Related papers: Time Observables in a Timeless Universe
We propose a natural strategy to deal with compatible and incompatible binary questions, and with their time evolution. The strategy is based on the simplest, non-commutative, Hilbert space $\mathcal{H}=\mathbb{C}^2$, and on the (commuting…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
The Page-Wootters formalism is a proposal for reconciling the background-dependent, quantum-mechanical notion of time with the background independence of general relativity. However, the physical meaning of this framework remains debated.…
Quantum chaos in hermitian systems concerns the sensitivity of long-time dynamical evolution to initial conditions. The skin effect discovered recently in non-hermitian systems reveals the sensitivity to the spatial boundary condition even…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
Group field theory posits that spacetime is emergent and is hence defined without any background notion of space or time; dynamical questions are formulated in relational terms, in particular using (scalar) matter degrees of freedom as…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
We give a consistent quantum description of time, based on Page and Wootters' conditional probabilities mechanism, that overcomes the criticisms that were raised against similar previous proposals. In particular we show how the model allows…
Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to…
In the past decade, the concept of parity-time ($\mathcal{PT}$) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying,…
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…
Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics of quantum and classical systems coupled non-conservatively to an environment. Once primarily an interest of mathematical physicists, the theory of non-Hermitian…
In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schr\"odinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of…
We consider the classical concept of time of permanence and observe that its quantum equivalent is described by a bona fide self-adjoint operator. Its interpretation, by means of the spectral theorem, reveals that we have to abandon not…
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).…