We challenge the common belief that if there is no absolute time parameter in physics, a quantum system described without reference to an external clock can be assumed to be in a stationary state of its Hamiltonian. We present a time-reparameterisation invariant quantum evolution law, which for a given initial condition predicts the same trajectory in state space as the Schr\"odinger equation, except that for nontrivial trajectories it does not predict the speed at which the trajectory is traversed. The solutions of this evolution law are all time-reparameterised solutions of the Schr\"odinger equation. We show how the predictions of the Schr\"odinger equation are recovered relative to an internal clock in this framework. In contrast to the Page-Wootters formalism or Dirac's quantisation of the Hamiltonian constraint, here the global sate is not stationary. We discuss the assumptions leading to the common conclusion that the state can be taken stationary and suggest that they need to be revisited.
Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many a...
We investigate the unitarity of quantum evolution relative to an internal time defined by a local observer's clock. The observer is modeled as a relativistic particle carrying both a clock and a matter-field detector, analyzed first on a fixed curved background and subsequently within a fully diffeomorphism-invariant t...
We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocati...
Gabriele de Mauro, Manas Kulkarni, S. Majumdar· 0 citations
Reverse Physics is a methodology that breaks physical theories into separate mathematical and physical conditions to establish their logical relationships. To showcase the power of the methodology, we present several results for quantum mechanics and their related insights. The standard Hilbert-space formulation confli...
G. Carcassi, Tobias Thrien, C. Aidala· 0 citations
We present an improved autonomization method for quantum simulation of time-dependent homogeneous dissipative linear systems, combining a clock-variable reformulation with Schr\"odingerization to obtain a time-independent Hamiltonian system. To control both discretization error and recovery probability, we construct th...
Xiao-Jing Dong, Chu-Wen Ma, Yi-Zhen Peng et al.· 1 citation
In timeless formulations of quantum theory, the Page-Wootters proposal (PW) recovers time and dynamics as relative clock-and-world states. By interpreting the total timeless system as a clock entangled with the world, the states having a definite clock reading appear to recover the temporal states of the world as relat...
O. C. Stoica· 0 citations
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