In this paper we discuss to what extent one can infer details of the interior structure of a black hole based on its horizon. Recalling that black hole thermal properties are connected to the non-classical nature of gravity, we circumvent the restrictions of the no-hair theorem by postulating that the black hole interior is singularity free due to violations of the usual energy conditions. Further these conditions allow one to establish a one-to-one, holographic projection between Planckian areal “bits” on the horizon and “voxels”, representing the gravitational degrees of freedom in the black hole interior. We illustrate the repercussions of this idea by discussing an example of the black hole interior consisting of a de Sitter core postulated to arise from the local graviton quantum vacuum energy. It is shown that the black hole entropy can emerge as the statistical entropy of a gas of voxels.
Physics at its core is an experimental pursuit. If one theory does not agree with experimental results, then the theory is wrong. However, it is becoming harder and harder to directly test some theories of fundamental physics at the high energy/small distance frontier exactly because this frontier is becoming technologically harder to reach. The Large Hadron Collider is getting near the limit of what we can do with present accelerator technology in terms of directly reaching the energy frontier. The motivation for this special issue was to try and collect together ideas and potential approaches to experimentally probe some of our ideas about physics at the high energy/small distance frontier. Some of the papers in this special issue directly deal with the issue of what happens to spacetime at small distance scales. In the paper by A. Aurilia and E. Spallucci a picture of quantum spacetime is given based on the effects of ultrahigh velocity length contractions on the structure of the spacetime. The work of P. Nicolini et al. further pursues the idea that spacetime has a minimal length. The consequences of this minimal length are investigated in terms of the effects it would have on the gravitational collapse of a star to form a black hole. In the article by G. Amelino-Camelia et al. the quantum structure of spacetime is studied through the Fermi LAT data on the Gamma Ray Burst GRB130427A. The article by S. Hossenfelder addressed the question of whether spacetime is fundamentally continuous or discrete and postulates that in the case when spacetime is discrete it might have defects which would have important observational consequences. ...
We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is `compressed' into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.
We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is ‘compressed’ into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.
We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is ‘compressed’ into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.
