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Atomic clocks can measure the gravitational redshift predicted by general relativity with great accuracy and for height differences as little as 1 cm. All existing experiments, however, involve the comparison of two independent clocks at different locations rather than a single clock in a delocalized quantum superposition. Here we present an interferometry scheme employing group-II-type atoms, such as Sr or Yb, capable of measuring the gravitational time dilation in a coherent superposition of atomic wave packets at two different heights. In contrast to other recent proposals, there is no need for pulses that can efficiently diffract both internal states. Instead, the scheme relies on very simple atom optics for which high diffraction efficiencies can be achieved with rather mild requirements on laser power. Furthermore, the effects of vibration noise are subtracted by employing a simultaneous Rb interferometer that acts as an inertial reference. Remarkably, the recently commissioned VLBAI facility in Hannover, a 10-m atomic fountain that can simultaneously operate Yb and Rb atoms and enables up to 2.8 s of free evolution time, meets all the requirements for a successful experimental implementation. [ABSTRACT FROM AUTHOR]

Recently, Takamoto et al. (2020) have discussed high precision measurements of gravity induced time dilation effects on optical lattice clocks located near the Earth surface. A relative tick frequency change, δν/ν0=(49 337.8±4.3)10-18, is found between two optical lattice clocks, one located at the ground floor, h=0 m, and the second one at an altitude hexp=452.596 m, on the Skytree tower in Tokyo. The results are compared with the predictions of Einstein's equivalence principle (EEP) estimated as an average over gravimeter measurements at h=0 m and h=450 m. We present a different derivation of the EEP prediction based on the calculation of the effective gravitational potential on the ground floor and at h=hexp, in excellent agreement with the value δν/ν0, providing an independent method to validate the differences in time dilation measured experimentally. In addition, we obtain the next-order correction to the present results, which may be tested in future more accurate experiments. [ABSTRACT FROM AUTHOR]

Planck scale modified dispersion relations are one way to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer's or particle's proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the κ-Poincaré dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the κ-Poincaré dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon's lifetime. [ABSTRACT FROM AUTHOR]

The Wheeler equation, for electromagnetic disturbances in a gravitational field, was found by Fiziev to have exact solutions both above and below the event horizon, in the form of waves propagating both inwardly and outwardly. This observation can be interpreted and verified from the optical point of view, entirely on the basis of the Schwarzschild metric for length contraction and time dilation, in order to derive a differential version of Snell's law for the Schwarzschild black hole. It reveals interesting physics, including the correct amount of light deflection by the Sun, internal and external Oppenheimer-Snyder cones of the black hole, properties of its phonon sphere and the conclusion that light rays are kept below the horizon by length contraction and time dilation rather than deflection. [ABSTRACT FROM AUTHOR]

We propose a novel probe of fundamental physics that involves the exploration of temporal correlations between the multi-frequency electromagnetic (EM) signal and the subthreshold GW signal or stochastic gravitational wave background (SGWB) originating from coalescing binaries. This method will be useful for the detection of EM counterparts associated with the subthreshold/SGWB signal. Exploiting the time delay between concomitant emission of the gravitational wave and EM signals enables inference of the redshifts of the contributing sources by studying the time delay dilation due to cosmological expansion, provided that the time-lag between the emission of gravitational wave signal and the EM signal acts like a standard clock. Measurement of the inevitable time-domain correlations between different frequencies of gravitational and EM waves, most notably in gamma-rays, will test several aspects of fundamental physics and gravitation theory, and enable a new pathway for current and future gravitational wave telescopes to study the universal nature of binary compact objects to high redshifts. [ABSTRACT FROM AUTHOR]

We study the tunneling probability of a massive (mw) uncharged scalar packet out from a near-extremal, static charged black hole (with mass M and charge Q≲M). We show that there is indeed a net probability that a massive uncharged particle tunnels out from the black hole so that the final state (with new mass M′≡M-mw

In order to solve the Tolman-Oppenheimer-Volkoff equations for neutron stars, one routinely uses the equations of state which are computed in the Minkowski spacetime. Using a first-principle approach, it is shown that the equations of state which are computed within the curved spacetime of the neutron stars include the effect of gravitational time dilation. It arises due to the radially varying interior metric over the length scale of the star and consequently it leads to a much higher mass limit. As an example, for a given set of parameters in a σ-ω model of nuclear matter, the maximum mass limit is shown to increase from 1.61 M⊙ to 2.24 M⊙ due to the inclusion of gravitational time dilation. [ABSTRACT FROM AUTHOR]

We have studied the nonlinear structure formation of the environmentally dependent dilaton model using N-body simulations. We find that the mechanism of suppressing the scalar fifth force in high-density regions works very well. Within the parameter space allowed by the solar-system tests, the dilaton model predicts small deviations of the matter power spectrum and the mass function from their ΛCDM counterparts. The importance of taking full account of the nonlinearity of the model is also emphasized. [ABSTRACT FROM AUTHOR]

We obtain a remarkable semianalytic expression concerning the role of purely tidal curvature on accelerated probes, revealing some novel insights into the role of absolute vs tidal acceleration in the response of such probes. The key quantity we evaluate is the relation between geodesic (τgeod) and proper time (τacc) intervals between events on the probe trajectory. This is obtained as a covariant power series in curvature using a combination of analytical and numerical tools. A serendipitous observation then reveals that one can exactly sum all terms involving the purely tidal component ℰn=Rabcdϵabϵcd of curvature, with ϵab the binormal to the plane of motion, τgeod=.... For classical clocks, the above result represents an interesting closed form contribution of tidal curvature to the differential ageing of twins in the classic twin paradox. For quantum probes, it gives a thermal contribution to the detector response with a modified Unruh temperature, [kBT]ℰn=.... As an operational tool, the computational framework we present and the corresponding results should find applications to a wide range of physical problems that involve measurements and observations by use of accelerated probes in curved spacetimes. [ABSTRACT FROM AUTHOR]

It is commonly believed that the fidelity of quantum teleportation using localized quantum objects with one party or both accelerated in vacuum would be degraded due to the heat up by the Unruh effect. In this paper, we point out that the Unruh effect is not the whole story in accounting for all the relativistic effects in quantum teleportation. First, there could be degradation of fidelity by a common field environment even when both quantum objects are in inertial motion. Second, relativistic effects entering the description of the dynamics, such as frame dependence, time dilation, and Doppler shift, already existent in inertial motion, can compete with or even overwhelm the effect due to uniform acceleration in a quantum field. We show it is not true that larger acceleration of an object would necessarily lead to a faster degradation of fidelity. These claims are based on four cases of quantum teleportation we studied using two Unruh-DeWitt detectors coupled via a common quantum field initially in the Minkowski vacuum. We find the quantum entanglement evaluated around the light cone, rather than the conventional ones evaluated on the Minkowski time slices, is the necessary condition for the averaged fidelity of quantum teleportation beating the classical one. These results are useful as a guide to making judicious choices of states and parameter ranges and estimation of the efficiency of quantum teleportation in relativistic quantum systems under environmental influences. [ABSTRACT FROM AUTHOR]

We investigate the possibility of estimating the mass of an isolated rapidly rotating neutron star (NS) from a continuous gravitational wave (GW) signal emitted by the NS. When the GW passes through the gravitational potential of the NS, the GW takes a slightly longer time to travel to an observer than it does in the absence of the NS. Such a time dilation effect holds also for photons and is often referred to as the gravitational time delay (or the Shapiro time delay). Correspondingly, the phase of the GW from the NS shifts due to the Coulomb-type gravitational potential of the NS, and the resulting logarithmic phase shift depends on the mass, the spin frequency of the NS, and the distance to the NS. We show that the NS mass can, in principle, be obtained by making use of the phase-shift difference between two modes of the continuous GW such as once and twice spin frequency modes induced by a freely precessing NS or a NS containing a pinned superfluid core. We estimate the measurement accuracy of the NS mass using Monte Carlo simulations and find that the mass of the NS with its spin frequency 500 Hz and its ellipticity 10-6 at 1 kpc is typically measurable with an accuracy of 20% using the Einstein Telescope. [ABSTRACT FROM AUTHOR]

We discuss the nonrelativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, and attempt to highlight and clarify several subtleties. In particular, we study the following issues: (a) While the action for a relativistic free particle is invariant under the Lorentz transformation, the corresponding action for a nonrelativistic tree particle is not invariant under the Galilean transformation, but picks up extra contributions at the end points. This leads to an extra phase in the nonrelativistic wave function under a Galilean transformation, which can be related to the rest energy of the particle even in the nonrelativistic limit. We show that this is closely related to the peculiar fact that the relativistic action for a free particle remains invariant even if we restrict ourselves to O(1/c²) in implementing the Lorentz transformation. (b) We provide a brief critique of the principle of equivalence in the quantum mechanical context. In particular, we show how solutions to the generally covariant Klein-Gordon equation in a noninertial frame, which has a time-dependent acceleration, reduce to the nonrelativistic wave function in the presence of an appropriate (time-dependent) gravitational field in the c → ∞ limit, and relate this fact to the validity of the principle of equivalence in a quantum mechanical context. We also show that the extra phase acquired by the nonrelativistic wave function in an accelerated frame, actually arises from the gravitational time dilation and survives in the nonrelativistic limit. (c) While the solution of the Schrödinger equation can be given an interpretation as being the probability amplitude for a single particle, such an interpretation fails in quantum field theory. We show how, in spite of this, one can explicitly evaluate the path integral using the (nonquadratic) action for a relativistic particle (involving a square root) and obtain the Feynman propagator. Further, we describe how this propagator reduces to the standard path integral kernel in the nonrelativistic limit. (d) We show that the limiting procedures for the propagators mentioned above work correctly even in the presence of a weak gravitational field, or in the Rindler frame, and discuss the implications for the principle of equivalence. [ABSTRACT FROM AUTHOR]

The strong gravitational field around a proto-neutron star can modify the neutrino flavor transformations that occur above the neutrinosphere via three general relativistic (GR) effects: time dilation, energy redshift, and trajectory bending. Depending on the compactness of the central object, the neutrino self-interaction potential is up to three times as large as that without GR principally due to trajectory bending which increases the intersection angles between different neutrino trajectories, and time dilation which changes the fluxes. We determine whether GR effects are important for flavor transformation during the different epochs of a supernova by using multiangle flavor transformation calculations and consider a density profile and neutrino spectra representative of both the accretion and cooling phases. We find the GR effects are smaller during the accretion phase due to low compactness of the proto-neutron star and merely delay the decoherence; the neutrino bipolar oscillations during the cooling phase are also delayed due to the GR effects but the delay may be more important because the delay occurs at radii where it might alter the nucleosynthesis in the neutrino driven wind. [ABSTRACT FROM AUTHOR]

We study a scalar particle of mas m1 decaying into two particles of mass m2 during the radiation and matter dominated epochs of a standard cosmological model. An adiabatic approximation is introduced that is valid for degrees of freedom (d.o.f.) with typical wavelengths much smaller than the particle horizon (∝ Hubble radius) at a given time. We implement a nonperturbative method that includes the cosmological expansion and obtain a cosmological Fermi's Golden Rule that enables one to compute the decay law of the parent particle with mass m1, along with the build up of the population of daughter particles with mass m2. The survival probability of the decaying particle is P(t)=e-Γk(t)t with Γk(t) being an effective momentum and time dependent decay rate. It features a transition timescale tnr between the relativistic and nonrelativistic regimes and for k≠0 is always smaller than the analogous rate in Minkowski spacetime, as a consequence of (local) time dilation and the cosmological redshift. For t≪tnr the decay law is a "stretched exponential" P(t)=e-(t/t*)3/2, whereas for the nonrelativistic stage with t≫tnr, we find P(t)=e-Γ0t(t/tnr)Γ0tnr/2, with Γ0 the Minkowski space time decay width at rest. The Hubble timescale ∝1/H(t) introduces an energy uncertainty ΔE~H(t) which relaxes the constraints of kinematic thresholds. This opens new decay channels into heavier particles for 2πEk(t)H(t)≫4m²2-m²1, with Ek(t) the (local) comoving energy of the decaying particle. As the expansion proceeds this channel closes and the usual two particle threshold restricts the decay kinematics. [ABSTRACT FROM AUTHOR]

The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of the spacetime, like the classical Michelson-Morley, Ives-Stilwell, Kennedy-Thorndike experiments or frequency comparison experiments in general, it is necessary to describe them in theories, which go beyond the Lorentzian metric structure. However, this requires a description of an observer's measurement without relying on a metric. We provide such a description of an observer's measurement of the fundamental quantities time and length derived from a premetric perturbation of Maxwell's electrodynamics and a discussion on how these measurements influence classical relativistic observables like time dilation and length contraction. Most importantly, we find that the modification of electrodynamics influences the measurements at two instances: the propagation of light is altered as well as the observer's proper time normalization. When interpreting the results of a specific experiment, both effects cannot be disentangled, in general, and have to be taken into account. [ABSTRACT FROM AUTHOR]

Core-collapse supernovae emit on the order of 3×1053 ergs in high-energy neutrinos over a time of order 10 seconds, and so decrease their mass by about 0.2M?. If the explosion is nearly spherically symmetric, there will be little gravitational-wave emission. Nevertheless, the sudden decrease of mass of the progenitor may cause a change in the gravitational time delay of signals from a nearby pulsar. We calculate the change in arrival times as successive pulses pass through the neutrino shell at different times, and find that the effect may be detectable in ideal circumstances. [ABSTRACT FROM AUTHOR]

Cosmic rays are the highest energy particles available for our study, and as such serve as excellent probes of the effects of Lorentz invariance violations which are expected to increase with energy. This general paradigm is investigated in this paper by studying the effects of such violations within the Coleman-Glashow model in which each particle species may have its own maximum attainable velocity, even exceeding that of light in vacuo. The particular focus here is that the muon neutrino may have the maximum speed exceeding that of light. We show that such an assumption leads to the elongation of the decay lifetime of the pion which increases with energy over and above the time dilation effects. We provide a transparent analytical derivation of the spectral intensities of muon neutrinos and muons generated in the Earth's atmosphere by cosmic rays. In this derivation we not only account for elongation of the pion lifetime, but also for the loss of energy by the neutrinos by radiation of the electron-positron pairs through the Cohen-Glashow process during their propagation. We then compare the theoretical spectra with observations of neutrinos and muons from large instruments like IceCube and BUST to set a limit of ~10-13 on the fractional excess speed of neutrinos over that of light. We also show that the ratio of the spectral intensities of downward and upward moving neutrinos at various angles constitute an exclusive diagnostic for the Cohen-Glashow process, which may be searched for in the IceCube data set. We conclude the paper with several comments, including those related to improvements of these tests when definite signals of Griesen-Zatsepin-Kuzmin neutrinos will be observed. [ABSTRACT FROM AUTHOR]