Quantization of the universe as a black hole

It has been shown that black holes can be quantized by using Bohr's idea of quantizing the motion of an electron inside the atom. We apply these ideas to the universe as a whole. This approach reinforces the suggestion that it may be a way to unify gravity with quantum theory.Comment: 7 pages. Accepted for publication in Astrophysics & Space Science in 25th Octuber 201

Seeable universe and its accelerated expansion: an observational test

From the equivalence principle, one gets the strength of the gravitational effect of a mass $M$ on the metric at position r from it. It is proportional to the dimensionless parameter $\beta^2 = 2GM/rc^2$, which normally is $<< 1$. Here $G$ is the gravitational constant, $M$ the mass of the gravitating body, $r$ the position of the metric from the gravitating body and $c$ the speed of light. The seeable universe is the sphere, with center at the observer, having a size such that it shall contain all light emitted within it. For this to occur one can impose that the gravitational effect on the velocity of light at $r$ is zero for the radial component, and non zero for the tangential one. Light is then trapped. The condition is given by the equality $R_g = 2GM/c^2$, where $R_g$ represents the radius of the {\it seeable} universe. It is the gravitational radius of the mass $M$. The result has been presented elsewhere as the condition for the universe to be treated as a black hole. According to present observations, for the case of our universe taken as flat ($k = 0$), and the equation of state as $p = - \rho c^2$, we prove here from the Einstein's cosmological equations that the universe is expanding in an accelerated way as $t^2$, a constant acceleration as has been observed. This implies that the gravitational radius of the universe (at the event horizon) expands as $t^2$. Taking $c$ as constant, observing the galaxies deep in space this means deep in time as $ct$, linear. Then, far away galaxies from the observer that we see today will disappear in time as they get out of the distance ct that is $< R_g$. The accelerated expanding vacuum will drag them out of sight. This may be a valid test for the present ideas in cosmology. Previous calculations are here halved by our results.Comment: 15 pages, 2 figure

Three-Dimensional Wave Packet Approach for the Quantum Transport of Atoms through Nanoporous Membranes

Quantum phenomena are relevant to the transport of light atoms and molecules through nanoporous two-dimensional (2D) membranes. Indeed, confinement provided by (sub-)nanometer pores enhances quantum effects such as tunneling and zero point energy (ZPE), even leading to quantum sieving of different isotopes of a given element. However, these features are not always taken into account in approaches where classical theories or approximate quantum models are preferred. In this work we present an exact three-dimensional wave packet propagation treatment for simulating the passage of atoms through periodic 2D membranes. Calculations are reported for the transmission of $^3$He and $^4$He through graphdiyne as well as through a holey graphene model. For He-graphdiyne, estimations based on tunneling-corrected transition state theory are correct: both tunneling and ZPE effects are very important but competition between each other leads to a moderately small $^4$He/$^3$He selectivity. Thus, formulations that neglect one or another quantum effect are inappropriate. For the transport of He isotopes through leaky graphene, the computed transmission probabilities are highly structured suggesting widespread selective adsorption resonances and the resulting rate coefficients and selectivity ratios are not in agreement with predictions from transition state theory. Present approach serves as a benchmark for studies of the range of validity of more approximate methods.Comment: 4 figure