Relative Time Research Articles

The BepiColombo solar conjunction experiments revisited

BepiColombo ESA/JAXA mission is currently in its 7 year cruise phase towards Mercury. The Mercury orbiter radioscience experiment (MORE), one of the 16 experiments of the mission, will start its scientific investigation during the superior solar conjunction (SSC) in March 2021 with a test of general relativity (GR). Other solar conjunctions will follow during the cruise phase, providing several opportunities to improve the results of the first experiment. MORE radio tracking system allows to establish precise ranging and Doppler measurements almost at all solar elongation angles (up to 7–8 solar radii), thus providing an accurate measurement of the relativistic time delay and frequency shift experienced by a radio signal during an SSC. The final objective of the experiment is to place new limits to the accuracy of the GR as a theory of gravity in the weak-field limit. As in all gravity experiments, non-gravitational accelerations acting on the spacecraft are a major concern. Because of the proximity to the Sun, the spacecraft will undergo severe solar radiation pressure acceleration, and the effect of the random fluctuations of the solar irradiance may become a significant source of spacecraft buffeting. In this paper we address the problem of a realistic estimate of the outcome of the SSC experiments of BepiColombo, by including in the dynamical model the effects of random variations in the solar irradiance. We propose a numerical method to mitigate the impact of the variable solar radiation pressure on the outcome of the experiment. Our simulations show that, with different assumptions on the solar activity and observation coverage, the accuracy attainable in the estimation of γ lays in the range [–] ×10−6.

The World According to Physics

The World According to Physics

The World According to Physics

The World According to Physics

Radio timing in a millisecond pulsar – extreme/intermediate mass ratio binary system

Radio timing observations of a millisecond pulsar in orbit around the Galactic centre black hole (BH) or a BH at the centre of globular clusters could answer foundational questions in astrophysics and fundamental physics. Pulsar radio astronomy typically employs the post-Keplerian approximation to determine the system parameters. However, in the strong gravitational field around the central BH, higher order relativistic effects may become important. We compare the pulsar timing delays given by the post-Keplerian approximation with those given by a relativistic timing model. We find significant discrepancies between the solutions derived for the Einstein delay and the propagation delay (i.e. Roemer and Sharpiro delay) compared to the fully relativistic solutions. Correcting for these higher order relativistic effects is essential in order to construct accurate radio timing models for pulsar systems at the Galactic centre and the centre of globular clusters and informing issues related to their detection.

Signaling to Relativistic Observers: An Einstein–Shannon–Riemann Encounter

A communication scenario is described involving a series of events triggered by a transmitter and observed by a receiver experiencing relativistic time dilation. The message selected by the transmitter is assumed to be encoded in the events' timings and is required to be perfectly recovered by the receiver, regardless of the difference in clock rates in the two frames of reference. It is shown that the largest proportion of the space of all $ k $-event signals that can be selected as a code ensuring error-free information transfer in this setting equals $ \zeta(k)^{-1} $, where $ \zeta $ is the Riemann zeta function.

Underlining possible effects of Coriolis acceleration in experiments with a Mössbauer source

In recent years it seems that, by measuring the transverse Doppler effect in experiments with a Mössbauer source, we observe a higher blue-shift compared to that provided by the standard relativistic time dilation. If this experimental measure will be officially recognized by the scientific community, we believe that the correct explanation must be sought within Einstein's General Relativity theory. Having this in mind, the aim of this paper is to suggest a possible interpretation of the experimental results. We immediately emphasize that ours is only an idea and does not claim to be certainly the correct explanation in the case in which the experimental data will be confirmed.

The relativistic tunneling flight time may be superluminal, but it does not imply superluminal signaling

Wavepacket tunneling, in the relativistic limit, is studied via solutions to the Dirac equation for a square barrier potential. Specifically, the arrival time distribution (the time-dependent flux) is computed for wavepackets initiated far away from the barrier, and whose momentum is well below the threshold for above-barrier transmission. The resulting distributions exhibit peaks at shorter times than those of photons with the same initial wavepacket transmitting through a vacuum. However, this apparent superluminality in time is accompanied by very low transmission probabilities. We discuss these observations, and related observations by other authors, in the context of published objections to the notion that tunneling can be superluminal in time. We find that many of these objections are not consistent with our observations, and conclude that post-selected (for transmission) distributions of arrival times can be superluminal. However, the low probability of tunneling means a photon will most likely be seen first and therefore the superluminality does not imply superluminal signaling.

Universal quantum modifications to general relativistic time dilation in delocalised clocks

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.

Deduction of relativistic length variations based on tests using a Cryogenic Optical Resonator

Experiments with the transverse Doppler effect have demonstrated that the wavelength of light increases with the speed of the source relative to the observer. The relativity principle implies that such a change cannot be detected by in situ measurements and this prediction has been verified by wavelength determinations carried out with a cavity resonator over an extended period of time during which the orbital speed of the Earth changes significantly. On this basis it can be concluded that the dimensions of the cavity resonator increase in direct proportion to the Doppler wavelength, and thus that isotropic length expansion occurs with relativistic time dilation, not the anisotropic Fitzgerald-Lorentz length contraction predicted by the special theory of relativity. The failure of the Lorentz space-time transformation to anticipate the length expansion effect is discussed and an alternative set of equations is introduced to eliminate the experimental contradiction in the existing theory.

New Insights on Time and Quantum Gravity

According to Einstein, a universal time does not exist. But what if time is different than what we think of it? Cosmic Microvawe Background Radiation was accepted as a reference for a universal clock and a new time concept has been constructed. According to this new concept, time was tackled as two-dimensional having both a wavelength and a frequency. What our clocks measure is actually a derivation of the frequency of time. A relativistic time dilation actually corresponds to an increase in the wavelength of time. At the point where time wavelength and time frequency is equal, where light is positioned, quantum-world and macro-world are seperated. Gravity was redefined with respect to time and the new two dimensional time fabric of the universe was speculated to be the source of dark energy causing the universe to expand. According to this new point of view quantum realm and macro-world can be better understood. This new time concept provide a basis for our understanding of quantum gravity and provide the long-sought answers to well known problems of it. A prediction of the presented theory is that the universe will expand at various rates at different regions due to the fact that particular surroundings will create different gravities and cause a different gravity- time wavelength effect yielding various time delays for calculating this rate of expansion. Keywords: General Relativity, Gravitation, Time and frequency, Quantum mechanics DOI : 10.7176/APTA/83-08 Publication date : May 30 th 2020

Testing Relativistic Time Dilation beyond the Weak-Field Post-Newtonian Approximation

In General Relativity, the gravitational field of a spherically symmetric non-rotating body is described by the Schwarzschild metric. This metric is invariant under time reversal, which implies that the power series expansion of the time dilation contains only even powers of v / c . The weak-field post-Newtonian approximation defines the relativistic time dilation of order ϵ (or of order ( v / c ) 2 ) of the small parameter. The next non-zero term of the time dilation is expected to be of order ϵ 2 , which is impossible to measure with current technology. The new model presented here, called Relativistic Newtonian Dynamics, describes the field with respect to the coordinate system of a far-removed observer. The resulting metric preserves the symmetries of the problem and satisfies Einstein’s field equations, but predicts an additional term of order ϵ 3 / 2 for the time dilation. This term will cause an additional periodic time delay for clocks in eccentric orbits. The analysis of the gravitational redshift data from the Galileo satellites in eccentric orbits indicates that, by performing an improved satellite mission, it would be possible to test this additional time delay. This would reveal which of the coordinate systems and which of the above metrics are real. In addition to the increase of accuracy of the time dilation predictions, such an experiment could determine whether the metric of a spherically symmetric body is time reversible and whether the speed of light propagating toward the gravitating body is the same as the speed propagating away from it. More accurate time dilation and one-way speed of light formulas are important for astronomical research and for global positioning systems.

Relative time seislet transform

The seislet transform uses the wavelet-lifting scheme and local slopes to analyze the seismic data. In its definition, the designing of prediction operators specifically for seismic images and data is an important issue. We have developed a new formulation of the seislet transform based on the relative time (RT) attribute. This method uses the RT volume to construct multiscale prediction operators. With the new prediction operators, the seislet transform gets accelerated because distant traces get predicted directly. We apply our method to synthetic and real data to demonstrate that the new approach reduces computational cost and obtains excellent sparse representation on test data sets.

Three routes to relativistic kinematics and time dilation and their connection to quantum-mechanical path integrals

The first calculation, similar to that of Lewis of 1908, takes as postulates Newton’s second law of motion and work-energy equivalence, the second makes use of the Hamilton–Jacobi equation for motion in free space and the third identifies the velocity of a freely moving particle with the group velocity of its associated de Broglie wave. In all cases the equivalence of mass and energy is also postulated. How the path integral formulation of quantum mechanics relates all the different calculations is demonstated. The essential roles of relativity, quantum mechanics and the particulate nature of light in the establishment of the current standard units of length, time and mass, are discussed, as well as the similar relations of the fundamental constants c, h and k to energy at the microscopic physics level.

Geopotential Determination Based on Precise Point Positioning Time Comparison: A Case Study Using Simulated Observation

Based on the general relativity theory, the geopotential difference can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two high-performance clocks for determining the geopotential difference using this approach, and conducted the simulation experiments to validate this approach. In the experiment, we consider three cases for evaluating the performance of this approach with different types of atomic clocks, namely, the fractional frequency stabilities of the clocks equipped at three selected ground stations (BRUX, OPMT, and PTBB) are $4.0 \times 10^{-13} / \sqrt {\tau }$ (Case 1), $2.3 \times 10^{-14} / \sqrt {\tau }$ (Case 2), and $2.8 \times 10^{-15} / \sqrt {\tau }$ (Case 3) at averaging time ${\tau }$ , respectively, and the accuracy of these clock have been evaluated to be $5.3 \times 10^{-16}$ , $7.8 \times 10^{-17}$ , and $8.6 \times 10^{-18}$ . Two main conclusions can be drawn from the experimental results. First, high-performance clocks can significantly improve the precision for GNSS PPP time transfer. Compared to Case 1, the long-term stabilities of the time link OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. Second, the geopotential difference between any two stations can be determined at the decimeter level, and the accuracy of geopotential difference is consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64, m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with an uncertainty of 1.11 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , whereas the deviation error between PTBB and BRUX is 0.76 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with an uncertainty of 1.79 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The results of this study suggest that a one decimeter-level geopotential difference between two arbitrary stations can be determined based on this approach.

Comment on “The Mössbauer rotor experiment and the general theory of relativity” [Ann. Physics 368 (2016) 258–266

In present article the original proposition is a generalization of the Einstein's world tensor $g_{ij}$ by the introduction of pure inertial field tensor $g^{ac}_{ij}$ such that $R_{{\mu}{\nu}{\lambda}}^{{\alpha}}(g^{ac}_{ij})\neq0$.Bimetric theory of gravitational-inertial field is considered for the case when the gravitational-Inertial field is governed by either a perfect magnetic fluid.In a series of papers published during the past decade with respect to M\"ossbauer experiments in a rotating system [71]-[75],it has been experimentally shown that the relative energy shift {\Delta}E/E between the source of resonant radiation (situated at the center of the rotating system) and the resonant absorber (located on the rotor rim) is described by the relationship ${\Delta}E/E=-ku^2/c^2$, where u is the tangential velocity of the absorber, c the velocity of light in vacuum, and k some coefficient, which -- contrary to what had been classically predicted equal 1/2 (see for example [35]) -- turns out to be substantially larger than 1/2. It cannot be stressed enough that the equality $k=1/2$ had been predicted by general theory of relativity (GTR) on account of the special relativistic time dilation effect delineated by the tangential displacement of the rotating absorber, where the "clock hypothesis" by Einstein (i.e., the non-reliance of the time rate of any clock on its acceleration [35]) was straightly adopted. Hence, the revealed inequality $k>1/2$ indicates the presence of some additional energy shift (next to the usual time dilation effect arising from tangential displacement alone) between the emitted and absorbed resonant radiation. By using Bimetric Theory of Gravitational-Inertial Field [76] we obtain $k=0.75$ in a good agreement with experimental result $k=0.69+(-)0.03$ [75].

O fatalismo relativístico

In this article, I will argue that the argument for fatalism based on the relativity of simultaneity (RoS) fails. The original proponents of the argument (Rietdijk 1966, Putnam 1967 and Penrose 1989) called the thesis in terms of ‘determinism’, but Levin (Levin 2007) refers to it as ‘relativistic fatalism’. Relativistic fatalism is a view supported by the alleged dependence of the property of being future on an arbitrary choice of some coordinate system. First I will try to explain the classic argument, attributed to it a dialectic that justified to call it in the same terms as Levin did. Subsequently, I will refuse the relativistic fatalism using many strategies to deal with it.

New Insights into Time and Quantum Gravity

According to Einstein, a universal time does not exist. But what if time is different than what we think of it? Cosmic Microwave Background Radiation was accepted as a reference for a universal clock and a new time concept has been constructed. According to this new concept, time was tackled as two-dimensional having both a wavelength and a frequency. What our clocks measure is actually a derivation of the frequency of time. A relativistic time dilation actually corresponds to an increase in the wavelength of time. At the point where time wavelength and time frequency is equal, where light is positioned, quantum-world and macro- world are separated. Gravity was redefined with respect to time and the new two dimensional time fabric of the universe was speculated to be the source of dark energy causing the universe to expand. According to this new point of view quantum realm and macro-world can be better understood. This new time concept provide a basis for our understanding of quantum gravity and provide the long-sought answers to well known problems of it. A prediction of the presented theory is that the universe will expand at various rates at different regions due to the fact that particular surroundings will create different gravities and cause a different gravity- time wavelength effect yielding various time delays for calculating this rate of expansion.

Relativistic length contraction and time dilation as dynamical phenomena

It is commonly accepted that a rod after having been accelerated and then left free contracts by the Lorentz factor , and also that a clock after having been accelerated and then returned to rest exhibits time dilation in accordance with the proper time formula . Although both issues have been debated numerous times, no models have been proposed to trace the dynamical nature of these phenomena. The purpose of the present paper is to propose a simple relativistic model of an elastic rod, which allows exact analytical solutions for a number of problems. The solutions of two problems are presented: (i) acceleration of the rod by a constant force applied at one of its ends during a finite time interval, resulting in the Lorentz contraction, (ii) acceleration and deceleration of a light clock, resulting in time dilation.

Demonstration of special relativity effects with specialized software

A software development project designed to demonstrate some effects of the special theory of relativity (STR) is considered. The software visualizes a uniform relativistic motion of one inertial reference frame, associated with a rocket, relative to another inertial reference frame, associated with the ground. The main idea behind the visualization is to reduce the speed of light down to perceived value, such that relativistic time dilation and relativistic length contraction effects can be explored. The basic mathematical expressions describing the model are given, and the interface of the software is presented. It is expected that the developed software will help to provide intuition behind relativistic mechanics for students starting their immersion in this topic.

A significant feature in the general relativistic time evolution of the redshift of photons coming from a star orbiting Sgr A*

Abstract The star S0-2, orbiting the Galactic central massive black hole candidate Sgr A$^\ast$, passed its pericenter in 2018 May. This event is the first chance to detect the general relativistic (GR) effect of a massive black hole, free from non-gravitational physics. The observable GR evidence in the event is the difference between the GR redshift and the Newtonian redshift of photons coming from S0-2. Within the present observational precision, the first post-Newtonian (1PN) GR evidence is detectable. In this paper, we give a theoretical analysis of the time evolution of the 1PN GR evidence, under a presupposition that is different from used in previous papers. Our presupposition is that the GR/Newtonian redshift is always calculated with the parameter values (the mass of Sgr A$^\ast$, the initial conditions of S0-2, and so on) determined by fitting the GR/Newtonian motion of S0-2 with the observational data. It is then revealed that the difference of the GR redshift and the Newtonian one shows two peaks before and after the pericenter passage. This double-peak appearance is due to our presupposition, and reduces to a single peak if the same parameter values are used in both GR and Newtonian redshifts as considered in previous papers. In addition to this theoretical discussion, we report our observational data obtained with the Subaru telescope by 2018. The quality and the number of Subaru data in 2018 are not sufficient to confirm the detection of the double-peak appearance.