Related papers: Quantum Gravity and a Time Operator in Relativisti…
The problem of time in quantum mechanics concerns the fact that in the Schr\"odinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured…
The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The spacetime-position operator acts in the Hilbert space of functions of space…
Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schr\"odinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s).…
The problem of time in quantum gravity occurs because `time' is taken to have a different meaning in each of general relativity and ordinary quantum theory. This incompatibility creates serious problems with trying to replace these two…
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an…
Time plays different roles in quantum mechanics and gravity. These roles are examined and the problems that the conflict in the roles presents for quantum gravity are briefly summarised.
Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames (RF) quantum effects is considered in Relativistic Quantum Mechanics framework. For RF connected with some macroscopic object its free quantum motion - wave…
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…
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…
Time in quantum gravity is not a well-defined notion, despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we shortly review the problem and illustrate it with two proposed solutions.…
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…
We introduced with coauthors some years ago a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. It combines Page and Wootters' relational proposal with Rovelli's…
In this article I introduce a distinction between two types of reparametrization invariant models and I argue that while both suffer from a problem of time at the time of applying canonical quantization methods to quantize them, its…
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator…
The problem of time emerging in the canonical quantization procedure of gravity signals a necessity to properly define a relational time parameter. Previous approaches, which are here briefly discussed, make use of the dependence of the…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) has been shown to provide a unified origin for the existence of Dirac's Hamiltonian and a self adjoint time operator that…
The question about the appearance of time in the semiclassical limit of quantum gravity continues to be discussed in the literature. It is believed that a temporal Schrodinger equation for matter fields on the background of a classical…
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space…
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…