相关论文: What properties of numbers are needed to model acc…
We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of…
Relying on the equivalence principle, a first approach of the general theory of relativity is presented using the spacetime metric of an observer with a constant proper acceleration. Within this non inertial frame, the equation of motion of…
Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and,…
The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The…
We begin with a scenario that involves point-like observers starting at t=0 from the origin O of an inertial reference frame. They move with all possible proper accelerations in the positive direction of the OX axis. Equipped with light…
The standard relativistic theory of accelerated reference frames in Minkowski spacetime is described. The measurements of accelerated observers are considered and the limitations of the standard theory, based on the hypothesis of locality,…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
There are three goals of this thesis. First: to present a concise yet accessible description of basic mathematical logic and model theory. Second: to develop an axiomatization of special relativity using only two undefined predicates.…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
The measurement of an electromagnetic radiation field by a linearly accelerated observer is discussed. The nonlocality of this process is emphasized. The nonlocal theory of accelerated observers is briefly described and the consequences of…
We introduce in the explicit form the tetrads of arbitrary observers in spacetimes with spherical and axial symmetries. The observers confined to the equatorial plane are parametrized by the pair of functions. We apply this description in…
Within an axiomatic framework, we investigate the possible structures of numbers (as physical quantities) in different theories of relativity.
We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an…
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and…
We present axioms for the real numbers by omitting the field axioms and then derive the field properties of the real numbers. We prove all our theorems constructively.
The acceleration transformations form a 4-parameter Abelian subgroup of the conformal group of Minkowski spacetime. The passive interpretation of acceleration transformations leads to a congruence of uniformly accelerated observers in…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
Physicists have been interested in accelerated observers for quite some time. Since the advent of special relativity, many authors have tried to understand these observers in the framework of Minkowski spacetime. One of the most important…
We formulate and discuss a general axiomatic theory of arbitrary objects. This theory is expressed in a simple first-order language without modal operators, and it is governed by classical logic.