Spinning Object Research Articles

Upper limit on NUT charge from the observed terrestrial Sagnac effect

The exact Sagnac delay in the Kerr–Taub–NUT (Newman–Unti–Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin , the delay does not vanish. This fact is similar to the non-vanishing of Lense–Thirring precession under even though the two effects originate from different premises. Assuming a reasonable input that the Kerr–Taub–NUT corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge n. It is found that the upper limits on n are far larger than the Earth’s gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain n to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known ‘twin paradox’ of special relativity.

Measuring average angular velocity with a smartphone magnetic field sensor

The angular velocity of a spinning object is, by standard, measured using a device called a tachometer. However, by directly using it in a classroom setting, the activity is likely to appear as less instructive and less engaging. Indeed, some alternative classroom-suitable methods for measuring angular velocity have been presented. In this paper, we present a further alternative that is smartphone-based, making use of the real-time magnetic field (simply called B-field in what follows) data gathering capability of the B-field sensor of the smartphone device as the timer for measuring average rotational period and average angular velocity. The in-built B-field sensor in smartphones has already found a number of uses in undergraduate experimental physics. For instance, in elementary electrodynamics, it has been used to explore the well-known Bio-Savart law and in a measurement of the permeability of air.

Microwave imaging of spinning object using orbital angular momentum

The linear Doppler shift used for the detection of a spinning object becomes significantly weakened when the line of sight (LOS) is perpendicular to the object, which will result in the failure of detection. In this paper, a new detection and imaging technique for spinning objects is developed. The rotational Doppler phenomenon is observed by using the microwave carrying orbital angular momentum (OAM). To converge the radiation energy on the area where objects might exist, the generation method of OAM beams is proposed based on the frequency diversity principle, and the imaging model is derived accordingly. The detection method of the rotational Doppler shift and the imaging approach of the azimuthal profiles are proposed, which are verified by proof-of-concept experiments. Simulation and experimental results demonstrate that OAM beams can still be used to obtain the azimuthal profiles of spinning objects even when the LOS is perpendicular to the object. This work remedies the insufficiency in existing microwave sensing technology and offers a new solution to the object identification problem.

Tomographic polarization analyzer by polarization-mode-frequency mapping.

A tomographic polarization analyzer is presented by polarization-mode-frequency mapping. Two orthogonal circularly polarized components of the unknown polarization state of light are converted to two orbital angular momentum (OAM) modes by a q-plate, and then the OAM modes are mapped to two frequencies by using time-varying spatial modulation. The polarization state of light can be retrieved by tomographic reconstruction of the temporal intensity signal collected by a photodetector. The time-varying spatial modulation can be achieved by either a programmable spatial device or a spinning object. Our method can directly measure the Jones matrix of light with high accuracy due to the high-volume time sampling.

A modern approach to superradiance

In this paper, we provide a simple and modern discussion of rotational super-radiance based on quantum field theory. We work with an effective theory valid at scales much larger than the size of the spinning object responsible for superradiance. Within this framework, the probability of absorption by an object at rest completely determines the superradiant amplification rate when that same object is spinning. We first discuss in detail superradiant scattering of spin 0 particles with orbital angular momentum ℓ = 1, and then extend our analysis to higher values of orbital angular momentum and spin. Along the way, we provide a simple derivation of vacuum friction — a “quantum torque” acting on spinning objects in empty space. Our results apply not only to black holes but to arbitrary spinning objects. We also discuss superradiant instability due to formation of bound states and, as an illustration, we calculate the instability rate Γ for bound states with massive spin 1 particles. For a black hole with mass M and angular velocity Ω, we find Γ ∼ (GM μ)7Ω when the particle’s Compton wavelength 1/μ is much greater than the size GM of the spinning object. This rate is parametrically much larger than the instability rate for spin 0 particles, which scales like (GM μ)9Ω. This enhanced instability rate can be used to constrain the existence of ultralight particles beyond the Standard Model.

Theoretical analysis and experimental verification on optical rotational Doppler effect.

We present a theoretical model to sufficiently investigate the optical rotational Doppler effect based on modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the difference of mode index between input and output orbital angular momentum (OAM) light, and linear to the rotating speed of spinning object as well. An experiment is carried out to verify the theoretical model. We explicitly suggest that the spatial spiral phase distribution of spinning object determines the frequency content. The theoretical model makes us better understand the physical processes of rotational Doppler effect, and thus has many related application fields, such as detection of rotating bodies, imaging of surface and measurement of OAM light.

Rotational Doppler effect in nonlinear optics

The change in pitch of a passing car engine is a classic example of the translational Doppler effect, but rotational Doppler shifts can also arise, as shown for circularly polarized light passing through a spinning nonlinear optical crystal. The translational Doppler effect of electromagnetic and sound waves has been successfully applied in measurements of the speed and direction of vehicles, astronomical objects and blood flow in human bodies1,2,3,4,5,6,7,8, and for the Global Positioning System. The Doppler effect plays a key role for some important quantum phenomena such as the broadened emission spectra of atoms9 and has benefited cooling and trapping of atoms with laser light10,11,12. Despite numerous successful applications of the translational Doppler effect, it fails to measure the rotation frequency of a spinning object when the probing wave propagates along its rotation axis. This constraint was circumvented by deploying the angular momentum of electromagnetic waves13—the so-called rotational Doppler effect. Here, we report on the demonstration of rotational Doppler shift in nonlinear optics. The Doppler frequency shift is determined for the second harmonic generation of a circularly polarized beam passing through a spinning nonlinear optical crystal with three-fold rotational symmetry. We find that the second harmonic generation signal with circular polarization opposite to that of the fundamental beam experiences a Doppler shift of three times the rotation frequency of the optical crystal. This demonstration is of fundamental significance in nonlinear optics, as it provides us with insight into the interaction of light with moving media in the nonlinear optical regime.

Launches and Captures of the Space “Frisbees”: Dynamics Modelling and Simulation

The current paper presents a concept of the non-conventional method of handling/transfer of the space objects/payloads, using single and multiple cooperative robotic manipulators with extremely flexible arms. Practical cases may involve launch only (as in the case of the ejection of the spacecraft), capture only (as in the case of the capture of the dysfunctional spacecraft or debris) or launch and capture, combined together (as in the case of a payload transfer from one platform to another). This method is seen as having numerous advantages over the traditional methods, employing propulsive systems on the payloads. These include: simplicity,reliability, re-usability, ability to handle passive payloads, and small power requirements. In this study, various operational scenarios of the launches and captures of the payloads are considered and designed in detail. In particular, we demonstrate the feasibility of the launch of the outgoing rotating payloads (called "frisbees") using a highly elastic robotic arm, capable of transferring its potential energy of the pre-deformed shape into the kinetic energy of the payload. Using the co-rotational FEM, we firstly simulate pre-launch phases, coiling the elastic elements in different shapes, for example, "U", "S" or even more complex shapes, and then propose and simulate the scenarios of ejecting the payloads utilising the kinetic energy of the elastic members (playing role of catapults). We also demonstrate the feasibility of the ejection of the payloads with required dynamic parameters, using cooperative robotic manipulator arms, performing coordinated throwing manoeuvres. This is done in compliance with the kinematics of the system and dynamics laws. The cases of the ejection of the payload is simulated using fully non-linear formulation, employing so-called co-rotational FEM,which enables to deal with large deformations, large rotations and large translations of the simulated elastic robotic arms. Numerical simulation allows to observe, to analyse and to suppress the transient strains and stresses in the flexible arms. In the cases of the payload capture, the co-rotational FEM method is used to simulate the process of de-spin, slowing and stopping the spinning object. This is also supplemented with the analysis of the strains and stresses on the members of the robotic arm manipulators. Various study cases are illustrated with the animations of the representative cases in Virtual Reality.

Electromagnetic source for the Kerr–Newman geometry

Source-free equations of nonlinear electrodynamics minimally coupled to gravity (NED-GR) admit regular axially symmetric asymptotically Kerr–Newman solutions which describe electrically charged rotating black holes and spinning solitons. Asymptotic analysis of solutions shows the existence of de Sitter vacuum interior which has the properties of a perfect conductor and an ideal diamagnetic. The Kerr ring singularity (a naked singularity in the case without horizons) is replaced with a superconducting current which serves as a nondissipative source of the Kerr–Newman fields and can be responsible for an unlimited life time of a spinning object.

Dragging of inertial frames in the composed black-hole–ring system

A well-established phenomenon in general relativity is the dragging of inertial frames by a spinning object. In particular, due to the dragging of inertial frames by a ring orbiting a central black hole, the angular-velocity of the black-hole horizon in the composed black-hole-ring system is no longer related to the black-hole angular-momentum by the simple Kerr-like (vacuum) relation $\Omega^{\text{Kerr}}_{\text{H}}(J_{\text{H}})=J_{\text{H}}/2M^2R_{\text{H}}$. Will has performed a perturbative treatment of the composed black-hole-ring system in the regime of slowly rotating black holes and found the explicit relation $\Omega^{\text{BH-ring}}_{\text{H}}(J_{\text{H}}=0,J_{\text{R}},R)=2J_{\text{R}}/R^3$ for the angular-velocity of a central black hole with zero angular-momentum. Analyzing a sequence of black-hole-ring configurations with adiabatically varying (decreasing) circumferential radii, we show that the expression found by Will implies a smooth transition of the central black-hole angular-velocity from its asymptotic near-horizon value $\Omega^{\text{BH-ring}}_{\text{H}}(J_{\text{H}}=0,J_{\text{R}},R\to R^{+}_{\text{H}})$ to its final Kerr (vacuum) value $\Omega^{\text{Kerr}}_{\text{H}}(J^{\text{new}}_{\text{H}})$. We use this important observation in order to generalize the result of Will to the regime of black-hole-ring configurations in which the central black holes possess non-zero angular momenta. Remarkably, we find the simple universal relation $\Delta\Omega_{\text{H}}\equiv\Omega^{\text{BH-ring}}_{\text{H}}(J_{\text{H}},J_{\text{R}},R\to R^{+}_{\text{H}})-\Omega^{\text{Kerr}}_{\text{H}}(J_{\text{H}})={{J_{\text{R}}}/{4M^3}}$ for the asymptotic deviation of the black-hole angular-velocity in the composed black-hole-ring system from the corresponding angular-velocity of the unperturbed (vacuum) Kerr black hole with the same angular-momentum.

Tidal deformations of a spinning compact object

The deformability of a compact object induced by a perturbing tidal field is encoded in the tidal Love numbers, which depend sensibly on the object's internal structure. These numbers are known only for static, spherically-symmetric objects. As a first step to compute the tidal Love numbers of a spinning compact star, here we extend powerful perturbative techniques to compute the exterior geometry of a spinning object distorted by an axisymmetric tidal field to second order in the angular momentum. The spin of the object introduces couplings between electric and magnetic deformations and new classes of induced Love numbers emerge. For example, a spinning object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second order in the spin. The deformations are encoded in a set of inhomogeneous differential equations which, remarkably, can be solved analytically in vacuum. We discuss certain subtleties in defining the tidal Love numbers in general relativity, which are due to the difficulty in separating the tidal field from the linear response of the object in the solution, even in the static case. By extending the standard procedure to identify the linear response in the static case, we prove analytically that the Love numbers of a Kerr black hole remain zero to second order in the spin. As a by-product, we provide the explicit form for a slowly-rotating, tidally-deformed Kerr black hole to quadratic order in the spin, and discuss its geodesic and geometrical properties.

SU‐E‐U‐02: The Development of a Practical Ultrasonic System for Cross‐Sectional Imaging of Small Animals

Purpose:To test the feasibility of developing a practical medium frequency ultrasound tomography method for small animal imaging. The ability to produce cross‐sectional or full body images of a live small animal using a low‐cost tabletop ultrasound scanner without any special license would be very beneficial to long term biological studies, where repeated scanning is often required over an extended period of time.Methods:The cross sectional images were produced by compounding multiple B‐scans of a laboratory phantom or an animal acquired at different projection angles. Two imaging systems were used to test the concept. The first system included a programmable 64‐channel phased array controller driving a 128‐channel, 5–10 MHz linear probe to produce 143 B‐Mode projections of the spinning object. The second system designed and manufactured in house, produced 64 or 128 B‐Mode projections with a single unfocused 8 MHz transducer scanning with a 0.116 mm step size.Results:The phased array system provided good penetration through the phantoms/mice (with the exception of the lungs) and allowed to acquire data in a very short time. The cross‐sectional images have enough resolution and dynamic range to detect both high‐ and low‐contrast organs. The single transducer system takes longer to scan, and the data require more sophisticated processing. To date, our images allow seeing details as small as 1–2 mm in the phantoms and in small animals, with the contrast mostly due to highly reflecting bones and air inclusions.Conclusion:The work indicates that very detailed and anatomically correct images can be created by relatively simple and inexpensive means. With more advanced algorithms and improved system design, scan time can be reduced considerably, enabling high‐resolution full 3D imaging. This will allow for quick and easy scans that can help monitor tumor growth and/or regression without contributing any dose to the animal.The authors would like to acknowledge the financial and engineering support from Tessonics.

Eggs and milk: Spinning spheres partially immersed in a liquid bath

When a hard-boiled egg spins through a pool of milk on the kitchen counter, the milk rises up the sides of the egg and droplets are ejected. This phenomenon occurs when any partially submerged object whose radius increases upward from the fluid surface (e.g., spheres, inverted cones, and rings) spins in a liquid bath. The fluid ejects from the surface near the maximum radius in one of three ejection modes: jets, sheets, or sheet breakup. Additionally, a surprisingly large flow rate is induced by the spinning object. In this study, we used spheres to determine the effects of experimental parameters on the induced flow rate. We characterized the modes of ejection and measured the sheet breakup distance using high-speed imaging. The basis of our closed form analytical model utilizes an integral momentum boundary layer analysis both beneath the free surface and in the thin film attached to the sphere. We present criteria defining the transitions between ejection modes and the radius where liquid sheets break up in the sheet ejection regime. Criteria defining the transitions between ejection modes and the radius where liquid sheets break up in the sheet ejection regime shows good agreement with experiments.

Research progress on preparation, manipulation, and remote sensing applications of high-order orbital angular momentum of photons

Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.

Factor Graph Modeling of Rigid‐body Dynamics for Localization, Mapping, and Parameter Estimation of a Spinning Object in Space

This paper presents a new approach for solving the simultaneous localization and mapping problem for inspecting an unknown and uncooperative object that is spinning about an arbitrary axis in space. This approach probabilistically models the six degree‐of‐freedom rigid‐body dynamics in a factor graph formulation. Using the incremental smoothing and mapping system, this method estimates a feature‐based map of the target object, as well as this object's position, orientation, linear velocity, angular velocity, center of mass, principal axes, and ratios of inertia. This solves an important problem for spacecraft proximity operations. Additionally, it provides a generic framework for incorporating rigid‐body dynamics that may be applied to a number of other terrestrial‐based applications. To evaluate this approach, the Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) were used as a testbed within the microgravity environment of the International Space Station. The SPHERES satellites, using body‐mounted stereo cameras, captured a dataset of a target object that was spinning at ten rotations per minute about its unstable, intermediate axis. This dataset was used to experimentally evaluate the approach described in this paper, and it showed that it was able to estimate a geometric map and the position, orientation, linear and angular velocities, center of mass, and ratios of inertia of the target object.

Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals

The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of the two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.

Thomas precession: where is the torque? Another solution to the problem

Special relativity predicts that a spinning object with a constant angular momentum in its rest frame, when transported around an orbit, will undergo the Thomas precession in the laboratory frame. As no torque is applied in the rest frame of the gyroscope, it appears that the principle of conservation of angular momentum is violated. In this paper, we show that in fact the Thomas precession of the gyroscope is accompanied by a torque emerging due to the Lorentz transformation of the force acting on segments of the gyroscope. Using the derived formula for torque, we find the standard expression for the Thomas precession rate. Advantages of our approach compared to a work on the same problem, by Muller (1992 Am. J. Phys. 60 313–317), are discussed.

Determining angular frequency from images of rotating objects via a generalized fast Fourier transform

In certain real-world applications, one needs to estimate the angular frequency of a spinning object. We consider the image processing problem of estimating this rate of rotation from a video of the object taken by a camera aligned with the axis of rotation. For many types of spinning objects, this problem can be addressed with existing techniques: simply register two consecutive video frames. We focus, however, on objects whose shape and intensity changes greatly from frame to frame, such as spinning plumes of plasma that emerge from a certain type of spacecraft thruster. To estimate the angular frequency of such objects, we introduce the Geometric Sum Transform (GST), a new rotation-based generalization of the discrete Fourier transform (DFT). Taking the GST of a given video produces a new sequence of images, the most coherent of which corresponds to the object's true rate of rotation. After formally demonstrating this fact, we provide a fast algorithm for computing the GST which generalizes the decimation-in-frequency approach for performing a Fast Fourier Transform (FFT). We further show that computing a GST is, in fact, mathematically equivalent to computing a system of DFTs, provided one can decompose each video frame in terms of an eigenbasis of a rotation operator. We conclude with numerical experimentation.

Next-to-next-to-leading order spin–orbit effects in the equations of motion of compact binary systems

We compute next-to-next-to-leading order spin contributions to the post-Newtonian equations of motion for binaries of compact objects, such as black holes or neutron stars. For maximally spinning black holes, those contributions are of third-and-a-half post-Newtonian (3.5 PN) order, improving our knowledge of the equations of motion, already known for non-spinning objects up to this order. Building on previous work, we represent the rotation of the two bodies using a pole–dipole matter stress–energy tensor and iterate Einstein's field equations for a set of potentials parametrizing the metric in harmonic coordinates. Checks of the result include the existence of a conserved energy, the approximate global Lorentz invariance of the equations of motion in harmonic coordinates and the recovery of the motion of a spinning object on a Kerr background in the test-mass limit. We verified the existence of a contact transformation, together with a redefinition of the spin variables that makes our result equivalent to a previously published reduced Hamiltonian, obtained from the Arnowitt–Deser–Misner formalism.

On the connection between accreting X-ray and radio millisecond pulsars

AbstractFor many years it has been recognized that the terminal stages of mass transfer in a low-mass X-ray binary (LMXB) should cause the magnetosphere of the accreting neutron star to expand, leading to a braking torque acting on the spinning pulsar. After the discovery of radio millisecond pulsars (MSPs) it was therefore somewhat a paradox (e.g. Ruderman et al. 1989) how these pulsars could retain their fast spins following the Roche-lobe decoupling phase, RLDP. Here I present a solution to this so-called “turn-off problem” which was recently found by combining binary stellar evolution models with torque computations (Tauris 2012). The solution is that during the RLDP the spin equilibrium of the pulsar is broken and therefore it remains a fast spinning object. I briefly discuss these findings in view of the two observed spin distributions in the populations of accreting X-ray millisecond pulsars (AXMSPs) and radio MSPs.