相关论文: Time Machines and the Breakdown of Unitarity
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…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
Three postulates are discussed: first that well-defined properties cannot be assigned to an isolated system, secondly that quantum unitary evolution is atemporal, and thirdly that some physical processes are never reversed. It is argued…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
Some principles underpinning the running of the Universe are discussed. The most important, the machine principle, states that the Universe is a fully autonomous, self-organizing and self-testing quantum automaton. Continuous space and…
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…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
The purpose of this paper is to present a model of a quantum space-time in which the global symmetries of space-time are unified in a coherent manner with the internal symmetries associated with the state space of quantum-mechanics. If we…
The model of a stationary universe and the notion of local times presented in [10] are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves…
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,…
The ontology proposed in this paper is aimed at demonstrating that it is possible to understand the counter-intuitive predictions of quantum mechanics while still retaining much of the framework underlying classical physics, the implication…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
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…
From the Physics point of view, time is now best described through General Relativity, as part of space-time which is a dynamical object encoding gravity. Time possesses also some intrinsic irreversibility due to thermodynamics, quantum…
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…
The time reversal and irreversibility in conventional quantum mechanics are compared with those of the rigged Hilbert space quantum mechanics. We discuss the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged Hilbert…