Observable Velocity Research Articles

Fast and spurious: a robust determination of our peculiar velocity with future galaxy surveys

To date, the most precise measurement of the observer's peculiar velocity comes from the dipole in the Cosmic Microwave Background (CMB). This velocity also generates a dipole in the source number counts, whose amplitude is governed not only by the observer velocity, but also by specific properties of the sources, that are difficult to determine precisely. Quantitative studies of the source number counts currently give dipoles which are reasonably well aligned with the CMB dipole, but with a significantly larger amplitude than that of the CMB dipole. In this work, we explore an alternative way of measuring the observer velocity from the source number counts, using correlations between neighboring spherical harmonic coefficients, induced by the velocity. We show that these correlations contain both a term sensitive to the source properties and another one directly given by the observer velocity. We explore the potential of a Euclid-like survey to directly measure this second contribution, independently of the characteristics of the population of sources. We find that the method can reach a precision of 4%, corresponding to a detection significance of 24σ, on the observer velocity. This will settle with precision the present “dipole tension”.

Управление развязкой для модели типа "половина машины": сравнительный анализ алгоритмов линейного и линейно-квадратичного управления с активным подавлением помех

The linear multi-independent and multivariate linear-quadratic approaches to the implementation of active disturbance rejection control are considered. The first approach is based on controlling multidimensional systems whose input number is equal to the output number, using several separate elements of active disturbance rejection control. The second approach is based on the transformation of the control problem into a multidimensional controlled system using a linear quadratic regulator LQR. The parameters of the two proposed control synthesis algorithms are tuned using the desired closed-loop cutoff frequency and the observer's dynamic velocity multiplier. A multi-criteria optimization procedure is performed using the NSGA-II algorithm. The proposed approaches are verified by modelling the car's suspension active control system. The testing was performed considering the vehicle motion at relatively high speeds under the assumption that the perturbed motion occurs only in the vertical direction. As a result of the simulation, it was found that using the proposed approaches, the responses of the quality indicators improved with respect to the displacement of the suspension mass with no significant deterioration in its acceleration. The first approach can be considered effective in controlling multidimensional systems, in addition to the simplicity of design and ease of its parameters adjustment. The second approach gives better results than the first approach, but with higher costs in mathematical calculations

Speed Measurement in an Accomoving Reference System

A method of direct measurement of the observer's velocity (peculiar velocity) relative to the accompanying reference system is proposed and investigated. To measure peculiar velocity, it is proposed to use the measurement of stellar light aberration. A comparison of the use of light aberration and the Doppler Effect for measuring velocity relative to relic radiation was made. When using the Doppler Effect, the total speed of the observer was measured - the Hubble speed and the radial component of the peculiar speed of the observer. As a result of the analysis of the components of the observer's velocity in the comoving reference frame, the Hubble and peculiar velocities of the observer, their essential features are formulated. The analysis of the shape of the wave fronts of the CMB radiation, the radiation of quasars, the radiation of stars and the radiation of ground sources is given. As a consequence of this analysis, the decisive influence of the shape of their wave fronts on the possibilities of measuring stellar aberration and the absence of such an effect when measuring velocity using the Doppler Effect are shown. Measurement of light aberration in an inertial system enables direct measurement of the observer's peculiar velocity in an comoving reference frame. Knowing the observer's peculiar velocity is important for increasing the accuracy of determining the Hubble velocity of especially objects of relatively small remoteness. The proposed structures of devices for measuring the peculiar velocity of an inertial reference system were investigated. Peculiar speed is determined by the measured light aberration without switching to another frame of reference. Their expected accuracy and reliability were evaluated. The practical use of the proposed structures is possible in astronomy and spacecraft.

Large disparity in cosmic reference frames determined from the sky distributions of radio sources and the microwave background radiation

The angular distribution of the cosmic microwave background radiation (CMBR) in the sky shows a dipole asymmetry, ascribed to the peculiar velocity of the observer (or rather of the Solar system), where peculiar velocity is defined as motion relative to the local comoving coordinates. The peculiar velocity thus determined turns out to be $370\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ in the direction $\mathrm{RA}=168\ifmmode^\circ\else\textdegree\fi{}$, $\mathrm{Dec}=\ensuremath{-}7\ifmmode^\circ\else\textdegree\fi{}$. On the other hand, a dipole asymmetry in the sky distribution of radio sources in the NRAO VLA Sky Survey (NVSS), carried out by the Very Large Array (VLA) of the National Radio Astronomy Observatory (NRAO), comprising a catalog of 1.8 million sources, yielded a value for the observer's velocity approximately four times larger than the CMBR value, though the direction turned out to be in agreement with that of the CMBR dipole. This large difference in the observer's speeds with respect to the reference frames of NVSS radio sources and of CMBR, confirmed since by many independent groups, is rather disconcerting, as the observer's motion with respect to local comoving coordinates should be independent of the technique used to determine it. A genuine difference in relative speeds of two cosmic reference frames could jeopardize the cosmological principle; thence, it is crucial to confirm such discrepancies using independent samples of radio sources. We investigate here the dipole in the sky distribution of radio sources in the recent TIFR GMRT Sky Survey (TGSS), carried out by the Giant Metrewave Radio Telescope (GMRT) of the Tata Institute of Fundamental Research (TIFR), comprising a dataset of 0.62 million sources, to determine the observer's motion. We find a significant disparity in the observer's speeds relative to all three reference frames, determined from the radio source datasets and the CMBR, which does not fit with the cosmological principle, a starting point for the standard modern cosmology.

Art and Science Einstein’s Universe via Art

The essence of Einstein’s world lies in the concept of relativity. He described it once in the following way: "When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours; that's relativity he said." Einstein also boldly stated that there are no absolute quantities, that the magnitude of quantities depends on the relative velocity between an object and the observer, and that every event and measurement is viewed differently depending on the observer's velocity. However, the only measurement that remains constant is the speed of light C in vacuum.

Direction and redshift drifts for general observers and their applications in cosmology

High precision astrometry now enables to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and direction drifts for general observers. It is then applied to the standard cosmological framework of a Friedmann-Lemaitre space- time including all effects at first order in the cosmological perturbations, as well as in the class of spatially anisotropic universe models of the Bianchi I family. It shows that for a general observer, the direction drift splits into a parallax and an aberration drifts and order of magnitude estimates of these two components are provided. The multipolar decomposition of the redshift and aberration drifts is also derived and shows that the observer's peculiar velocity contributes only as a dipole whereas the anisotropic shear contributes as a quadrupole.

The spacetime DoF surface density as canonically conjugate variables driven by acceleration

Padmanabhan found a definition for the surface density of spacetime degrees of freedom assuming a canonical ensemble for accelerating observers in stationary systems. We find that this density is constructed from a pair of canonically conjugate variables. These variables should be derived with respect to a special space like vector field, which is in the direction of the accelerating observers. Moreover, we show that this density is actually a pair of canonically conjugate variables projected along the observer's velocity vector field, during one period of the Euclidean time of the canonical ensemble. We use our derivation to estimate the number of internal states of the “atoms of spacetime”. We find that this number is independent on the gravitational theory and its dimensions.

Art and Science Einstein’s Universe via Art

The essence of Einstein’s world lies in the concept of relativity. He described it once in the following way: "When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours; that's relativity he said." Einstein also boldly stated that there are no absolute quantities, that the magnitude of quantities depends on the relative velocity between an object and the observer, and that every event and measurement is viewed differently depending on the observer's velocity. However, the only measurement that remains constant is the speed of light C in vacuum.

Art and Science Einstein’s Universe via Art

The essence of Einstein’s world lies in the concept of relativity. He described it once in the following way: "When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours; that's relativity he said." Einstein also boldly stated that there are no absolute quantities, that the magnitude of quantities depends on the relative velocity between an object and the observer, and that every event and measurement is viewed differently depending on the observer's velocity. However, the only measurement that remains constant is the speed of light C in vacuum.

Signature of Local Motion in the Microwave Sky

For observers moving with respect to the cosmic rest frame, the microwave background temperature fluctuations will no longer be statistically isotropic. Aside from the familiar temperature dipole, an observer's velocity will also induce changes in the temperature angular correlation function and create nonzero off-diagonal correlations between multipole moments. We show that both of these effects should be detectable in future full-sky maps from the Planck satellite, and can constrain modifications of the standard cosmological model proposed to explain anomalous current observations.

Counterposition and negative phase velocity in uniformly moving dissipative materials

We considered the phenomena of counterposition and negative phase velocity, which are relevant to certain metamaterials and certain astrophysical scenarios. The Lorentz transformations of electric and magnetic fields were implemented to study (i) the refraction of linearly polarized plane waves into a half-space occupied by a uniformly moving material and (ii) the traversal of linearly polarized Gaussian beams through a uniformly moving slab. Motion was taken to occur tangentially to the interface(s) and in the plane of incidence. The moving materials were assumed to be isotropic, homogeneous and dissipative dielectric materials from the perspective of a co-moving observer. Two different moving materials were considered: from the perspective of a co-moving observer, material A supports planewave propagation with only positive phase velocity, whereas material B supports planewave propagation with both positive and negative phase velocity, depending on the polarization state. For both materials A and B, the sense of the phase velocity and whether or not counterposition occurred, as perceived by a non-co-moving observer, could be altered by varying the observer's velocity. Furthermore, the lateral position of a beam upon propagating through a uniformly moving slab made of material A, as perceived by a non-co-moving observer, could be controlled by varying the observer's velocity. In particular, at certain velocities, the transmitted beam emerged from the slab laterally displaced in the direction opposite to the direction of incident beam. The transmittances of a uniformly moving slab made of material B were very small and the energy density of the transmitted beam was largely concentrated in the direction normal to the slab, regardless of the observer's velocity.

Positive-, negative-, and orthogonal-phase-velocity propagation of electromagnetic plane waves in a simply moving medium

Planewave propagation in a simply moving, dielectric-magnetic medium that is isotropic in the co-moving reference frame, is classified into three different categories: positive-, negative-, and orthogonal-phase-velocity (PPV, NPV, and OPV). Calculations from the perspective of an observer located in a non-co-moving reference frame show that, whether the nature of planewave propagation is PPV or NPV (or OPV in the case of non-dissipative mediums) depends strongly upon the magnitude and direction of that observer's velocity relative to the medium. PPV propagation is characterized by a positive real wavenumber, NPV propagation by a negative real wavenumber. OPV propagation only occurs for non-dissipative mediums, but weakly dissipative mediums can support nearly OPV propagation.

The covariance of GPS coordinates and frames

We explore, in the general relativistic context, the properties of the recently introduced global positioning system (GPS) coordinates, as well as those of the associated frames and coframes that they define. We show that they are covariant and completely independent of any observer. We show that standard spectroscopic and astrometric observations allow any observer to measure (i) the values of the GPS coordinates at his position, (ii) the components of his 4-velocity and (iii) the components of the metric in the GPS frame. This provides this system with a unique value both for conceptual discussion (no frame dependence) and for practical use (involved quantities are directly measurable): localization, motion monitoring, astrometry, cosmography and tests of gravitation theories. We show explicitly, in the general relativistic context, how an observer may estimate his position and motion, and reconstruct the components of the metric. This arises from two main results: the extension of the velocity fields of the probes to the whole (curved) spacetime, and the identification of the components of the observer's velocity in the GPS frame with the (inversed) observed redshifts of the probes. Specific cases (non-relativistic velocities, Minkowski and Friedmann–Lematre spacetimes, geodesic motions) are studied in detail.

Relativistic corrections to the Sunyaev-Zeldovich effect for clusters of galaxies: effect of the motion of the observer

We extend the formalism of the relativistic thermal and kinematical Sunyaev-Zeldovich effects to the observer's system (the Solar System) moving with a velocity $\vec{\beta}_{\rm S} \equiv \vec{v}_{\rm S}/c$ with respect to the cosmic microwave background radiation. The present formulation makes full use of the Lorentz covariance properties of the problem and gives solutions with high precision. We confirm the results recently obtained by Chluba, Huetsi, and Sunyaev in the lowest order of the observer's velocity $\beta_{\rm S}$. We give a more general analytic expression for the thermal and kinematical Sunyaev-Zeldovich effects corresponding to the observer's system (the Solar System) with the power series expansion approximation in terms of $\theta_{\rm e} \equiv k_{\rm B}T_{\rm e}/mc^{2}$, where T e and m are the electron temperature and the electron mass, respectively.

Beyond the small-angle approximation for MBR anisotropy from seeds.

In this paper we give a general expression for the energy shift of massless particles traveling through the gravitational field of an arbitrary matter distribution as calculated in the weak field limit in an asymptotically flat space-time. It is [ital not] assumed that matter is nonrelativistic. We demonstrate the surprising result that if the matter is illuminated by a uniform brightness background that the brightness pattern observed at a given point in space-time (modulo a term dependent on the observer's velocity) depends only on the matter distribution on the observer's past light cone. These results apply directly to the cosmological MBR anisotropy pattern generated in the immediate vicinity of an object such as a cosmic string or global texture. We apply these results to cosmic strings, finding a correction to previously published results in the small-angle approximation. We also derive the full-sky anisotropy pattern of a collapsing texture knot.

Mean Streets: The Median of a Size-Biased Sample and the Population Mean

Abstract In a size-biased or weighted sample, the probability that a unit is sampled depends on a property of the sampling unit. Cars sampled by an observer traveling at a fixed velocity, v0, can be modeled as a size-biased sample because a car with a large absolute difference between its velocity and v0, is more likely to be sampled. A consistent estimator of the population mean velocity is found that depends solely on counts of the number of cars the observer passes and the number of cars that pass the observer. This estimator has the unusual property that when counts of passed and passing cars are equal, the sample median velocity and the estimated population mean velocity are both the observer's velocity, v0.

COORDINATE-INDEPENDENT DEFINITION OF TIME AND VACUUM IN CURVED SPACE–TIME

We propose a definition of time and of the vacuum such that they are intrinsic to a given globally hyperbolic 1 + (n − 1)-dimensional space–time geometry and independent of the choice of coordinates. To arrive at this definition we use the new physical principle that a 1 + 1-dimensional Poincaré algebra, including Killing conditions on the generators, should be valid on the hypersurface of instantaneity. Given a timelike vector at a point (an observer's velocity) we define "an instant of time" to be the spacelike surface of geodesics which pass through that point and are orthogonal to that timelike vector. Gaussian coordinates erected on this surface yield 1 + 1-dimensional subspaces with Poincaré symmetry valid on that surface. The generator associated with time translation now uniquely picks out the direction of time on that surface. This fact permits unambiguous quantization on the surface of a field evolving in this background metric. For flat space–time the corresponding vacuum is always the Minkowski vacuum. We also consider in detail the case of static and Robertson–Walker metrics in 1 + 1 dimensions and find our vacuum to be different from those given before. The vacuum for the de Sitter metric in 1 + 1 dimensions is compared with the results in the literature and found to be different. Our definition of particles, and hence particle production, is consequently different also.

Electromagnetism in noninertial coordinates

The electromagnetic equations are expressed in a form appropriate to an observer in arbitrary motion in flat spacetime. The field equations preserve their form, dependence on the motion being confined to the material constitutive relations which are assumed linear and non-dispersive. The 4-metric is uniquely defined by the geometry of the observer's worldline. Two conceivable metrics for the 3-space are noticed and the choice judged unimportant for most purposes. An equation for the eikonal of geometrical optics is found and an approximate solution exhibits the leading contributions that are made to the optical length of a ray by the observer's angular velocity and translational acceleration, the former contribution being independent of the refractive index of material traversed by the ray and at rest in the observer's coordinate system.

Fundamental Limitations to Optical Doppler Measurements for Space Navigation

Theoretical consideration is given to the problem of optical Doppler velocity determination of the high accuracy (about 1 ft/sec) required to be useful for space navigation. From the physical theory of line-broadening and -shifting mechanisms in stellar atmospheres, it is concluded that an intrinsic variability of ±200 ft/sec may be expected in the measurement of an observer's Doppler velocity. Examination of the current state of the art in measuring equipment suggests that it does not set the limits on accuracy.