Related papers: Space and time transformations with a minimal leng…

Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in…

The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…

We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically…

The combined action of gravity and quantum mechanics gives rise to a minimum time uncertainty in the lowest order approximation of a perturbative scheme, in which quantum effects are regarded as corrections to the classical spacetime…

During the last two decades or so much effort has been devoted to the discussion of quantum mechanics (QM) that in some way incorporates the notion of a minimum length. This upsurge of research has been prompted by the modified uncertainty…

For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and…

Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to…

We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…

Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the…

The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity…

We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first order, the algebra we use…

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…

We proved that under quantum mechanics a momentum-energy and a space-time are dual vector spaces on an almost complex manifold in position representation, and the minimal uncertainty relations are equivalent to the inner-product relations…

I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…

We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…

In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…

The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…

Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an…