Gravitational Time Dilation Research Articles

Gravitational time dilation in a high school lesson

Abstract In almost all countries, the Ministry of Public Education has introduced the topics of special and general relativity into the high school curriculum. For example, in Italy the teaching of so-called modern physics (quantum mechanics and relativity) was introduced in the last year of high school. The students are approximately 18 years old and, although the arguments are addressed in an introductory and qualitative way, they are also a topic for the final exam. Einstein’s theory fascinates young students, but it is not always easy to explain the revolutionary effects it predicts. For this reason, we have organized a series of in-depth lessons trying to derive the space-time distortions in a way suitable for the young age of the students. In this frontline we summarize a derivation, suitable for high school pupils, regarding gravitational time dilation.

Precession of planets' orbits between Newtonian gravity and Einstein's general relativity

The recent result that, contrary to a longstanding conviction older than 160 years, the precession of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury's mass is confirmed. Orbit's precession does not occur in an inertial (in Newtonian sense) frame of reference, but it occurs in the non-inertial frame of reference of the Sun because in Newtonian theory, the distance which is travelled by a body depends on the frame of reference in which the motion of the body is analyzed. After reviewing a previous solution, the precession is directly obtained from the orbit equation in the non-inertial frame of reference of the Sun. The Newtonian formula of the precession of planets' perihelion breaks down for the other planets because the predicted Newtonian result is indeed too large for Venus and Earth. In a previous paper, it was shown that corrections due to gravitational and rotational time dilation, in an intermediate framework (a particular post-Newtonian approximation of general relativity) which analyzes gravity between Newton and Einstein, solve the problem in accordance with some other results in the literature. By adding such corrections, a result consistent with the one of general relativity was indeed obtained. Those corrections also are re-analyzed in this paper by stressing the difference between general relativity and Newtonian physics by evoking the Einstein Equivalence Principle, and the third postulate of relativity. This framework of gravity between Newton and Einstein seems consistent with global covariance. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a better understanding of the famous Dark Matter and Dark Energy problems.

Universality of quantum time dilation

Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually associated with classically defined trajectories, characterized by position, momentum, and acceleration. However, when spatial degrees of freedom are treated in a quantum way and a clock is allowed to be in a coherent superposition of either two momenta or two heights, additional quantum corrections to classical time dilation appear, called kinematic and gravitational quantum time dilations, respectively. We show that similarly to its classical counterpart, kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system’s Hamiltonian.

Quantum time dilation in a gravitational field

According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.

A review of the explanations to the twin paradox

The Twin Paradox is a representative problem in special relativity. It proposed a problem that from a spacecraft that is moving at a speed close to light, the earths time will be slower; in contrast, the earth will also consider the time of the spacecraft slower. However, this paradoxs solution can expand beyond the special relativity and Lorentz transformation. Basically, the seeming paradox can be solved using the period when the spacecraft turns around. Therefore, it can be considered a good way to have a better understanding of relativity. In this paper, this paradox is explained in three ways: the Lorentz transformation, the Minkowski geometry, a special geometry including both space and time, which is proposed to have a better explanation of the special relativity and gravitational time dilation in general relativity, and will also expand to other effects in relativity, such as the gravitational redshift. This paper hopes to offer some references for a better understanding of the Twin Paradox.

Decoherence of a composite particle induced by a weak quantized gravitational field

Even though we have some proposals for the quantum theory of gravity like string theory or loop quantum gravity, we do not have any experimental evidence supporting any of these theories. Actually, we do not have empirical evidence pointing in the direction that we really need a quantum description of the gravitational field. In this scenario, several proposals for experimentally investigating quantum gravitational effects far from the Planck scale have recently appeared in literature, like gravitationally induced entanglement, for instance. An important issue of these approaches is the decoherence introduced by the quantum nature not only of the system under consideration but also from the gravitational field itself. Here, by means of the Feynman–Vernon influence functional, we study the decoherence of a quantum system induced by the quantized gravitational field—in the linearized gravity regime—and also by its own quantum nature. Our results may be significant in better understanding many phenomena like the decoherence induced by the gravitational time-dilation, the quantum reference frames, and the quantum equivalence principle.

The discussion about the influence of gravitational time dilation on gravity propagation speed and on light propagation speed

In this article, we will demonstrate, based upon strictly logical reasoning, thought experiment examination, and cosmic observations results, how gravitational time dilation exerts influences upon light propagation and upon gravity propagation. Neutron stars mergers have shown that the speed of gravity coincides with the speed of light (c). However, does gravitational time dilation has the same effect upon the propagation of gravity field as it has on light/electric field/magnetic field? The answer to this question can be concluded by examining such a thought experiment: according to E=mc2, it is theoretically possible to transfer an enormous amount of energy to a place near a black hole and create some matter. Once created, the matter will start to generate both gravity field and light and the gravity field and light will propagate in each direction. The light it generates will NEVER enter into the black hole so it will never interact with the black hole, according to observers on the earth. But, according to current cosmic observation results, the gravity field it generates will quickly enter into the black hole and interact with the black hole, according to observers on the earth. Thus, if gravitational time dilation theory is correct, near a black hole, gravity speed is faster than light speed.

Does gravitational time dilation influence the propagation of the change of gravitational field?

This article uses thought experiments and strict logical deductions to discuss the propagation the change of gravity field and find that all current gravity fields are generated some time before and they are not static but are constantly propagating. If there is a change of the gravity field of a celestial body, it takes time for this change to propagate before interacting with this another celestial body. However, for a binary black hole system, the positions of the two black holes constantly changes relative to each other, resulting in changes of the gravity fields of both black holes, and, it also takes time for the change of gravity field of one black hole to reach the other black hole. If gravitational time dilation governs, it takes forever for the change of the gravity field of one black hole to propagate across the event horizon of the other black hole and interact gravitationally with it. If so, one black hole will never be able to respond to the change of the location of the other black hole. This is impossible. Thus, gravitational time dilation should not have the same influence upon the propagation of the change of gravity field as it has on light.

Mental Gravity: Depression as Spacetime Curvature of the Self, Mind, and Brain.

The principle of mental gravity contends that the mind uses physical gravity as a mental model or simulacrum to express the relation between the inner self and the outer world in terms of "UP"-ness and "DOWN"-ness. The simulation of increased gravity characterises a continuum of mental gravity which states includes depression as the paradigmatic example of being down, low, heavy, and slow. The physics of gravity can also be used to model spacetime curvature in depression, particularly gravitational time dilation as a property of MG analogous to subjective time dilation (i.e., the slowing of temporal flow in conscious experience). The principle has profound implications for the Temporo-spatial Theory of Consciousness (TTC) with regard to temporo-spatial alignment that establishes a "world-brain relation" that is centred on embodiment and the socialisation of conscious states. The principle of mental gravity provides the TTC with a way to incorporate the structure of the world into the structure of the brain, conscious experience, and thought. In concert with other theories of cognitive and neurobiological spacetime, the TTC can also work towards the "common currency" approach that also potentially connects the TTC to predictive processing frameworks such as free energy, neuronal gauge theories, and active inference accounts of depression. It gives the up/down dimension of space, as defined by the gravitational field, a unique status that is connected to both our embodied interaction with the physical world, and also the inverse, reflective, emotional but still embodied experience of ourselves.

Review on non-relativistic gravity

This study reviews the history of Newton–Cartan (NC) gravity with an emphasis on recent developments, including the covariant, off-shell large speed of light expansion of general relativity. Depending on the matter content, this expansion leads to either NC geometry with absolute time or NC geometry with non-relativistic gravitational time dilation effects. The latter shows that non-relativistic gravity (NRG) includes a strong field regime and goes beyond Newtonian gravity. We start by reviewing early developments in NC geometry, including the covariant description of Newtonian gravity, mainly through the works of Trautman, Dautcourt, Künzle, and Ehlers. We then turn to more modern developments, such as the gauging of the Bargmann algebra and describe why the latter cannot be used to find an off-shell covariant description of Newtonian gravity. We review recent work on the 1/c expansion of general relativity and show that this leads to an alternative “type II” notion of NC geometry. Finally, we discuss matter couplings, solutions, and odd powers in 1/c and conclude with a brief summary of related topics.

Gravitational time dilation as a resource in quantum sensing

Atomic clock interferometers are a valuable tool to test the interface between quantum theory and gravity, in particular via the measurement of gravitational time dilation in the quantum regime. Here, we investigate whether gravitational time dilation may be also used as a resource in quantum information theory. In particular, we show that for a freely falling interferometer and for a Mach-Zehnder interferometer, the gravitational time dilation may enhance the precision in estimating the gravitational acceleration for long interferometric times. To this aim, the interferometric measurements should be performed on both the path and the clock degrees of freedom.

Topological quantum computation using analog gravitational holonomy and time dilation

Non-universal topological quantum computation models, such as the Majorana fermion-based Ising anyon model, have to be supplemented with an additional non-topological noisy gate in order to achieve universality. Here we endeavour to remedy this using an Einstein­—Cartan analog gravity picture of scalar fields. Specifically, we show that the analog gravity picture enables unitary transformations to be realized in two distinct ways: (i) via space-time holonomy and (ii) as gravitational time dilation. The non-abelian geometric phases are enabled by gravitational interactions, which are mediated by the spin-connection. We analytically compute its matrix elements as a function of the scalar field density distribution. This density can be regarded as the gravitating distribution of matter in an analog universe. We show via explicit calculations that there exists an infinite set of asymptotically flat analog gravitational fields, each of which implements a unique unitary transformation, that render the interactions topological. We emphasise the generality of this result by asserting that such gravitational gates could potentially be implemented in a broad range of real systems modeled by scalar field with an acoustic metric.

Gravitational time dilation in extended quantum systems: The case of light clocks in Schwarzschild spacetime

The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step toward a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius.

Quantum clocks, gravitational time dilation, and quantum interference

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.

Absurd: Einstein’s special relativity (SR) causes an inconstant speed of light, claiming to explain the consequences of a constant speed c

Einstein was led astray by a physically incorrect calculation by Michelson and Morley in the context of the Michelson‐Morley experiment. For the light beam in the horizontal light path, their calculation yields the claim that [(1 − v/c) × c] + [(1 + v/c) × c] = 2[(1 − v2/c2) × c]. This is incorrect and mathematically increases the horizontal light path 2d 0 by the factor [(1 + v2/c2)], which Einstein’s theory of special relativity corrects by introducing the time dilation factor γ and the length contraction factor 1/γ. When we calculate correctly, the mathematical increase in the length of horizontal light path no longer happens and Einstein’s mathematical corrections of the horizontal light path imply an inconstancy of the speed of light. This means that Einstein’s special relativity is just a mathematical correction of a physical calculation error, not a true physical theory, and it was thus pure chance that Einstein found the physically real kinematic time dilation factor γ. The null result of the Michelson‐Morley experiment, along with the kinematic and gravitational time dilation, must instead be explained by a constant value for the speed c of light with respect to the gravitational potentials of predominant gravitational fields, resulting from the principles of minimum energy and energy conservation. On this basis, it becomes possible to predict so-called general relativistic phenomena, e.g., the precession of Mercury’s perihelion or the phenomena observed in the binary pulsar PSR B1913 + 16, just by applying Kepler’s second law and simple quantum physical considerations. [R. G. Ziefle, Phys. Essays 33, 99 (2020)].

Do we need dense matter equation of state in curved spacetime for neutron stars?

Neutron stars are regarded as natural laboratories for the study of dense strong interaction matter. The equation of state (EoS) of dense matter computed in flat spacetime is used to predict the structure of neutron stars by solving the Tolman-Oppenheimer-Volkoff (TOV) equation. Recently, it has been reported that the curved spacetime effect or specifically gravitational time dilation effect on the EoS of dense matter leads to a significant increase of the maximum mass limit of neutron stars [Phys. Rev. D \textbf{104}, 123005 (2021) and J. Cosmol. Astropart. Phys. 02 (2021) 026]. However, in this work, we show that to study the hydrostatic equilibrium of dense matter within the framework of general relativity and relativistic fluid dynamics, the grand canonical EoS of dense matter, $p(T,\mu)$, should be the same as that computed in flat spacetime, otherwise it is not consistent with local thermodynamic relations and energy-momentum conservation of the fluid. The gravitation influences the pressure $p$ only through enhancing the temperature $T$ and the chemical potential $\mu$, known as Tolman's law and Klein's law. We rewrite the TOV equation as an alternative version so that the grand canonical EoS computed by using field theoretical methods can be used as a direct input. This may provide a tool to study the grand canonical EoS of dense matter via deep learning.

Equation of states in the curved spacetime of slowly rotating degenerate stars

We compute the equation of state for an ensemble of degenerate fermions by using the curved spacetime of a slowly rotating axially symmetric star. We show that the equation of state computed in such curved spacetime depends on the gravitational time dilation as well as on the dragging of inertial frames, unlike an equation of state computed in a globally flat spacetime. The effect of gravitational time dilation leads to a significant enhancement of the maximum mass limit of a degenerate neutron star. However, such an enhancement due to the frame-dragging effect is extremely small. Nevertheless, in general relativity the frame-dragging effect is crucial for computing angular momentum of the star which is also shown to be enhanced significantly due to the usage of curved spacetime in computing the equation of state.

Reframing the general theory of relativity

The general theory of relativity extends the special theory of relativity to account for gravity (acceleration) and results in the postulation that matter curves spacetime, where gravitation is the embodiment of the spacetime curvature. The curvature of spacetime is modeled using Riemannian geometry. In this paper, it is proposed that matter rotates spacetime hyperbolically, rather than curves spacetime. As a result, gravitation is the embodiment of the hyperbolic rotation of spacetime. Regions in spacetime that have a larger magnitude of rotation relative to other regions of spacetime, ceteris paribus, experience stronger gravity, gravitational time dilation, gravitational length contraction, and gravitational frequency shift toward the red (blue) in the electromagnetic waves moving away (toward).

Einstein’s photon box revisited

We present a reformulation of Bohr’s analysis of Einstein’s thought experiment with the photon box, which hopefully settles some unclear issues. The box is weighed by two position measurements, the first immediately before the emission of the photon and the second after a quarter period of oscillation of the box, or alternatively after a half period. These times are precisely defined with respect to the moving clock installed in the box, but vary statistically when measured with a stationary clock outside the box, due to gravitational time dilation in accordance with Bohr’s original idea. Moreover, we will discuss two other proposals to solve the apparent inconsistency without invoking the theory of general relativity.

Contradiction in Einstein’s subjective explanation of the gravitational and kinematic time dilation

Einstein’s special and general relativity are relics from before quantum physics. If forces are transmitted by quanta, this must also apply to gravity. As light consist of quanta, it is only logical that gravitational quanta interact with light. In my article “Cognitive bias in physics with respect to Einstein’s relativity, demonstrated by the famous experiment of Pound and Rebka (1960), which in reality refutes Einstein’s general relativity” [R. G. Ziefle, Phys. Essays 35, 91 (2022)], I could demonstrate that Einstein’s “proper time” t 0 does not refer to reference frames but to gravitational potentials. That is why “Newtonian quantum gravity” [R. G. Ziefle, Phys. Essays 33, 99 (2020)] can predict the correct curvature of a light beam at the surface of the Sun. Also, the phenomena observed at the binary pulsar PSR B1913 + 16 can precisely be predicted by merely applying Kepler’s second law. If gravitational quanta move away from masses with the constant speed c of light, this coincides with Einstein’s postulate of a constant speed c of light with respect to reference frames, as a mass, such as a star or a planet, can also be defined as a reference frame. Therefore, Einstein’s found by chance an artificial and complicated method to calculate changes in space-time caused by motion, which are in reality additional gravitational effects caused by the relative velocity between gravitational quanta emitted by masses and other masses or photons.