The Clock Paradox in a Static Homogeneous Gravitational Field1

Jones, P. B.; Wanex, Lucas

doi:10.1007/s10702-006-1850-3

Cited by 13 publications

(13 citation statements)

References 8 publications

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“…Clocks in hyperbolic motion are discussed in a number of papers, e.g. [9,13,14,24,27,32]. In the conventional clock paradox, of two clocks A and Ā originally at rest in an inertial system, Ā is accelerated and departs from A.…”

Section: Clocks In a Compact Spacementioning

confidence: 99%

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The twin paradox and Mach’s principle

Lichtenegger

Iorio

2011

Eur. Phys. J. Plus

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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 been appreciated. However, the ultimate cause of the behavior of the clocks must be attributed to the autonomous status of spacetime, thereby proving the relational program advocated by Mach as impracticable.PACS. 03.30.+p Special relativity -04.20.-q Classical general relativity -04.20.Cv Fundamental problems and general formalism 1 The philosophical basis of Mach's principle is rooted in the rejection against the introduction of any unobservable quantities in the natural sciences. Hence in scientific investigations economy is the ultimate ambition, i.e. not more given quantities should be assumed than are absolutely needed. According to Mach, the starting point of all our perception is the immediate experience

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Section: Clocks In a Compact Spacementioning

confidence: 99%

“…Observer in K Since the acceleration ḡ of Ā is constant in K, the acceleration of Ā in relation to K is given by means of the Lorentz transformations 2 via [29] dv dt = ḡ γ 3 (v) (14) and integration yields the time in K needed for Ā to attain the velocity v…”

Section: Clocks In Non-uniform Motionmentioning

confidence: 99%

The twin paradox and Mach’s principle

Lichtenegger

Iorio

2011

Eur. Phys. J. Plus

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“…Indeed in the 'three brothers' version of the twin paradox due to Lord Halsbury [48], described by Marder [49], where the clock setting of the brother moving away from the Earth is transfered at the distant star to his brother moving towards the Earth at the same speed, the same global DAE effect occurs and no acceleration of deceleration occurs in the problem. Other author's [50,51,52,53,54,55] following Tolman [56] have used the Equivalence Principle of general relativity to replace a constant proper frame acceleration of the travelling twin by an artificial 'gravitational field' in the instantaneous rest frame of this twin. However all these authors made the same error of confusing the base frame of the reciprocal experiment with the travelling frame of the primary experiment, explained above in Section 7, when considering the phases of uniform motion of the round trip.…”

Section: Summary and Closing Remarksmentioning

confidence: 99%

The physics of space and time III: Classification of space-time experiments and the twin paradox

Field¹

2008

Preprint

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A nomenclature for inertial frames and a notation for space and time coordinates is proposed to give an unambigous description of space-time experiments in special relativity. Of particular importance are the concepts of 'base ' and 'travelling' frames and 'primary' and 'reciprocal' experiments. A detailed discussion of the twin paradox is presented. The physical basis of the differential aging effect is found to be a relativistic relative-velocity transformation relation, not, as hitherto supposed, the spurious 'length contraction' effect.PACS 03.30.+p which he passes by the two ends of the train and calculates its length with Eqn(2.1). This method is also applicable when both the observer and the measured train are in motion with known speeds, when an appropriate velocity addition formula is used to calculate the speed, v, to be substituted in (2.1).The fifth method involves observation, in the frame S, of the time difference of spatial coincidences of the front end of the moving train, with rest frame S', used in the fourth method, with the back and front ends of the stationary to-be-measured train. Again the length of the train is given by Eq. (2.1).Suppose now that two independent measurements of the length of a train are made, one using the fourth and the other the fifth of the methods just described. If different results are obtained for the length of the train, three different causes, in one-to-one correspondence with the quantities in Eqn(2.1), may be cited:(i) The train changed length between the two measurements.(ii) The observer's train, was moving at a different speed during the two measurements.(iii) The clocks employed in the two measurements, one in the frame S, the other in the frame S', are running relatively fast (or slow) with respect to each other.

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“…After studying a few spacetimes, we have realized that † lech.sokolowski@uj.edu.pl ‡ zdzislaw.golda@uj.edu.pl some results are universal and need not be separately derived for each spacetime of the class (this observation is not quite obvious since spacetimes with similar isometry groups may considerably differ in their geodesic structure). The programme of investigating the geodesic structure of various spacetimes has originally been motivated by the famous "twin paradox" considered in curved spacetimes [1][2][3][4][5]. It turns out that contrary to the conjecture stated in [5], no general rule concerning of which twin is younger exists and one must study each case separately.…”

Section: Introductionmentioning

confidence: 99%

Jacobi Fields and Conjugate Points on Timelike Geodesics in Special Spacetimes

Sokołowski¹,

Golda²

2015

Acta Phys. Pol. B

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Several physical problems such as the "twin paradox" in curved spacetimes have a purely geometrical nature and are reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic investigations of the geodesic structure of physically relevant spacetimes. These are focussed on the search of locally maximal timelike geodesics. The method is based on determining conjugate points on chosen geodesic curves. The method presented here is effective at least in the case of radial and circular geodesics in static spherically symmetric spacetimes. Our approach shows that even in Schwarzschild spacetime (as well as in other static spherically symmetric ones), one can find a new unexpected geometrical feature: each stable circular orbit contains besides the obvious set of conjugate points two other sequences of conjugate points. The obvious limitations of the approach arise from one's inability to solve involved ordinary differential equations and the recent progress in the field allows one to increase the range of metrics and types of geodesic curves tractable by this method.

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The Clock Paradox in a Static Homogeneous Gravitational Field1

Cited by 13 publications

References 8 publications

The twin paradox and Mach’s principle

The twin paradox and Mach’s principle

The physics of space and time III: Classification of space-time experiments and the twin paradox

Jacobi Fields and Conjugate Points on Timelike Geodesics in Special Spacetimes

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