相关论文: On the Problem of Time(s) in Quantum Mechanics and…

We point out that for a large class of parametrized theories, there is a constant in the constrained Hamiltonian which drops out of the classical equations of motion in configuration space. Examples include the mass of a relativistic…

It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…

In the present work we consider a time-dependent Schr\"odinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not…

The problem of time in quantum gravity calls for a relational solution. Using quantum reduction maps, we establish a previously unknown equivalence between three approaches to relational quantum dynamics: 1) relational observables in the…

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays…

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…

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The…

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…

Starting from a re-analysis of previous work, we construct the proper low energy quantum field theory (QFT) limit of a full quantum gravity theory in the Born-Oppenheimer approach. We separate the gravitational sector into a classical…

Motivated by the parametrization invariance of cosmological Lagrangians and their equivalence to systems describing the motion of particles in curved backgrounds, we identify the phase space analogue of the notion of proper time. We define…

The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on…

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line…

It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic…

In this review, we analyse different aspects concerning the possibility to separate a gravity-matter system into a part which lives close to a quasi-classical state and a "small" quantum subset. The considered approaches are all relying on…

The problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to…

A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schr\"odinger equation and a discussion of semiclassical time as well…

Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…

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…

We formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (\partial_t^2+D)\psi(t)=0, where D is a positive-definite operator acting in a Hilbert space \tilde H. We determine all the positive-definite inner…