Entanglement between two gravitating universes

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard “island formula” for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Ζ n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a “swap wormhole”, a geometry in which the boundaries of the two universes are glued together by a “swaperator”. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes – a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

Fuzzy covering-based rough set on two different universes and its application

In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of thefuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not onlyenrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.

Rough approximations of bipolar soft sets by soft relations and their application in decision making

The rough set theory is an effective method for analyzing data vagueness, while bipolar soft sets can handle data ambiguity and bipolarity in many cases. In this article, we apply Pawlak’s concept of rough sets to the bipolar soft sets and introduce the rough bipolar soft sets by defining a rough approximation of a bipolar soft set in a generalized soft approximation space. We study their structural properties and discuss how the soft binary relation affects the rough approximations of a bipolar soft set. Two sorts of bipolar soft topologies induced by soft binary relation are examined. We additionally discuss some similarity relations between the bipolar soft sets, depending on their roughness. Such bipolar soft sets are very useful in the problems related to decision-making such as supplier selection problem, purchase problem, portfolio selection, site selection problem etc. A methodology has been introduced for this purpose and two algorithms are presented based upon the ongoing notions of foresets and aftersets respectively. These algorithms determine the best/worst choices by considering rough approximations over two universes i.e. the universe of objects and universe of parameters under a single framework of rough bipolar soft sets.

Reformulating Special Relativity on a Two-World Background II

The exposition of the two-world background of the special theory of relativity started in the first part of this paper is continued in this second part. The negative sign of mass in the negative universe is derived from the generalized mass expression in special relativity (SR) in the two-world picture. Four-dimensional inversion is shown to be a special Lorentz transformation in the two-world picture. Also by starting with the negativity of spacetime dimensions (that is, negativity of distances in space and of intervals of time) in the negative universe, derived in part one of this paper, and requiring the symmetry of natural laws between the positive and negative universes, the signs of mass and other physical parameters and physical constants in the negative universe are derived and tabulated. The invariance of natural laws, including the fundamental interactions, in the negative universe is demonstrated. The derived negative sign of mass in the negative universe is a conclusion of a century and a score years of efforts toward the incorporation of the concept of negative mass into physics. It is shown that the anti-particles observed in our universe originate from the negative universe, and conversely, but how a particle can make transition across the event horizon separating the universes without hitting singularity in the Lorentz transformation is as yet unexplained. Experimental test of the two-world picture depends on the possibility of exchange of particles between the two universes without hitting the singularity in LT at the point of making transition across the universes.

Knitting wormholes by entanglement in supergravity

We construct a single-boundary wormhole geometry in type IIB supergravity by perturbing two stacks of N extremal D3-branes in the decoupling limit. The solution interpolates from a two-sided planar AdS-Schwarzschild geometry in the interior, through a harmonic two-center solution in the intermediate region, to an asymptotic AdS space. The construction involves a CPT twist in the gluing of the wormhole to the exterior throats that gives a global monodromy to some coordinates, while preserving orientability. The geometry has a dual interpretation in $$ \mathcal{N} $$ N = 4 SU(2N) Super Yang-Mills theory in terms of a Higgsed SU(2N) → S(U(N) × U(N)) theory in which $$ \mathcal{O} $$ O (N2) degrees of freedom in each SU(N) sector are entangled in an approximate thermofield double state at a temperature much colder than the Higgs scale. We argue that the solution can be made long-lived by appropriate choice of parameters, and comment on mechanisms for generating traversability. We also describe a construction of a double wormhole between two universes.

Multiset concepts in two-universe approximation spaces

Rough set theory over two universes is a generalization of rough set model to find accurate approximations for uncertain concepts in information systems in which uncertainty arises from existence of interrelations between the three basic sets: objects, attributes, and decisions. In this work, multisets are approximated in a crisp two-universe approximation space using binary ordinary relation and multi relation. The concept of two universe approximation is applied for defining lower and upper approximations of multisets. Properties of these approximations are investigated, and the deviations between them and corresponding notions are obtained; some counter examples are given. The suggested notions can help in the modification of the decision-making for events in which objects have repetitions such as patients visiting a doctor more than one time; an example for this case is given.