Gravitational memory for uniformly accelerated observers

SummaryIf the metric of an n-dimensional space is taken in the form ds2 = u2dτ2+dσ2, where dτ2 and dσ2 are cartesian metrics of r and (n−r) dimensions, respectively, the various forms of u for flat space are quite simple. The study of accelerated motions in special relativity by various authors has led to four dimensional metrics of this form. Those in which u = ±1 at the space origin for all values of time are of particular interest. They are locally cartesian at the accelerated observer, and so the coordinates in the neighbourhood of the observer correspond directly to physical measurements. Hence, such metrics provide convenient means of describing physical conditions experienced by accelerated observers. If the τ-space contains the time direction and is of one or two dimensions, arbitrary rectilinear motions are allowed.

Download Full-text

Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814500868 ◽

2014 ◽

Vol 11 (10) ◽

pp. 1450086 ◽

Cited By ~ 1

Author(s):

Horace W. Crater ◽

Luca Lusanna

Keyword(s):

Quantum Mechanics ◽

Minkowski Space ◽

Relativistic Quantum ◽

Classical Mechanics ◽

Space Time ◽

Relativistic Quantum Mechanics ◽

Minkowski Space Time ◽

Accelerated Observers ◽

Inertial Frames ◽

Locality Principle

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

Download Full-text

Absolute nature of the thermal ambience of accelerated observers

Physical Review D ◽

10.1103/physrevd.27.2310 ◽

1983 ◽

Vol 27 (10) ◽

pp. 2310-2315 ◽

Cited By ~ 12

Author(s):

Ulrich H. Gerlach

Keyword(s):

Accelerated Observers

Download Full-text

Conformal Symmetry, Accelerated Observers, and Nonlocality

Symmetry ◽

10.3390/sym11080978 ◽

2019 ◽

Vol 11 (8) ◽

pp. 978 ◽

Cited By ~ 2

Author(s):

Bahram Mashhoon

Keyword(s):

Abelian Subgroup ◽

Conformal Symmetry ◽

Minkowski Spacetime ◽

Conformal Group ◽

Accelerated Observers ◽

Spacetime Metric

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 Minkowski spacetime. The properties of this congruence are studied in order to illustrate the kinematics of accelerated observers in relativistic physics. The generalization of this approach under conformal rescaling of the spacetime metric is examined.

Download Full-text

Accelerated Observers in Special Relativity

Physics Essays ◽

10.4006/1.3028793 ◽

1999 ◽

Vol 12 (4) ◽

pp. 629-648

Author(s):

Michael L. Fontenot

Keyword(s):

Special Relativity ◽

Accelerated Observers

Download Full-text

A new mathematical formulation of accelerated observers in general relativity. II

Journal of Mathematical Physics ◽

10.1063/1.525194 ◽

1982 ◽

Vol 23 (1) ◽

pp. 105-108 ◽

Cited By ~ 4

Author(s):

D. G. Retzloff ◽

B. DeFacio ◽

P. W. Dennis

Keyword(s):

General Relativity ◽

Mathematical Formulation ◽

Accelerated Observers

Download Full-text

An investigation of some quantum correlations of Dirac fields in noninertial frames

Canadian Journal of Physics ◽

10.1139/cjp-2017-0489 ◽

2019 ◽

Vol 97 (1) ◽

pp. 42-50

Author(s):

Mohammad Bagher Arjmandi

Keyword(s):

Single Mode ◽

Quantum Correlations ◽

Initial State ◽

Dirac Fields ◽

Acceleration Parameter ◽

Entanglement Of Formation ◽

Single Mode Approximation ◽

Accelerated Observers ◽

Werner States

In this paper, some concepts of quantum correlations, such as one-way quantum deficit, purity, and entanglement of formation are investigated between the modes of Dirac fields in noninertial frames. We consider two bipartite divisions of a tripartite system constructed by initial Werner states, which is shared between two relatively accelerated observers. The degradation of these quantum correlations is shown when the acceleration parameter increases. However, a nonzero amount of correlations survives even at infinite acceleration limit. Furthermore, we study the inevitable influence of mixedness factor of initial state on the quantum correlations behaviour. Finally, we review our calculation beyond single-mode approximation and point out some differences and similarities between the two regimes.

Download Full-text