such a prediction is possible, we correspondingly propose a prediction in this study that the thermal radiation appears in the inertial frame from an electron heated by the Unruh effect in the accelerating frame. The point in our prediction is, although the Unruh effect is only in the accelerating frame, if the appearance of the Brownian motion rooted in the Unruh effect in the inertial frame can be predicted, the heat that the particle gets in its body by the Unruh effect in the accelerating frame could survive in the inertial frame. Based on such a prediction, in this paper we investigate phenomena in the neighborhood of an accelerating electron in the inertial frame. The model we consider is the four-dimensional Klein-Gordon real scalar field model with the Higgs type potential term at the finite temperature identified with the Unruh temperature on the de Sitter space-time. We calculate the one-loop effective potential in the inertial frame with the corrections by the thermal radiation rooted in the Unruh effect in the accelerating frame. In this calculation, we take into account that the background space-time is deformed due to the field theory's corrected one-loop effective potential. Based on such an analysis, we illustrate the restoration of the spontaneous symmetry breaking and the variation of the background space-time, and we examine the accelerating particle's world-line and the amount of the energy corresponding to the change of the acceleration.Comment: v3: 16 pages, 8 figures, version after published (description was improved

Lensing by gravitational waves in scalar-tensor gravity: Einstein frame analysis

The amplification of a light beam due to intervening gravitational waves is studied. The previous Jordan frame result according to which the amplification is many orders of magnitude larger in scalar-tensor gravity than in general relativity does not hold in the Einstein conformal frame. Lensing by gravitational waves is discussed in relation to the ongoing and proposed VLBI observations aimed at detecting the scintillation effect.Comment: 12 pages, LaTeX, to appear in Astronomy & Astrophysic

Quantum Preferred Frame: Does It Really Exist?

The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by such physicists as J. S. Bell and D. Bohm. The possibility of the existence of preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen-type experiment for testing the possible existence of a quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists it is enough to perform an EPR type experiment with pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin one-half or spin one particles.Comment: 5 pp., 6 fig

Emission and absorption lines of gamma-ray bursts affected by the relativistic motion of fireball ejecta

We display by numerical calculation how rest frame spectral lines appear in the observed spectrum of gamma-ray bursts due to the Doppler effect in the fireball framework. The analysis shows that: a) in the spectrum of a relativistically expanding fireball, all rest frame lines would shift to higher energy bands and would be significantly smoothed; b) rest frame weak narrow emission lines as well as narrow absorption lines and absorption line forests would be smoothed and would hardly be detectable; c) the features of rest frame broad emission lines as well as both strong and weak broad absorption lines would remain almost unchanged and therefore would be easier to detect; d) deep gaps caused by rest frame broad absorption lines would be significantly filled; e) a rest frame emission line forest would form a single broad line feature; f) the observed relative width of the rest frame very narrow line would approach $0.162$; g) when the Lorentz factor $\Gamma$ is large enough, the observed line frequency $\nu_{line}$ and the rest frame line frequency $\nu_{0,line}$ would be related by $\nu_{line}\approx 2\Gamma \nu_{0,line}$. We also investigate the effect of time dependence of the line intensity and the effect of variation of $\Gamma$. We find that the feature of rest frame dimming narrow emission lines would disappear when $\Gamma$ is very large. The form of emission lines would be sharp on both edges when $\Gamma$ varies with time. This phenomenon depends not only on the initial Lorentz factor but also on the observation time.Comment: 28 pages, 18 figure

Bound and Radiation Fields in the Rindler Frame

The energy-momentum tensor of the Li\'enard-Wiechert field is split into bound and emitted parts in the Rindler frame, by generalizing the reasoning of Teitelboim applied in the inertial frame. Our analysis proceeds by invoking the concept of ``energy'' defined with respect to the Killing vector field attached to the frame. We obtain the radiation formula in the Rindler frame (the Rindler version of the Larmor formula), and it is found that the radiation power is proportional to the square of acceleration $\alpha^\mu$ of the charge relative to the Rindler frame. This result leads us to split the Li\'enard-Wiechert field into a part II', which is linear in $\alpha^\mu$, and a part I', which is independent of $\alpha^\mu$. By using these, we split the energy-momentum tensor into two parts. We find that these are properly interpreted as the emitted and bound parts of the tensor in the Rindler frame. In our identification of radiation, a charge radiates neither in the case that the charge is fixed in the Rindler frame, nor in the case that the charge satisfies the equation $\alpha^\mu=0$. We then investigate this equation. We consider four gedanken experiments related to the observer dependence of the concept of radiation.Comment: 30 pages 2 figure

Optimally Sparse Frames

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of the frame measurements of a signal typically requires a large number of additions and multiplications, and this makes a frame decomposition intractable in applications with limited computing budget. To address this problem, in this paper, we focus on frames in finite-dimensional Hilbert spaces and introduce sparsity for such frames as a new paradigm. In our terminology, a sparse frame is a frame whose elements have a sparse representation in an orthonormal basis, thereby enabling low-complexity frame decompositions. To introduce a precise meaning of optimality, we take the sum of the numbers of vectors needed of this orthonormal basis when expanding each frame vector as sparsity measure. We then analyze the recently introduced algorithm Spectral Tetris for construction of unit norm tight frames and prove that the tight frames generated by this algorithm are in fact optimally sparse with respect to the standard unit vector basis. Finally, we show that even the generalization of Spectral Tetris for the construction of unit norm frames associated with a given frame operator produces optimally sparse frames

Electrodynamics in accelerated frames revisited

Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above.Comment: 17 pages, no figure

Fire responses and resistance of concrete-filled steel tubular frame structures

This paper presents the results of dynamic responses and fire resistance of concretefilled steel tubular (CFST) frame structures in fire conditions by using non-linear finite element method. Both strength and stability criteria are considered in the collapse analysis. The frame structures are constructed with circular CFST columns and steel beams of I-sections. In order to validate the finite element solutions, the numerical results are compared with those from a fire resistance test on CFST columns. The finite element model is then adopted to simulate the behaviour of frame structures in fire. The structural responses of the frames, including critical temperature and fire-resisting limit time, are obtained for the ISO-834 standard fire. Parametric studies are carried out to show their influence on the load capacity of the frame structures in fire. Suggestions and recommendations are presented for possible adoption in future construction and design of these structures

Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions

We study sharp frame bounds of Gabor frames with the standard Gaussian window and prove that the square lattice optimizes both the lower and the upper frame bound among all rectangular lattices. This proves a conjecture of Floch, Alard & Berrou (as reformulated by Strohmer & Beaver). The proof is based on refined log-convexity/concavity estimates for the Jacobi theta functions $\theta_3$ and $\theta_4$.Comment: 13 pages, 3 figures, available online, Journal of Mathematical Analysis and Applications, August 2016 to appear in Journal of Mathematical Analysis and Applications, 445(1):407-422, January 201