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We investigate the advantage of coherent superposition of two different coded channels in quantum metrology. In a continuous variable system, we show that the Heisenberg limit 1/N can be beaten by the coherent superposition without the help of indefinite causal order. And in parameter estimation, we demonstrate that the strategy with the coherent superposition can perform better than the strategy with quantum switch which can generate indefinite causal order. We analytically obtain the general form of estimation precision in terms of the quantum Fisher information and further prove that the nonlinear Hamiltonian can improve the estimation precision and make the measurement uncertainty scale as 1/Nm for m ≥ 2. Our results can help to construct a high-precision measurement equipment, which can be applied to the detection of coupling strength and the test of time dilation and the modification of the canonical commutation relation. [ABSTRACT FROM AUTHOR]

We present quantities which characterize the sensitivity of gravitational-wave observatories to sources at cosmological distances. In particular, we introduce and generalize the horizon, range, response, and reach distances. These quantities incorporate a number of important effects, including cosmologically well-defined distances and volumes, cosmological redshift, cosmological time dilation, and rate density evolution. In addition, these quantities incorporate unique aspects of gravitational wave detectors, such as the variable sky sensitivity of the detectors and the scaling of the sensitivity with inverse distance. An online calculator (https://users.rcc.uchicago.edu/~dholz/gwc/) and python notebook (https://github.com/hsinyuc/distancetool) to determine GW distances are available. We provide answers to the question: 'How far can gravitational-wave detectors hear?' [ABSTRACT FROM AUTHOR]

Recently, the physics education community has taken a keen interest in modernising physics education. However, while topics in modern physics have great potential to engage students, these topics are abstract and hard-to-visualise. Therefore, many students hold mistaken pictures and misconceptions, which can impede learning. In this article, we expose a pervasive misconception about relativistic time dilation by presenting a thought experiment illustrating the difference between visual observation and coordinate measurement. We also point out how existing language can mislead and confuse students. In response, we describe an instructional approach that introduces world-maps, world-pictures and event-diagrams to clarify the applicability of key equations in special relativity for improved understanding. By unpacking 'the invisibility of time dilation' from the perspectives of both physics and pedagogy, we aim to help teachers provide clearer instruction. [ABSTRACT FROM AUTHOR]

Well-developed tools from cartography are adapted and used to visualize curved and flat spacetime to further understanding of relativistic effects, while interpretation of these tools is aided through their application to the familiar world map. First spacetime is cut into two-dimensional subspaces that are mapped to the Minkowski or Euclidean plane using map projections. Then, exploiting the cartographic technique of map interruptions, the two-dimensional subspaces are further cut into 'wedges' to minimize the distortion. The mental exercise of sewing the wedges back together aids in visualizing and interpreting the geometry of the spacetime slice. Map distortion indicators alert the reader to the inevitable effects of distortion. This wedge diagram provides a simple yet powerful tool to visualize both flat and curved spacetime geometry. It is more general than the familiar embedding diagram and avoids the pitfall of confusing the space in question with the embedding space. The wedge diagram is applied first to Minkowski spacetime with the cartographers' azimuthal equidistant map projection and, when combined with the wedge technique, provides a simple visualization of the twin paradox. The wedge diagram is then applied to the exterior Schwarzschild spacetime to visualize the physical significance of spacetime curvature. In particular it is shown how gravitational time dilation results from intrinsic curvature of a radial-time slice of spacetime. Then this diagram is applied to the Friedmann–Robertson–Walker (FRW) spacetime revealing how expansion of the Universe results from a qualitatively similar curvature of a radial-time slice, but with the roles of space and time reversed. The analogy between the two spacetimes suggests novel interpretations of the two spacetimes. We interpret the Schwarzschild spacetime as time expanding with increasing distance from the horizon. And we interpret the FRW spacetime as the Universe expanding as the influence of the big bang peters out. [ABSTRACT FROM AUTHOR]

Introductory textbooks for the theory of special relativity discuss the time dilation effect after introducing the Lorentz transformations. Reading the dictum 'moving clocks run slow' a student is likely to have the impression that this is a measured effect. On the other hand, after considering the relativistic Doppler effect the same student might be puzzled that this effect depends on the relative emitter-observer direction, contrary to Einstein's time dilation. Simple thought experiments are presented here where the inferred time dilation and the observed relativistic Doppler effect give quite opposite answers. Before solving the puzzle, we show how easily one can get confused and obtain apparently contradictory results. [ABSTRACT FROM AUTHOR]

In order to explain the origin of skewness in the gamma-ray burst (GRB) duration distribution, a statistical model, based on the cosmological time dilation and taking into account the GRB formation rate and instrumental effects, is examined. It is concluded that the considered effects are able to account for only a small fraction of the observed skewness. Therefore, its origin needs to be searched for in the processes governing the progenitors of GRBs​. [ABSTRACT FROM AUTHOR]

We consider gravitational time dilation between stationary observers and present examples which contradict the statement that ‘time slows down as gravity increases’. We furthermore show that this statement cannot be true in general, if gravity strength is defined in an observer independent manner. We also provide a pedagogical introduction to gravitational time dilation, and discuss aspects of this phenomenon, which are often omitted in textbooks on general relativity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The transformation of canonical decay laws of moving unstable quantum systems is derived from the basic principles of quantum theory and special relativity by approximating, over intermediate times, the decay laws at rest with superpositions of exponential modes via the Prony analysis. The survival probability , which is detected in the laboratory reference frame where the unstable system moves with constant linear momentum p , is represented by the transformed form of the survival probability at rest . The transformation of the intermediate times, which is induced by the change of reference frame, is obtained by evaluating the function . Under determined conditions, this function grows linearly and the survival probability transforms, approximately, according to a scaling law over an estimated time window. The relativistic dilation of times holds, approximately, over the time window if the mass of resonance of the mass distribution density is considered to be the effective mass at rest of the moving unstable quantum system. [ABSTRACT FROM AUTHOR]

The "Breakthrough Starshot" program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Because the probe velocity is designed to be a good fraction of the light speed, Zhang & Li recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including the parametric general Doppler effect and the Doppler effect with massive photons. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Additionally, using the imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity v ∼ 0.2c, aperture D ∼ 3.5 cm, and spectral resolution R ∼ 100 (or 1000), we find that the probe velocity uncertainty can be constrained to σv ∼ 0.01c (or 0.001c), and the time dilation factor uncertainty can be constrained to (or 0.001), where is the time dilation factor and γ is the Lorentz factor. Meanwhile, the photon mass limit is set to mγ ≲ 10−33 g, which is slightly lower than the energy of the optical photon. [ABSTRACT FROM AUTHOR]

Quantum theory and relativity offer different conceptions of time. To explore the conflict between them, we study a quantum version of the light-clock commonly used to illustrate relativistic time dilation. This semiclassical model combines elements of both theories. We show for Gaussian states of the light field that the clock time is independent of the initial state. We calculate the discrepancy between two such clocks when one is held in a gravitational field and the other is left to fall a certain distance. Contrasting our results with the case of pointlike observers in general relativity, as well as classical light-clocks, we find both quantitative and qualitative differences. We find that the quantum contribution to the discrepancy between the two clocks increases with the gravitational field strength, and results in a minimum resolution of the dropped clock (distinct from the quantum uncertainty in its measurement). [ABSTRACT FROM AUTHOR]

The decay of a moving system is studied in case the system is initially prepared in a superposition of two, approximately orthogonal, unstable quantum states. The survival probability is evaluated over short and long times in the reference frame where the unstable system moves with constant linear momentum p. The mass distribution densities, which describe the two unstable states of the superposition, exhibit thresholds near the non-vanishing lower bounds and of the mass spectra. If these lower bounds coincide, the long-time survival probability shows a dominant inverse-power-law decay and is approximately related to the survival probability at rest via a time dilation. The scaling factor reads . If the lower bounds and differ, damped oscillations of the survival probability appear over long times and the scaling relation is lost. These oscillations are enveloped in an inverse-power-low profile which is determined by the thresholds. By changing reference frame, the period T0 of the oscillations at rest transforms in the longer period Tp according to a factor which is the weighted mean of the factors and , with non-normalized weights and . The oscillations tend to vanish in the ultrarelativistic limit. [ABSTRACT FROM AUTHOR]

The imaginary part of the inter-quark potential of moving heavy quarkonia is investigated in the context of dual super-gravity in an AdS background, deformed by a dilaton which induces the gauge field condensate in the dual gauge theory. A quark–anti-quark pair is analyzed, moving transverse and parallel to the plasma wind, in turn. It is shown that in both cases increased D-instanton density tends to increase the inter-distance and decrease the imaginary potential, opposite to the effect of the pair’s velocity. Moreover, it is found that the D-instanton density has stronger effects in the parallel case than the transverse. [ABSTRACT FROM AUTHOR]

The apparent length of a relativistically moving rod and visualization of the Einstein time dilation are studied. The description of events in space-time is given geometrically as viewed from two different inertial frames that are in relative motion with one another. These relativistic phenomena are graphically illustrated using one-dimensional Loedel diagrams. The equations that describe these effects are then deduced using elementary geometry. The aim of this paper is to outline a procedure that complements the standard algebraic presentation of these effects, and show that the kinematic concepts of special relativity can be deduced from the geometry. [ABSTRACT FROM AUTHOR]

The issue of the condition for simultaneous arrival of light signals emitted simultaneously from the opposite ends of a rigidly accelerating spaceship, raised in Ben-Ya’acov (2016 Eur. J. Phys.37 055601), is resolved. [ABSTRACT FROM AUTHOR]

In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys.18 093050) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer. [ABSTRACT FROM AUTHOR]

Although time is one of the fundamental notions in physics, it does not have a unique description. In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the system's world line, due to time dilation. It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different magnitudes of time dilation. Here we propose a realization of such an experiment with a single electron in a Penning trap. The clock can be implemented in the electronic spin precession and its time dilation then depends on the radial (cyclotron) state of the electron. We show that coherent manipulation and detection of the electron can be achieved already with present day technology. A single electron in a Penning trap is a technologically ready platform where the notion of time can be probed in a hitherto untested regime, where it requires a relativistic as well as quantum description. [ABSTRACT FROM AUTHOR]

Since the Lorentz boost is symmetric under exchange of x and ct, special relativistic phenomena will also manifest this symmetry. Firstly, simultaneity becomes paired with ‘colocality’ (‘at the same place’), and the ‘Relativity of Colocality’ becomes the dual to the well-known ‘Relativity of Simultaneity’. Further, Lorentz time contraction arises from reversal of the observation conditions pertaining to time dilation, expressible figuratively as ‘Moving clocks run slow, but moving time runs fast’. Symmetry also dictates that the most fundamental observational modes are: (1) the simultaneous observation of length, a process involving both the relativity of simultaneity and length contraction; and (2) the colocal measurement of duration, involving both the relativity of colocality and time contraction. Only the first of these modes is well known. The adoption of this symmetrical lexicon provides a necessary logical basis for interpretational studies of observation and measurement in special relativity. [ABSTRACT FROM AUTHOR]

Relativistic rigid motion suggests a new version for the so-called ‘twin paradox’, comparing the ages of two astronauts on a very long spaceship. Although there is always an instantaneous inertial frame in which the whole spaceship, being rigid, is simultaneously at rest, the twins’ ages, measured as the proper-times along their individual world lines, are different when they are located at remote parts of the spaceship. The age, or proper-time, difference depends on the distance at rest between the astronauts and the rapidity difference between start to end. The relation of the age difference with the relative Doppler shift of light signals transmitted between the astronauts and implications for the possibility to assign a common age (proper-time) to complex, spatially extended, relativistic systems are also discussed. [ABSTRACT FROM AUTHOR]

We treat, as an illustrative example of gravitational time dilation in relativity, the observation that the centre of the Earth is younger than the surface by an appreciable amount. Richard Feynman first made this insightful point and presented an estimate of the size of the effect in a talk; a transcription was later published in which the time difference is quoted as ‘one or two days’. However, a back-of-the-envelope calculation shows that the result is in fact a few years. In this paper we present this estimate alongside a more elaborate analysis yielding a difference of two and a half years. The aim is to provide a fairly complete solution to the relativity of the ‘aging’ of an object due to differences in the gravitational potential. This solution—accessible at the undergraduate level—can be used for educational purposes, as an example in the classroom. Finally, we also briefly discuss why exchanging ‘years’ for ‘days’—which in retrospect is a quite simple, but significant, mistake—has been repeated seemingly uncritically, albeit in a few cases only. The pedagogical value of this discussion is to show students that any number or observation, no matter who brought it forward, must be critically examined. [ABSTRACT FROM AUTHOR]

We use apparatus based on two Geiger–Müller tubes, a simple electronic circuit and a Raspberry Pi computer to illustrate relativistic time dilation affecting cosmic-ray muons travelling through the atmosphere to the Earth’s surface. The experiment we describe lends itself to both classroom demonstration to accompany the topic of special relativity and to extended investigations for more inquisitive students. [ABSTRACT FROM AUTHOR]