Uncertainty In Position Measurement Research Articles

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

Optimized design method study for cavity BPM system

Beam-based alignment and feedback systems are essential for the operation of the Free Electron Lasers (FELs) and Linear colliders. They require a certain number of beam position monitors (BPMs) at selected locations and that their resolution can reach hundreds of nanometers or even the order of nanometers. Cavity BPMs adopting a resonant cavity structure having the advantage of high position resolution are widely used in the field of accelerators. A typical system includes a cavity BPM pickup, a radio frequency signal conditioning front-end and a digital signal processing electronic. How to systematically analyze the impact of the key parameters of each subsystem on the performance of the whole system, and combine the requirements of the system, operation mode of the facilities, the current level of equipment processing and the development of the electronics, so as to achieve the optimal and balanced allocation of the key technical indicators of each subsystem, is the primary issue to be considered when designing a CBPM system. In this paper, based on theoretical analysis, the relationship between the relative amplitude extraction uncertainty of the CBPM system and the key parameters of each subsystem is proposed, which could provide clear guidance for the design and optimization of a CBPM system. In addition, considering the engineering requirements of the Shanghai High repetition rate X-ray Free Electron Laser and Extreme Light facility (SHINE) for beam position monitor, the allocation of the key technical indicators of the CBPM system using the optimized design method is also introduced. Accordingly, the development of each subsystem was completed, and the beam test bench was also built at the Shanghai Soft X-ray FEL facility (SXFEL), based on the evaluation method of divided power, the beam experiment results show that the position measurement uncertainty of the CBPM system can reach 40 nm at the bunch charge of 100 pC, which is consistent with the theoretical analysis results and better than the requirements of the SHINE.

A naturally regularized path integral formalism

A minimal uncertainty in position measurement comes into play if, for instance, one incorporates gravitational interaction of photon and electron in the Heisenberg’s Electron Microscope Gedanken Experiment. This interaction modifies the Heisenberg’s standard uncertainty principle (HUP) to the so-called Generalized (Gravitational) Uncertainty Principle (GUP). The finite resolution of spacetime structure (through a minimal uncertainty in position measurement) nontrivially reflects the existence of a minimal measurable length of the order of the Planck length. The existence of such a minimal length is addressed in several approaches to quantum gravity proposal. On the other hand, Doubly Special Relativity (DSR) theories have revealed that due to the existence of a minimal measurable length, there would be also a maximal momentum for a test particle. These are actually two faces of one fact, that is, a natural ultraviolet cutoff which plays the role of a regulator in quantum field theory. A GUP consisting these cutoffs has some important impacts on the foundation of standard quantum mechanics; one of which is the discreteness of the spacetime manifold. In this paper we study Kernel and Feynman Path Integrals in the framework of a GUP that admits a minimal length and a maximal momentum. We work in the quasi-space representation by adopting maximally localized states in position space. We perform our analysis for both the particle-like and wave-like scenarios. We show that unlike the ordinary quantum mechanics, it is possible to construct a path integral even in the wave-like approach due to the presence of natural cutoffs. As an important application, by using the connection between the path integral formalism and statistical mechanics we investigate the modifications imposed on some thermodynamical properties of an ideal gas in this setup.

Measurement Vertex Position of a Large Aspheric Mirror

We present a novel method to accurately measure the vertex position of a large aspheric mirror with a phasing measuring interferometer, a laser tracker, and a micro alignment telescope. The method consists of rotating the mirror by 180° about its mechanical axis and measuring the change in displacement. Use of a micro alignment telescope eliminates the need to adjust the mirror during the measurement, eases the alignment of the testing system, and improves the vertex position measurement accuracy. Using this method, we measured the vertex position of an aspheric mirror 1 m in diameter and 2 m in radius of curvature. The vertex position measurement uncertainty is 88 μm.

Sensitivity of shading calculations to horizon uncertainty

Planning for solar power installations requires assessment of potential shading by nearby obstacles on the horizon. A degree of uncertainty exists in measurements of the horizon from the point-of-view of the proposed solar collector. This uncertainty takes the form of errors in the measurement of the azimuth and altitude of obstacles that may cause shading. We modeled irradiance reductions due to shading simulated horizon position measurement uncertainty. Results indicate that the sensitivity of solar simulations to horizon measurements is relatively low (around 2% per degree error for the most sensitive case observed). Beam and diffuse irradiance showed similar sensitivity to horizon measurement errors, and experienced similar trends in sensitivity relative to azimuth and altitude errors. For all cases, sensitivity to altitude errors was observed to be greater than sensitivity to azimuth errors. Conservative estimates of uncertainty in predicted irradiance based upon an existing measurement technique were around 3%.

Probing deformed commutators with macroscopic harmonic oscillators.

A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.

Atom position measurement in a four-level Lambda-shaped scheme with twofold lower-levels

The two-dimensional position dependent probe absorption spectrum of a driven four-level Λ-type atomic system with twofold lower-levels interacting with two orthogonal standing wave laser fields and one microwave field is investigated. It is found that due to the position dependent nature of atom–field interaction, the spatial distribution of the atom can be controlled by scanning the resulting absorption spectra of the weak probe field. The effect of different controlling parameters of the system such as detunings, the intensity of standing wave fields as well as the relative phase of applied fields on the position measurement uncertainty of the atom is then discussed. We show that by properly adjusting the system parameters, different spatial structures of localization as ‘∞’-like, spot-like, deltoid-like and elliptic like patterns can be designed, so that high-precision and high-resolution atom localization can be engineered.

Single-molecule study for a graphene-based nano-position sensor

In this study we lay the groundwork for a graphene-based fundamental ruler at the nanoscale. It relies on the efficient energy-transfer mechanism between single quantum emitters and low-doped graphene monolayers. Our experiments, conducted with dibenzoterrylene (DBT) molecules, allow going beyond ensemble analysis due to the emitter photo-stability and brightness. A quantitative characterization of the fluorescence decayrate modification is presented and compared to a simple model, showing agreement with the dependence, a genuine manifestation of a dipole interacting with a 2D material. With DBT molecules, we can estimate a potential uncertainty in position measurements as low as 5 nm in the range below 30 nm.

Miniaturization of an interferometric distance sensor employing diffractive optics

Abstract In order to improve safety, lifetime and energy efficiency of turbo machines, the behavior of the turbine blades has to be monitored during operation. This is a great challenge for metrology, since small, robust and non-contact position measurement techniques are required that offer both micrometer accuracy and microsecond temporal resolution. The Laser-Doppler-Distance (LDD) -Sensor proved to be an adequate technique to perform such measurements. However, the usage in turbo machines requires a miniaturized and temperature-stable sensor-head. In this paper we introduce a miniaturized design of the LDD-sensor that is based on common-path detection. First results indicated that the numerical aperture of the common-path detection is small in comparison to former implementations that used separate paths for illumination and detection. We find that decreasing the numerical aperture strongly increases the systematic measurement uncertainty. For this purpose a novel diffractive optical element containing a diffracting-lens was designed and used to increase the numerical aperture of the common-path detection without affecting the sensor size. Experiments prove that the new element reduces the relative systematic measurement uncertainty by a factor of ten. The mean systematic position measurement uncertainty amounts to Δz mean≈16 μm. The resulting sensor has dimensions of 25×25×60 mm3, offers temperature-stability and achieves micrometer resolution.

Reanalysis of Casimir force measurements in the 0.6-to-6-μm range

A systematic correction for Casimir force measurements is proposed and applied to the results of an experiment that was performed more than a decade ago. This correction brings the experimental results into good agreement with the Drude model of the metallic plates' permittivity. The systematic is due to time-dependent fluctuations in the distance between the plates caused by mechanical vibrations, tilt, or position measurement uncertainty and is similar to the correction for plate roughness.

Minimal length uncertainty relation and gravitational quantum well

The dynamics of a particle in a gravitational quantum well is studied in the context of nonrelativistic quantum mechanics with a particular deformation of a two-dimensional Heisenberg algebra. This deformation yields a new short-distance structure characterized by a finite minimal uncertainty in position measurements, a feature it shares with noncommutative theories. We show that an analytical solution can be found in perturbation and we compare our results to those published recently, where noncommutative geometry at the quantum mechanical level was considered. We find that the perturbations of the gravitational quantum well spectrum in these two approaches have different signatures. We also compare our modified energy spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultracold neutrons moving above a mirror are studied. This comparison leads to an upper bound on the minimal length scale induced by the deformed algebra we use. This upper bound is weaker than the one obtained in the context of the hydrogen atom but could still be useful if the deformation parameter of the Heisenberg algebra is not a universal constant but a quantity that depends on the energetic content of the system.

Error Analysis of Attitude Measurement in Robotic Ground Vehicle Position Determination

: Position and attitude information from sensors employing carrier-phase differential GPS technology offer precise measurements that can be used for robotic ground vehicle control, notably in the automatic steering of farm tractors. The difference in location between the master GPS antenna on the vehicle's roof and the vehicle's control point requires that a lever-arm correction be added to the position measurement taken at the antenna to calculate the control point position. This lever-arm correction is a nonlinear function of noisy attitude and lever-arm measurements and introduces additional uncertainty into the position measurement at the control point. An approximation for the additional uncertainty is derived and verified through Monte Carlo simulations. Using realistic noise and lever-arm values for a medium-sized farm tractor, Gaussian attitude measurement noise above 0.4 deg (1 s) was shown to be the dominant source of position uncertainty at the control point when using carrier-phase differential GPS for centimeter-level position measurement. This analysis illustrates the importance of precise attitude measurements in minimizing the position measurement uncertainty at the vehicle's control point.

Hilbert space representation of the minimal length uncertainty relation.

The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation.

Observable Consequences of Fundamental-Length Hypotheses

The postulate of the existence of a fundamental length may be expressed in terms of a minimum uncertainty in position measurements, or equivalently as a minimum uncertainty in measurements of the gravitational field. The postulate is expressed mathematically by means of "indeterminate operators," whose properties are discussed. With their aid, it is shown that the postulate of a fundamental length has as a consequence a certain broadening of spectral lines. In the case of a fundamental length of the order of ${10}^{\ensuremath{-}13}$ cm, the predicted broadening is much larger than the widths of nuclear gamma transitions already observed. It is concluded that this fundamental length is already in serious contradiction with experiment. In the case of a fundamental length due to gravitational effects of the order of ${10}^{\ensuremath{-}33}$ cm, as previously suggested by the author, the broadening is too small to have been observed in any experiments done to date. A modified M\"ossbauer experiment is suggested which should be capable of detecting this small broadening, if it is present. The experiment is difficult, but appears to be possible with presently available techniques. The gravitational-field uncertainties calculated by DeWitt, Peres, and Rosen, and others, lead to a still smaller broadening, which our proposed method would be incapable of detecting.