Related papers: The dynamical nature of time
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…
The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational…
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct…
A human is a thing that moves in space. Like all things that move in space, we can in principle use differential equations to describe their motion as a set of functions that maps time to position (and velocity, acceleration, and so on).…
The process of identifying a time variable in time reparameterization invariant theories results in great ambiguities about the actual laws of physics described by a given theory. A theory set up to describe one set of physical laws can…
The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine…
We consider the equation $$ \dot x(t)=f(t,x(t),x(\eta(t))) $$ with a variable time-shift $\eta(t)$. Both the nonlinearity $f$ and the shift function $\eta$ are given, and are assumed to be analytic (that is, holomorphic) functions of their…
A clock is, from an information-theoretic perspective, a system that emits information about time. One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks. Here we show a…
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through…
This paper considers a new and deeply challenging face of the problem of time in the context of cosmology drawing on the work of Thiemann (2006, 2007). Thiemann argues for a radical response to the cosmic problem of time that requires us to…
The nature of time vis-a-vis relativity is critically examined. Based on the author's space-time interaction hypothesis of late 1970's, cosmological model with time-varying velocity of light is discussed.
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
Several physical concepts, including the concept of time, are clarified herein by taking into account existing experimental data. In addition, the missing links among these physical concepts are established. This allows us to take another…
In standard quantum theory, time is not an observable. It enters as a parameter in the Schr\"odinger equation, but there is no measurement operator associated to it. Nevertheless, one may take an operational viewpoint and regard time as the…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
In this paper a viewpoint that time is an informational and thermal entity is shown. We consider a model for a simple relaxation process for which a relationship among event, time and temperature is mathematically formulated. It is then…