Related papers: Clocks' synchronization without round-trip conditi…
We show that the relativistic analogue of the two types of time translation in a non-relativistic history theory is the existence of two distinct Poincar\'{e} groups. The `internal' Poincar\'{e} group is analogous to the one that arises in…
Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of…
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…
Both the classical and the relativistic composition law for velocities are applied to re-calculate the Sagnac Effect. The ensuing formulae for the fringe shift are found to differ already in first order of v/c. Whilst the classical formula…
In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for…
Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time.…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential 10^{10} enhancement of the rotational phase shift in…
We present a higher-dimensional version of the Poincar\'e-Birkhoff theorem which applies to Poincar\'e time maps of Hamiltonian systems. The maps under consideration are neither required to be close to the identity nor to have a monotone…
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…
Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
In special and general relativity the synchronization convention of distant clocks may be simulated with a mathematical definition of global non-inertial frames (the only ones existing in general relativity due to the equivalence principle)…
Motivated by the recent interest in underground experiments phenomenology, we review the main aspects of one specific non-commutative space-time model, based on the Groenewold-Moyal plane algebra, the $\theta$-Poincar\'e space-time. In the…
We show here that Common View Synchronization is valid to synchronize distant clocks. We describe the relativistic physics, noting that a prerequisite for synchronization is the existence of a space-time with a stationary metric. The…
In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
The aim of this paper it to establish sufficient conditions for consistency of moving block bootstrap for non-stationary time series with periodic and almost periodic structure. The parameter of the study is the mean value of the…
Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…