We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime. The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity. The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechanics in the flat spacetime.

The conflict between the Newtonian and the Leibnizian picture of spacetime is well-known and widely discussed in the literature. However, two competing metaphysical pictures of spacetime have not been addressed so far: The Newtonian and the Lagrangian pictures. According to the Newtonian picture, spacetime can be considered as the time evolution of a spatial hypersurface. According to the Lagrangian picture, spacetime is a unified whole that can be examined in an all-at-once manner, and its (temporal) evolution is not meaningful, except locally or quasi-locally. Although the Newtonian picture has been the dominant metaphysical picture since Newton's time, our explicit familiarity with these two competing pictures is recent. It is rooted in Smolin's criticism of modern cosmology and Wharton's research on the foundations of quantum mechanics. Here, we describe the views of Smolin and Wharton, then we will argue that two famous formulations of general relativity, namely the Hamiltonian formulation and the Lagrangian formulation, require the Newtonian and the Lagrangian picture, respectively. Also, we will argue that: (1) the Lagrangian picture is more compatible with the philosophy of relativity theory than the Newtonian picture, while the Newtonian picture is only acceptable for practical and computational purposes. And, (2) the Lagrangian picture is universal and applicable to any spacetime, while the Newtonian picture can only be used for certain spacetimes. Therefore, the Lagrangian picture is a more plausible metaphysical picture than the Newtonian.

Topological order is a new type order that beyond Landau's symmetry breaking theory. It has some interesting properties, such as producing quasi-particles with fractional quantum numbers and fractional/Fermi statistics, robust gapless boundary modes and emergent gauge excitations. In this essay, we will show that the quantum gravity in AdS3 spacetime can also have topological orders. Actually the theory has all the three features that define the topological order. We conjecture that quantum gravity in four dimension can also have topological orders.

The g-factor of the charged leptons has always been considered by many physicists, both experimentaly as well as theoretically. In fact the electron and muon g-factor play the main role in testing the QED as well as the standard model. Meanwhile, there is a discrepancy between the standard model prediction of the muon anomalies magnetic moment and its experimental determination as large as (25.5±8.0) ×10-10.Therefore the g-factor can be used as the best place to study the new physics beyond the standard model. In this article, we consider the g-factor of the lepton in the noncommutative space time as a new physics model. In the ordinary theory, Schwinger evaluated the first correction to the g-factor of free electron, which arises from the electron interaction with photon at one loop level in the QED. In noncommutative space time, we show that at one loop, there is an NC-contribution to the g-factor of leptons which leads to a new bound on the noncommutative parameter (NC parameter). The obtained bounds are comparable with the current bounds on the NC-parameters of the order TeV.

Isoparametric hypersurfaces of Lorentz-Minkowski spaces, which has been classi, ed by M. A. Magid in 1985, have motivated some researchers to study biconservative hypersurfaces. A biconservative hy-persurface has conservative stress-energy with respect to the bienergy functional...

A compatible theory of relativistic geodesy is quite necessary for future development of any formulation of the subject. In this paper, following recent studies which invoke an idea of relativistic geoid, i. e. the chronometric definition implied by the gravitational redshift, we revisit known calculations on some standard spacetimes. Among all, the notion of frame dragging in the Kerr spacetime and its relationship to the rotative observers needed for the consistent definition of the geoid is analyzed.

The entanglement entropy approach to study the dependence of entropy upon the location of degrees of freedom (dof ) (near/far) from the horizon is discussed in this article. We try to understand the physical deviation of the area law for the excited states by incorporating the logarithmic and power law corrections. We show that the dof near the horizon gives contribution to the total entropy of the system in the ground state and away from the event horizon gives contribution to the excited state.