Related papers: Quantizing time: Interacting clocks and systems
In a seminal paper (Page and Wootters 1983) Page and Wootters suggest time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature…
We investigate three aspects of the supposed problem of time: The disagreement between the treatments of time in general relativity and quantum theory, the problem of recovering time from within an isolated Universe and the prevalence of a…
In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of…
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
I show that the clock ambiguity cannot be solved by a purely relational condition like the noninteraction condition, and it is even stronger, extending to evolution laws. The ambiguity is solved by specifying the physical meaning of…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
The time-of-arrival problem asks for the probability distribution for when a quantum particle reaches a specified location. It has been the subject of decades of debate, exemplifying the lack of a self-adjoint time observable in quantum…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
Schroedinger's equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same…
We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of…
A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time…
In the Schroedinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the Schroedinger equation give rise to…
Every clock is a physical system and thereby ultimately quantum. A naturally arising question is how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related.…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
We reexamine the relationship between the path integral and canonical formulation of quantum general relativity. In particular, we present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum general…
We compare two different approaches to the treatment of the Wheeler-DeWitt equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints, while the…