Related papers: Time evolution in quantum cosmology
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
Physical systems are usually assumed to evolve relative to an external time parameter, which is problematic because in quantum theory that parameter is not a physical observable. Page & Wootters (1984) solved this by proposing that the…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
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…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of…
We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special…
The nature of time vis-a-vis relativity is critically examined. Based on the author's space-time interaction hypothesis of late 1970's, cosmological model with time-varying velocity of light is discussed.
A class of diffeomorphism invariant, physical observables, so-called astrometric observables, is introduced. A particularly simple example, the time delay, which expresses the difference between two initially synchronized proper time clocks…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
In the canonical approach to quantization of gravity, one often uses relational clock variables and an interpretation in terms of conditional probabilities to overcome the problem of time. In this essay we show that these suffer from…
The cosmological implications of an evolutionary quantum gravity are analyzed in the context of a generic inhomogeneous model. The Schr\"{o}dinger problem is formulated and solved in the presence of a scalar field, an ultrarelativistic…
An extrinsic time is identified in most isotropic and homogeneous cosmological models by matching them with the ideal clock - a parametrized system whose only "degree of freedom" is time -. Once this matching is established, the…
In this paper we propose that cosmological time is a quantum observable that does not commute with other quantum operators essential for the definition of cosmological states, notably the cosmological constant. This is inspired by…
The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of "observer" or the absence of a time variable in the Wheeler-DeWitt equation. I point out that a…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
The idea that the cosmological term, Lambda, should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, namely one that has…