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Register a new userGravity of Accelerations on Quantum Scales and its Consequences
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C Sivaram
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Gravity stands apart from other fundamental interactions in that it is locally equivalent to an accelerated frame and can be transformed away. Again it is indistinguishable from the geometry of space-time (which is an arena for all other basic interactions), its strength being linked with the curvature. This is a major reason why it has so far not been amenable to quantisation like other interactions. It is also evident that new ideas are required to resolve several conundrums in areas like cosmology, black hole physics, and particles at high energies. That gravity can have strong coupling at microscales has also been suggested in several contexts earlier. Here we develop some of these ideas, especially in connection with the high accelerations experienced by particles at microscales, which would be interpreted as strong local gravitational fields. The consequences are developed for various situations and possible experimental manifestations are discussed.
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We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified model for electrodynamics and gravitation, so that the influence of the gravitational field on the electrodynamics at very large distances leads to a reformulation of our understanding about space-time through the elimination of the classical idea of rest at quantum level. This leads us to a modification of the relativistic theory by introducing the idea of a universal minimum speed related to Planck minimum length. Such a speed, unattainable by the particles, represents a privileged inertial reference frame associated with a universal background field. The structure of space-time becomes extended due to such a vacuum energy density, which leads to a cosmological anti-gravity, playing the role of the cosmological constant. The tiny values of the vacuum energy density and the cosmological constant are successfully obtained, being in agreement with current observational results. We estimate the very high value of vacuum energy density at Planck length scale. After we find the critical radius of the universe, beyond which the accelerated expansion takes place. We show that such a critical radius is $R_{uc}=r_g/2$, where $r_g=2GM/c^2$, being $r_g$ the Shwarzschild radius of a sphere with a mass $M$ representing the total attractive mass contained in our universe. And finally we obtain the radius $R_{u0}=3r_g/4(>R_{uc})$ where we find the maximum rate of accelerated expansion. For $R_u>R_{u0}$, the rate of acceleration decreases to zero at the infinite, avoiding Big Rip.
It was recently advanced the argument that Unruh effect emerges from the study of quantum field theory in quantum space-time. Quantum space-time is identified with the Hilbert space of a new kind of quantum fields, the accelerated fields, which are defined in momentum space. In this work, we argue that the interactions between such fields offer a clear distinction between flat and curved space-times. Free accelerated fields are associated with flat spacetime, while interacting accelerated fields with curved spacetimes. Our intuition that quantum gravity arises via field interactions is verified by invoking quantum statistics. Studying the Unruh-like effect of accelerated fields, we show that any massive object behaves as a black body at temperature which is inversely proportional to its mass, radiating space-time quanta. With a heuristic argument, it is shown that Hawking radiation naturally arises in a theory in which space-time is quantized. Finally, in terms of thermodynamics, gravity can be identified with an entropic force guaranteed by the second law of thermodynamics.
The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in isolated quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study some equilibrium properties of many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Second, I exploited the Concentration of Measure phenomenon to study the macroscopic properties of the basis states of Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon, at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why a classical horizon exhibits thermal properties.
The metric of a homogenously accelerated system found by Harry Lass is a solution of the Einstein s equation. The metric of an isotropic homogenous field must satisfy the new gravitational equation.
The eigenstates and eigenenergies of a toy model, which arose in idealizing a local quenched tight-binding model in a previous publication [Zhang and Yang, EPL 114, 60001 (2016)], are solved analytically. This enables us to study its dynamics in a different way. This model can serve as a good exercise in quantum mechanics at the undergraduate level.
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