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By collecting both quantum and gravitational principles, a space-time uncertainty relation $(delta t)(delta r)^{3}geqslantpi r^{2}l_{p}^{2}$ is derived. It can be used to facilitate the discussion of several profound questions, such as computational capacity and thermodynamic properties of the universe and the origin of holographic dark energy. The universality and validity of the proposed relation are illustrated via these examples.
Discussion of physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.
Uncertainty relations between two general non-commuting self-adjoint operators are derived in a Krein space. All of these relations involve a Krein space induced fundamental symmetry operator, $J$, while some of these generalized relations involve an
The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a
Studies in string theory and quantum gravity suggest the existence of a finite lower limit $Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path
We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a mathematical