Related papers: On the Uncertainty Principle for Proper Time and M…
A generalized uncertainty principle is obtained from a conformally transformed action containing a scalar field and a unique constraint. The constraint's Lagrange multiplier is found to obey a relativistic diffusion equation transforming…
We work on the Lagrangian and the Hamiltonian formulations of the Palatini action. In the Lagrangian formulation, we find that we need to assume the metric compatibility and the torsion zero or to assume the tetrad compatibility to describe…
The time-energy uncertainty relation of Anandan-Aharonov is generalized to a relation involving a set of quantum state vectors. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the…
Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and solve the second class constraints,…
We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the…
We propose the relation $M_\Lambda \sim (M_{Pl} M_U)^{1/2}$ where $M_\Lambda$, $M_{Pl},$ and $M_U$ denote the mass scale associated with the cosmological constant, the gravitational interaction, and the size of the universe respectively.
Motivated by the parametrization invariance of cosmological Lagrangians and their equivalence to systems describing the motion of particles in curved backgrounds, we identify the phase space analogue of the notion of proper time. We define…
The mass contained in an arbitrary spacetime in general relativity is not well defined. However, for asymptotically flat spacetimes various definitions of mass have been proposed. In this paper I consider eight masses and show that some of…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
The microscopic structure of space and time is investigated. It is proposed that space and time of an inertial observer $\Sigma$ are most conveniently described as a crystal array $\Lambda$, with nodes representing measurement `tickmarks'…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…
The classical theory of strain in material continua is reviewed and generalized to space-time. Strain is attributed to "external" (matter/energy fields) and intrinsic sources fixing the global symmetry of the universe (defects in the…
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein's field equations. For static sources, the metric arises from a relativistic formulation of D'Alembert's principle, where the inertial…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
We develop a Lagrangian formulation for gravity with matter where the gravitational couplings are universally treated as being field-dependent. The solutions for FLRW geometries and the associated time evolution of the Newton and…
The problem studied is formulated in the title: proper mass variation under gravitational and Coulomb force action in Relativistic Mechanics of point particle. The novelty is that equations of motion are obtained in the relativistic…
The relativity of cosmic time is developed within the framework of Cosmological Relativity in five dimensions of space, time and velocity. A general linearized metric element is defined to have the form $ds^2 = (1+\phi) c^2 dt^2 - dr^2 +…
A new realization of the matter Lagrangian is introduced which models the dark energy component as a non-standard combination of thermodynamics quantities of the baryonic matter. We will prove that the present realization is independent of…
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-I) function of the 4-velocity $u^i$, plus a functional of $\eta_{ij}u^i u^j$. The second…