Related papers: Conditions for Unitarity in Timeless Quantum Theor…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
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.…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Given the lack of an absolute time parameter in general relativistic systems, quantum cosmology often describes the expansion of the universe in terms of relational changes between two degrees of freedom, such as matter and geometry.…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
We consider a global quantum system (the "Universe") satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3+1 dimensional,…
In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental time-evolution parameter) and the…
Time reversal symmetry occupies a distinctive role in quantum mechanics, fundamentally requiring an anti-unitary operator to ensure a physically consistent representation. As such, the time reversal operator combines a unitary…
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…
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…
For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq…
Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
We discuss a systematic way in which a relational dynamics can be established relative to periodic clocks both in the classical and quantum theories, emphasising the parallels between them. We show that: (1) classical and quantum relational…
The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the…