Related papers: The clock ambiguity: Implications and new developm…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
We study some limit theorems for the law of a generalized one-dimensional diffusion weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the…
The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative…
Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption…
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…
We continue our analysis of a quantum cosmology model describing a flat Friedmann--Lema\^itre--Robertson--Walker universe filled with a (free) massless scalar field and an arbitrary perfect fluid. For positive energy density in the scalar…
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…
Time's apparent passage has long been debated by philosophers, with no decisive argument for or against its objective existence. In this paper we show that introducing the issue of determinism gives the debate a new, empirical twist. We…
We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The…
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…
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…
We examine in greater detail the proposal that time is the conjugate of the constants of nature. Fundamentally distinct times are associated with different constants, a situation often found in "relational time" settings. We show in detail…
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in…
From a thermodynamic point of view, all clocks are driven by irreversible processes. Additionally, one can use oscillatory systems to temporally modulate the thermodynamic flux towards equilibrium. Focusing on the most elementary…
We investigate how the quantum dynamics of gravitational models depends on the internal clock employed in quantisation. Our previous result on the quantum Friedmann-Lemaitre model demonstrates that almost all physical predictions from the…
The cosmological applications of atomic clocks so far have been limited to searches of the uniform-in-time drift of fundamental constants. In this paper, we point out that a transient in time change of fundamental constants can be induced…
We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on $^{87}$Sr,…