The Clock Paradox in a Static Homogeneous Gravitational Field1

  title={The Clock Paradox in a Static Homogeneous Gravitational Field1},
  author={Preston Jones and Lucas Freor Wanex},
  journal={Foundations of Physics Letters},
The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of… 

Figures from this paper

Relativity solution for “Twin paradox”: a comprehensive solution
We have provided a complete and realistic solution to the problem of Twin Paradox, for the first time, in the frame work of general relativity. Some of the inspiration for this paper has come from
On the twin paradox in static spacetimes: I. Schwarzschild metric
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike
The task of the relativistic oscillator in a non-inertial frame of reference
In this paper the analogues of the Lorentz transformations for non-inertial reference frames have been obtained. A common case when the movement speed of one coordinate frame in relation to another
Minkowski’s Proper Time and the Status of the Clock Hypothesis
In this chapter I argue that the concept of proper time must be regarded as one of Minkowski’s enduring contributions to physics. I examine some confusions that still interfere with an appreciation
The Local and Global Geometrical Aspects of the Twin Paradox in Static Spacetimes: II. Reissner--Nordstr\"om and Ultrastatic Metrics
This is a consecutive paper on the timelike geodesic structure of static spherically symmetric spacetimes. First we show that for a stable circular orbit (if it exists) in any of these spacetimes all
The twin paradox and the principle of relativity
The twin paradox is intimately related to the principle of relativity. Two twins A and B meet, travel away from each other and meet again. From the point of view of A, B is the traveller. Thus, A
The Physics Surrounding the Michelson-Morley Experiment and a New Æther Theory
From the customary view the Michelson-Morley experiment is used to expose the failure of the aether theory. The key point in this experiment is the \emph{fringe shift} of the interference pattern.
Jacobi fields, conjugate points and cut points on timelike geodesics in special spacetimes
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a
Four twins for a paradox: on "sensitive" twins and the biological counterpart of the "twin paradox".
These results suggest a reconsideration of the Langevin-Einstein thought experiment known as the "twin paradox," where at least four twins are necessary in order to take into account the inertially independent divergent aging described here.
The twin paradox and Mach’s principle
The problem of absolute motion in the context of the twin paradox is discussed. It is shown that the various versions of the clock paradox feature some aspects which Mach might have appreciated.


An Analytical Treatment of the Clock Paradox in the Framework of the Special and General Theories of Relativity
No HeadingIn this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the
Accelerating Frames of Reference and the Clock Paradox
The Lorentz-Einstein transformations are obtained by a method which enables one to derive a coordinate transformation between an inertial frame of reference and a noninertial accelerating system.
Nonequivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field
A general expression is obtained for the space‐time interval between neighboring events in a one‐dimensional space in which it is possible to set up a rigid reference frame. Particular expressions
The Theory of Relativity
General coordinatisations of the flat space-time of constant proper-acceleration
We examine space-times which are described by a metric of the form ds2 = V2(X)dT2 - U2 (X)dX2 - dY2 - dZ2 in which V =V (X) and U = U(X) are continuous functions of X only and which admit
The Theory of Relativity
THE earlier portion of Dr. Carmichael's book is a reprint of the first edition, which received notice in NATURE for March 12, 1914. The later pages, which are grouped together under one large chapter
Kruskal Space and the Uniformly Accelerated Frame
The striking formal similarities between the diagram of Kruskal space in general relativity and that of the uniformly accelerated rigid rod in special relativity are shown to be the result of certain
Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes
Die Frage, ob die Ausbreitung des Lichtes durch die Schwere beeinflust wird, habe ich schon an einer vor vier Jahren erschienenen Abhandlung zu beantworten gesucht.2) Ich komme auf dies Thema wieder
The collected papers of Albert Einstein.
  • D. Siegel
  • Philosophy, Medicine
    Isis; an international review devoted to the history of science and its cultural influences
  • 2007
Nonequivalence of a uniform accelerating frame and a frame at rest in a uniform gravitational field,
  • American Journal of Physics
  • 1989