Discreteness of time in the evolution of the universe

Abstract

In this paper, we will first derive the Wheeler-DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler-DeWitt equation for the generalized geometry. We analyse such a deformed Wheeler-DeWitt equation in the minisuperspace approximation, and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time re-parametrization invariance.

Black Remnants from T-Duality

“…This is the main reason for the description of string theory below the length l s = α ′ being equivalent to its description above l s = α ′ . As the double field theory is constructed using T-duality [29,30], such a short distance behavior for double field theory has also been studied [36].…”

Quantum gravity corrections to the mean field theory of nucleons

“…It may be noted as the double field theory is constructed using the T-duality [11,12], it is expected that a such zero point length can also occur in the double field theory. It has been demonstrated that such a zero point length in double field theory can have important consequences for the generalized geometries used in string theory [13]. It may be noted that such a minimal length larger than the Planck length can make it possible for the mini black holes to form in particle physics colliders (due to the lowering of Planck scale) [14,15].…”

Corrections to scattering processes due to minimal measurable length

“…Then all other cuts with s 2 are on the next sheets. For the above case (11), (12), with N = 2, ǫ = 1/2, the next "kinematical" cut from the point E = −(8β) −1 (for small β) lies far away from the origin on the first sheet (for β > 0). Besides, it is screened by physical cut for β < 0.…”

“…It should be noted that an effective path integral of the center of mass of the string (for strings propagating in compactified extra dimensions) has been constructed, and T-duality has been used to demonstrate that such a system has a minimal length associated with it [7,8]. As the construction of double field theory has been motivated from T-duality [9, 10], it is expected that such a minimal length will also exist in the double field theory [11].It may be noted that even if the string theory does not turn to be the true theory of quantum gravity, the argument for the existence of a minimal measurable length in spacetime could still hold. As it can be argued, a minimal measurable length scale, at least of the order of Planck length, would exist in all approaches to quantum gravity.…”

“…It should be noted that an effective path integral of the center of mass of the string (for strings propagating in compactified extra dimensions) has been constructed, and T-duality has been used to demonstrate that such a system has a minimal length associated with it [7,8]. As the construction of double field theory has been motivated from T-duality [9,10], it is expected that such a minimal length will also exist in the double field theory [11].…”