Static Gravitational Field Research Articles

Decoherence in quantum systems in a static gravitational field

A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.

Investigation of Gravity-Related Spontaneous Wave Function Collapse for Non-static Gravitational Field

Diosi and Penrose have suggested a criterion for spontaneous wave function collapse. According to Penrose the profound conflict between the principle of superposition and general covariance entails the existence of reduction of quantum states, e.g. a quantum superposition of two different space–time geometries will collapse onto one of them. In his proposal, collapse time has an inverse relationship with ill-definedness in the gravitational self-energy, for the static gravitational fields. Anandan obtained the same result using the fluctuations of the connection of gravitational field. We show that in Newtonian limit of the superposition of a static and non-static gravitational field the results of the methods of Anandan and Penrose are different, but the numerical value of the extra term in Anandan’s approach, involving angular velocity, is not even considered in a case of practical interest. Then, we investigate the collapse time of the superposition of a static and non-static gravitational field.

Decoherence due to gravitational time dilation: Analysis of competing decoherence effects

Recently, a static gravitational field, such as that of the Earth, was proposed as a new source of decoherence [1]. We study the conditions under which it becomes the dominant decoherence effect in typical interferometric experiments. The following competing sources are considered: spontaneous emission of light, absorption, scattering with the thermal photons and collisions with the residual gas. We quantify all these effects. As we will see, current experiments are off by several orders of magnitude. New ideas are needed in order to achieve the necessary requirements: having as large a system as possible, to increase gravitational decoherence, cool it and isolate well enough to reduce thermal and collisional decoherence, and resolve very small distances.

Finite-temperature effective boundary theory of the quantized thermal Hall effect

A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two distinct types of the field theory have been proposed to describe the quantized thermal Hall effect. One of these, known as the gravitational Chern–Simons action, is a kind of topological field theory, and the other is a phenomenological theory relevant to the Strěda formula. In order to solve this problem, we derive microscopically an effective theory that accounts for the quantized thermal Hall effect. In this paper, the two-dimensional Dirac fermion under a static background gravitational field is considered in equilibrium at a finite temperature, from which an effective boundary free energy functional of the gravitational field is derived. This boundary theory is shown to explain the quantized thermal Hall conductivity and thermal Hall current in the bulk by assuming the Lorentz symmetry. The bulk effective theory is consistently determined via the boundary effective theory.

Thermal corrections to the Casimir energy in a general weak gravitational field

We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein–Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case.

Dark Matter and Dark Energy as a Derivate from Cosmic Photon Radiation

<p class="1Body">For many decades now, intensive efforts have been undertaken by physicists and cosmologists around the world to investigate dark matter (DM), without noticeable success to date. This situation leads me to believe that one of the assumptions underlying the current doctrine in physics may well be erroneous or incomplete <em>– </em>since a breakthrough in this field of physics and cosmology would otherwise surely have already taken place by now.</p><p class="1Body">For this year (2015) and the following two years, the CERN Nuclear Research Centre has set itself the task of using the LHC (now upgraded to 13 TeV) to investigate the still completely mysterious phenomenon of dark matter. The researchers at CERN favour the assumption – shared by the majority of physicists and cosmologists – that <strong>DM consists of massive non-baryonic particles (so-called WIMPs, Weakly Interacting Massive Particles)</strong> hitherto completely unknown to us, which produce a non-baryonic, static gravitational field distributed throughout the entire cosmos.</p><p class="1Body">I cast doubt on the above assumption that DM is massive in nature. As this paper will show, DM can be far better (and more simply) explained in terms of a non-massive gravitational derivate of those photons consumed in the expansion of cosmic space (by performing the work of expansion), those photons thereby being transformed into static physical quantities. This gravitational derivate creates a free gravitational field (decoupled from the other forces of nature) of non-baryonic, static nature, regionally varying in intensity, and this is known as <strong>dark matter</strong>.</p>

The effect of oscillating force field on the dynamics of free inner core in a rotating fluid-filled spherical cavity

This research involves experimental studies of the dynamics of a free spherical core in a fluid-filled spherical cavity rotating around the horizontal axis and subject to vibration perpendicular to the rotation axis. The core stays in the center of the cavity under the action of a centrifugal force (the core density is less than the fluid density). The vibration manifests itself in resonance regions when the vibration frequency coincides with one of the core’s natural frequencies. The amplitude of the core oscillations and generation of its intensive differential rotation rise steeply, with the differential rotation lagging or leading, depending on the frequency of the core oscillations. Excitation of leading rotation is accompanied by the core shift from the cavity center to one of the poles with the core rotation axis deviated from the cavity rotation axis. The research shows that the superposition of different force fields, oscillating vibrational field, and static gravitational force field determines the differential rotation rate of the core. The gravity field causes the lagging circular oscillations of the core with respect to the cavity, and consequently its steady lagging differential rotation, which decreases as the cavity rotation rate increases. The research shows that 2D steady flow in the form of a Taylor-Proudman column accompanies the differential rotation of the core. The resulting flow is a linear superposition of flows excited independently by gravity and vibration. The instability of the flow manifests itself, as an azimuthal two-dimensional wave is propagating on the Taylor-Proudman column boundary, and depends on the flow structure.

Some Properties of Stationary Gravitational Fields

The problem of stationary gravitational fields is still far from solved, since there is no exact general solution of the Einstein equations for stationary gravitational fields. This paper examines an approach to this problem employing isotropic coordinates which, in particular, make it possible to understand which simplifications yield the Kerr solution.

Weyl conformastatic perihelion advance

In this paper, we examine a static gravitational field with axial symmetry over probe particles in the solar system. Using the Weyl conformastatic solution as a model, we find a non-standard expression to perihelion advance due to the constraints imposed by the topology of the local gravitational field. We show that the application of the slow motion condition to the geodesic equations without altering Einstein's equations does not necessarily lead to the Newtonian limit; rather it leads to an intermediate nearly-newtonian gravitational stage, which can be applied to astrophysical problems in solar scale. We apply the model to the perihelion advance of inner planets and minor objects (NEO asteroids and the comets). As a result, we obtain an expression of a non-standard relativistic precession that reveals a close agreement to observational data calibrated with the Ephemerides of the Planets and the Moon (EPM2011). The study of perihelion advance of eight small celestial bodies (asteroids and comets) is also considered.

Thermal effective Lagrangian of generalized electrodynamics in static gravitational fields

In this paper we compute the effective Lagrangian of static gravitational fields interacting with thermal fields of generalized electrodynamics at high temperature. We employ the usual Matsubara imaginary-time formalism to obtain a closed form expression to the thermal effective Lagrangian at one-loop and two-loop order, in an arbitrary $\omega$-dimensional spacetime, in which the equivalence between the static hard thermal loops and those with zero external energy-momentum is widely explored. Afterwards, the symmetries of the resulting expressions are discussed as well as the presence of the Tolman \emph{local} temperature.

Can the Vacuum be Thermalized?

Accelerations do not cause time dependent Doppler shifts, which is usually caused by chirping. Lorentz transformations are not applicable to non-inertial systems like uniform accelerating bodies. Acceleration, whether it be linear or rotational, results in the breakdown of the conservation of linear, or angular momentum, and requires a non-flat metric implying a non-Euclidean geometry. Acceleration has been implicated in particle production through the mixing of positive and negative frequencies of the normal modes. In the vacuum an accelerating observer would see thermal, black body radiation, according to Unruh, so that by Einstein’s equivalence principle this radiation could be made to disappear when acceleration is replaced by a static gravitational field. However, the region of particle production is just the opposite of that of Ehrenfest’s adiabatic theorem so the putative radiation would not be thermal.

On slow flows of a weakly stratified relativistic fluid in a static gravitational field

Simplified equations for slow flows of a weakly stratified (in entropy) fluid inside or near a massive astrophysical object have been derived from the variational formulation of ideal general relativistic hydrodynamics under the conditions that the gravitational field in the leading order is centrosymmetric and static and that the effect of a magnetic field is negligibly small. Internal waves and vortices in such systems are soft modes as compared to sound. This circumstance allows the formulation of a “soundproof” Hamiltonian model. This model is an analog of nonrelativistic hydrodynamic anelastic models, which are widely used in studies of internal waves and/or convection in spatially inhomogeneous compressible media in atmospheric physics, geophysics, and astrophysics.

A New Method to Analyze the Stiffness of MEMS Accelerometer

The finite element method to obtain the stiffness of MEMS (Micro-Electro-Mechanical Systems) accelerometer is difficult to give an exact expression, so a new method to analyze the stiffness of MEMS accelerometer was purposed. Both Mechanics and electricity analysis were used to calculate the stiffness of vacuum microelectronic accelerometer developed in our laboratory, and the control and detection circuits were design according to the result. Finally, the sensitivity, linearity and other performance were measured through the static gravitational field experiments; the least squares curve fitting correlation coefficient 0.9999 and linear 0.9%. The result shows that this method to analyze the stiffness of the stiffness of vacuum microelectronics accelerometer is correct and feasible, and this method can also be applied to other MEMS accelerometer with symmetrical structure and electrostatic force balance mode.

Is Gravity, The Curvature of Spacetime or A Quantum Phenomenon?

Gravity is the curvature of spacetime, the structural property of static gravitational field, a geometric field, in curved coordinates, according the functions guv, that express geometric relations. Course, general relativity is a relational theory, however, gravity, a thinking category, has symetric physical effects with matter. Throught of relativist aether was attempted transform spacetime in a substantia without succes, the consequence was return to problematic geometric field. The philosophy of the science intervenes, and according the substantialist theory spacetime is a inmaterial, geometric substantia. Then, the metaphysics arrives to a full solution in the super-substantivalist theory, that affirms: matter arises from geometric spacetime. Thus, it explains consistently the symetric physical effects between spacetime and matter. Surely, this solution is a medieval speculation. Our goal is driver the debate on gravity, to the arena of the quantum physics, but without the ballast of the general relativity. Â Â

QED plasma in a background of static gravitational fields

We obtain the effective Lagrangian of static gravitational fields interacting with a QED plasma at high temperature. Using the equivalence between the static hard thermal loops and those with zero external energy-momentum, we compute the effective Lagrangian up to two-loop order. We also obtain a non-perturbative contribution which arises from the sum of all infrared divergent ring-diagrams. From the gauge and Weyl symmetries of the theory, we deduce to all orders that this effective Lagrangian is equivalent to the pressure of a QED plasma in Minkowski space-time, with the global temperature replaced by the Tolman local temperature.

Foldy–Wouthuysen transformation, scalar potentials and gravity

We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac–Coulomb and the Dirac–Schwarzschild Hamiltonians, and the corrections to the Dirac equation in a non-inertial frame, according to general relativity, are used as example cases in order to investigate the unitarity of the standard and ‘chiral’ approaches to the Foldy–Wouthuysen transformation, and spurious parity-breaking terms. Indeed, we find that parity-violating terms can be generated by unitary pseudo-scalar transformations (‘chiral’ Foldy–Wouthuysen transformations). Despite their interesting algebraic properties, we find that ‘chiral’ Foldy–Wouthuysen transformations change fundamental symmetry properties of the Hamiltonian and do not conserve the physical interpretation of the operators. Supplementing the discussion, we calculate the leading terms in the Foldy–Wouthuysen transformation of the Dirac Hamiltonian with a scalar potential (of the 1/r-form and of the confining radially symmetric linear form), and obtain compact expressions for the leading higher-order corrections to the Dirac Hamiltonian in a non-inertial rotating reference frame (‘Mashhoon term’).

Gravity field model calculated by using the GOCE data

Global static gravitational field determined by GOCE satellite data has become a hotspot in current research of geodesy. In this paper, a global static gravity field model entitled SWJTU-GO01S up to the degree and order 210 is recovered based on 12 months of GOCE orbit and gradient data from 2011-02-28 to 2012-03-05 with direct approach. GOCE gradient data are filtered by the zero phase finite impulse band-pass digital filter, and then a gradient observation equation is founded directly in gradiometer coordinates, which avoids high-accuracy gradient component loss in accuracy in the conversion process, while the orbit data is processed with short-arc integral approach. The optimal weight of combination result based on SST and SGG data is determined by variance component estimation and the polar gaps is dealt with the Kuala regularization method. Comparison of internal and external precision of SWJTU-GO01S with EGM2008 and with GPS leveling data of North America, shows that the geoid error and cumulative error of the SWJTU-GO01S model with the degree and order 210 are 2.1 cm and 13.7 cm respectively. Compared with the second generation models released by ESA and ITG-GRACE2010S, the accuracy of the model SWJTU-GO01S is higher than that of the model ITG-GRACE2010S and ESA official time-wise and space-wise model in the above degree and order 150. This study provides a reference to further joint multi-class satellite observation data to recover gravity field models.

Superfluid Picture for Rotating Space-Times

A new prescription, in the framework of condensate models for space-times, for physical stationary gravitational fields is presented. We show that the spinning cosmic string metric describes the gravitational field associated with the single vortex in a superfluid condensate model for space-time outside the vortex core. This metric differs significantly from the usual acoustic metric for the Onsager-Feynman vortex. We also consider the question of what happens when many vortices are present, and show that on large scales a Godel-like metric emerges. In both the single and multiple vortex cases the failure of general relativity exemplified by the presence of closed time-like curves is attributed to the breakdown of superfluid rigidity. The various developments of quantum field theory in curved space-time have left the false impression that gen- eral relativity and quantum mechanics are compatible. Actually though certain predictions of classical general relativity such as closed time-like curves and event hori- zons are in conflict with a quantum mechanical descrip- tion of space-time itself. In particular, a quantum me- chanical description of any system requires a universal time. In practice, universal time is defined by means of synchronization of atomic clocks, but such synchroniza- tion is not possible in space-times with event horizons or closed time-like curves. It has been suggested (1) that the way a global time is established in Nature is via the oc- currence of off-diagonal long-range quantum coherence in the vacuum state. This leads to a very different picture of compact astrophysical objects from that predicted by general relativity (2, 3, 4, 5, 6). In this Letter, we wish to point out the salient differences between the general relativistic description of rotating space-times and the picture offered by the assumption that the vacuum state is a quantum condensate.

Time transfer functions as a way to validate light propagation solutions for space astrometry

Given the extreme accuracy of modern space astrometry, a precise relativistic modeling of observations is required. Concerning light propagation, the standard procedure is the solution of the null-geodesic equations. However, another approach based on the time transfer functions (TTF) has demonstrated its capability to give access to key quantities such as the time of flight of a light signal between two point-events and the tangent vector to its null-geodesic in a weak gravitational field using an integral-based method. The availability of several models, formulated in different and independent ways, must not be considered like an oversized relativistic toolbox. Quite the contrary, they are needed as validation to put future experimental results on solid ground. The objective of this work is then twofold. First, we build the time of flight and tangent vectors in a closed form within the TTF formalism giving the case of a time-dependent metric. Second, we show how to use this new approach to obtain a comparison of the TTF with two existing modelings, namely the Gaia RElativistic Model (GREM) and the Relativistic Astrometric MODel (RAMOD). In this way, we highlight the mutual consistency of the three models, opening the basis for further links between all the approaches, which is mandatory for the interpretation of future space missions data. This will be illustrated through two recognized cases: a static gravitational field and a system of gravitational mass monopoles in uniform motion.

Comparison of Geodesics and Energy Variation Principles of Light Propagation

The propagation of light on a set of null paths in a pseudo-Riemannian manifold is studied using a variational principle of extremal energy. This method is compared with those based on the geodesics and Fermat principles. For the static space-time all three variational methods give the same solutions. The Fermat principle for stationary gravitational fields is identical to the principle of variation of energy of light-like particles. The approach proposed here is applied to a flat expanding space, corresponding to the LCDM-model, and generalized Godel space-time. In the first case a solution obtained by the method of energy variation coincides with the geodesic method, while in the second case they give different solutions.