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We have obtained high-quality Keck optical spectra at three epochs of the Type la supernova 1997ex, whose redshift z is 0.361. The elapsed calendar time between the first two spectra was 24.88 days, and that between the first and third spectra was 30.95 days. In an expanding universe where 1 + z represents the factor by which space has expanded between the emission and detection of light, the amount of aging in the supernova rest frame should be a factor of 1/(1 + z) smaller than the observed-frame aging; thus, we expect SN 1997ex to have aged 18.28 and 22.74 days between the first epoch and the second and third epochs, respectively. The quantitative method for determining the spectral-feature age of an SN la reveals that the corresponding elapsed times in the supernova rest frame were 16.97 ± 2.75 and 18.01 ± 3.14 days, respectively. This result is inconsistent with no time dilation with a significance level of 99.0%, providing evidence against "tired light" and other hypotheses in which no time dilation is expected. Moreover, the observed timescale of spectral evolution is inconsistent with that expected in the "variable mass theory." The result is within ∼1 σ of the aging expected from a universe in which redshift is produced by cosmic expansion. © 2005. The American Astronomical Society. All rights reserved.

We have obtained high-quality Keck optical spectra at three epochs of the Type la supernova 1997ex, whose redshift z is 0.361. The elapsed calendar time between the first two spectra was 24.88 days, and that between the first and third spectra was 30.95 days. In an expanding universe where 1 + z represents the factor by which space has expanded between the emission and detection of light, the amount of aging in the supernova rest frame should be a factor of 1/(1 + z) smaller than the observed-frame aging; thus, we expect SN 1997ex to have aged 18.28 and 22.74 days between the first epoch and the second and third epochs, respectively. The quantitative method for determining the spectral-feature age of an SN la reveals that the corresponding elapsed times in the supernova rest frame were 16.97 ± 2.75 and 18.01 ± 3.14 days, respectively. This result is inconsistent with no time dilation with a significance level of 99.0%, providing evidence against "tired light" and other hypotheses in which no time dilation is expected. Moreover, the observed timescale of spectral evolution is inconsistent with that expected in the "variable mass theory." The result is within ∼1 σ of the aging expected from a universe in which redshift is produced by cosmic expansion. © 2005. The American Astronomical Society. All rights reserved.

Smartphones and tablets are packed with sensors that allow us to take experimental data, essentially making them mobile physics labs. Apps exist that make it easy to capture and analyze data from these sensors, allowing users to study diverse phenomena such as free fall acceleration, the speed of sound,radioactivity, and many others. Commonly, the use of apps in the physics classroom focuses on existing apps rather than on the creation of apps themselves. This is for a good reason-writing an app usually requires advanced knowledge of programming languages and experience with app design. These skills are generally regarded as beyond the typical physics student. However, there are app development environments, such as MIT App Inventor 2 for Android, which make the process of creating an app and utilizing the sensors much more accessible to students. Putting the ability to create and configure apps within the reach of students can also help integrate computation into the curriculum. In this article, we discuss our creation of an Android app, Time Dilation Calculator, done as part of a senior undergraduate capstone project, which uses App Inventor and a mobile device's global positioning system (GPS) receiver to calculate the time dilation effect of special relativity.

A very simple, fundamental physical explanation is presented of time dilation and length contraction. This explanation is obtained from a classical model of physics that is Galilean. It assumes the existence of a medium (ether) that acts as an absolute reference in accordance with Mach's principle. Time and space are conventional, i.e., a three-dimensional space independent of time. In addition, the explanation relies on the assumption that all physics, including matter such as clocks and measuring rods, has a scalar wave structure. Matter is assumed to consist of locally stable scalar wave structures, specifically scalar standing wave structures. The scalar waves are just variations in space and time of medium density. Also, an element of special relativity is used, namely, the one taking into account the finite velocity of light. [ABSTRACT FROM AUTHOR]

A Lorentz transformation may involve the changes in a three-dimensional fixed reference frame when given a constant boost velocity v in a moving reference frame as measured by an observer in a specified fixed reference frame. A Lorentz transformation may also involve changes in the size and shape of a material object when given a constant boost velocity v in a moving (Galilean) reference frame as measured by an observer in a specified fixed reference frame receiving light signals along the straight axis of a connecting ether rope. The mass of the flux of primordial fluid moving with a boost velocity is increased by the Lorentz gamma factor so that the measured time is reduced by the factor gamma. This is known as time dilation. [ABSTRACT FROM AUTHOR]

We review a theorem of Gao‐Wald on a kind of a gravitational "time delay" effect in null geodesically complete spacetimes under NEC and NGC, and we observe that it is not valid anymore throughout its statement, as well as a conclusion that there is a class of cosmological models where particle horizons are absent, if one substituted the manifold topology with a finer (spacetime) topology. Since topologies of the Zeeman‐Göbel class incorporate the causal, differential, and conformal structure of a spacetime and there are serious mathematical arguments in favour of such topologies and against the manifold topology, there is a strong evidence that "time dilation" theorems of this kind are topological in nature rather than having a particular physical meaning. [ABSTRACT FROM AUTHOR]

A question in physics is whether Special Relativity (SR) is the only theory that explains relativistic behavior. SR measures time dilation by a relative velocity between two frames. Laboratory experiments with a single moving body fit this concept. However, GPS satellites and their ground clocks measure time dilation by a velocity relative to a common non-rotating Earth inertial frame. To better understand the conceptual difference, an experimental survey was undertaken. The survey analysis showed that laboratory experiments also fit into the non-rotating Earth frame concept. The laboratory experiments only need to add the Earth rotational velocity to both the laboratory frame and the moving frame. The analysis also revealed that the relative velocity calculation was astonishingly close to the common Earth frame calculation. The common Earth frame then becomes the explanation for all experimental types. And it signifies that a gravity field – moving body interaction causes relativistic effects. The experimental record also contained enough data to draft an empirical kinetic theory different than SR. The “no preferred reference frame” of SR is replaced by “there is a preferred reference frame.” And the preferred frame is the nearby Earth gravity field.

We investigate decoherence of quantum superpositions induced by gravitational time dilation and spontaneous emission between two atomic levels. It has been shown that gravitational time dilation can be a universal decoherence source by Pikovski et al. Here, we consider the decoherence induced by the gravitational time dilation only in the situation of spontaneous emission. We obtain the analytical results of the coherence of particle's position state. Then, we obtain that the coherence of particle's position state depends on reference frame because the time dilation changes the distinguishability of emitted photons from two positions of particle in different reference frames. For observing the decoherence effect induced by the gravitational time dilation, time-delayed feedback can be utilized to increase the decoherence of particle's superposition state. [ABSTRACT FROM AUTHOR]

Paper 1 suggests intuitively that as humans, we must continue to investigate physical Objects by our natural Geometry. At the same time, we may want to explore a Nongeometric tool to check some other aspects. The two positions presume two distinct scopes and two independent Logics, so they are not conflictual, and we should be able to form a single consistent picture (no-strange-things criterion). In Paper 2, we enter the technique of NBM more systematically. The text below comes from a compromise, as we want to make as clear as possible any assumption which hides into the Model. At the same time, we want it to remain a very straight and practical tool, so we formulate it in term of Rules, Procedures, and lists of instructions. [ABSTRACT FROM AUTHOR]

Inspired by the recent literature, we study the Einstein–de Sitter cosmological model coupled with a generalization of the relation between the redshift and time dilation of the kind δ t 0 = δ t e (1 + z) n . We find that this model fits the experimental data regarding 1048 supernovae, in a way which is competitive with the standard Λ CDM model and without the need of introducing a non-zero cosmological constant. Since the existence of dark energy, as a main ingredient of the composition of the cosmos, is still under debate, we propose our formalism as an example of an alternative description of the cosmological scenario. [ABSTRACT FROM AUTHOR]

Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. The lifetime of an excited hydrogenlike atom can be used as a clock, which we use to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared with the emission rate of an atom prepared in a mixture of momentum wave packets at order v^{2}/c^{2}. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order v/c. However, its effect on the decay rate is suppressed when compared with the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation.

Introduction. In studies concerning the problems of approaching moving objects, the authors, as a rule, use continuous dynamic models under integral constrains on controls. However, only discrete models under quadratic or resource constraints are suitable for practical applications. The purpose of the paper is to develop a discrete analog of the method of time dilation for solving the problem of guaranteed approaching a terminal set by a discrete conflict-controlled system trajectory. Results. We introduce the concept of integer function of time dilation. Its using, in the frames of the discrete analog of the Pontryagin First Direct method, makes it possible to deduce sufficient conditions for bringing the trajectory of the discrete conflict-controlled process to the terminal set. We outline the way of constructing current pursuer’s control, which brings the object trajectory to the terminal set under arbitrary admissible counteraction of the evader. It differs from the pursuer control choice in the continuous case, when the pursuer chooses his current control in view of the evader’s control at a certain moment of time in the past. In the discrete case, the pursuer constructs his control on the basis of information about the evader’s controls on a whole discrete interval of time in the past. We prove that such control satisfies original quadratic constraints. Conclusions. We derive conditions for approaching the trajectory of conflict-controlled discrete process a terminal set. In so doing, quadratic constraints on controls are fulfilled. The terminal set is supposed to be a subset that corresponds to the catching the evader by the pursuer.

The Friedmann–Lemaître–Robertson–Walker model establishes the correlation between redshifts and distances. It has a metric expansion of space. As a result, the wavelength of photons propagating through the expanding space is stretched, creating the cosmological redshift, z. It also relates the frequency of light detected by a local observer to that emitted from a distant source. In standard cosmology (i.e. a constant speed light model), this relation is given by a factor 1/(1 + z). However, this ratio is modified in the minimally extended varying speed of light model (meVSL, c  = c 0 a b /4) as 1/(1 + z)1 − b /4. This time dilation effect is detected as the observed rate of the time variation in the intensity of emitted radiation. The spectra of Type Ia supernovae (SNe Ia) provide a reliable way to measure the apparent aging rate of distant objects. We use data on 13 high-redshift (0.28 ≤ z ≤ 0.62) SNe Ia to obtain b  = 0.198 ± 0.415 at the 1-σ confidence interval. The current data is too sparse to give meaningful constrain on the meVSL and cannot distinguish the meVSL model from the standard model. [ABSTRACT FROM AUTHOR]

Both quantum mechanics and general relativity are based on principles that defy our daily intuitions, such as time dilation, quantum interference and entanglement. Because the regimes where the two theories are typically tested are widely separated, their foundational principles are rarely jointly studied. Recent works have found that novel phenomena appear for quantum particles with an internal structure in the presence of time dilation, which can take place at low energies and in weak gravitational fields. Here we briefly review the effects of time dilation on quantum interference and generalize the results to a variety of systems. In addition, we provide an extended study of the basic principles of quantum theory and relativity that are of relevance for the effects and also address several questions that have been raised, such as the description in different reference frames, the role of the equivalence principle and the effective irreversibility of the decoherence. The manuscript clarifies some of the counterintuitive aspects arising when quantum phenomena and general relativistic effects are jointly considered.

The common opinion that the Lorentz transformation distorts the Minkowski spacetime arises from a mathematically incorrect neglect of its non-diagonal terms. When the non-diagonal Lorentz transformation is properly treated, the time dilation and the space distortion disappear. Consequently, the Lorentz metric produced by the Lorentz transformation is identical to the Minkowski metric. The spacetime distortion in moving inertial frames is properly described by the so-called Doppler metric produced by the Doppler transformation. This transformation assumes the existence of a preferred frame and depicts the Doppler shift of light for a moving light source and/or observer. The Doppler metric is Lorentz invariant and leaves the Maxwell's equations unchanged from their form in the Minkowski spacetime. Moreover, the Doppler metric is experimentally confirmed because it yields the null result in the Michelson–Morley experiment and other interferometric experiments. The suitability of the Doppler metric for describing light properties in Special and General Relativity is supported by recent cosmological observations of the cosmic microwave background. [ABSTRACT FROM AUTHOR]