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Einstein's concept of a clock and clock paradox  [PDF]
Wang Guowen
Physics , 2005,
Abstract: A geometric illustration of the Lorentz transformations is given. According to similarity between space and time and correspondence between a ruler and a clock, like the division number in a moving ruler, the tick number of a moving clock is independent of its relative speed and hence invariant under the Lorentz transformations. So the hand of the moving clock never runs slow but the time interval between its two consecutive ticks contracts. Thus it is Einstein's concept of slowing of the hands of moving clocks to create the clock paradox or twin paradox. Regrettably, the concept of the clock that Einstein retained is equivalent to Newton's concept of absolute time that he rejected. This is a blemish in Einstein's otherwise perfect special relativity.
On the Clock Paradox in the case of circular motion of the moving clock  [PDF]
Lorenzo Iorio
Physics , 2004, DOI: 10.1088/0143-0807/26/3/018
Abstract: In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in which (1) is at rest and (2) moves is I and, finally, the accelerated frame in which (2) is at rest and (1) rotates is A. By using the General Theory of Relativity in order to describe the motion of (1) as seen in A we will show the following features. I) A differential aging between (1) and (2) occurs at their reunion and it has an absolute character, i.e. the proper time interval measured by a given clock is the same both in I and in A. II) From a quantitative point of view, the magnitude of the differential aging between (1) and (2) does depend on the kind of rotational motion performed by A. Indeed, if it is uniform there is no any tangential force in the direction of motion of (2) but only normal to it. In this case, the proper time interval reckoned by (2) does depend only on its constant velocity v=romega. On the contrary, if the rotational motion is uniformly accelerated, i.e. a constant force acts tangentially along the direction of motion, the proper time intervals $do depend$ on the angular acceleration alpha. III) Finally, in regard to the sign of the aging, the moving clock (2) measures always a $shorter$ interval of proper time with respect to (1).
The clock paradox in a static homogeneous gravitational field  [PDF]
Preston Jones,Lucas F. Wanex
Physics , 2006, DOI: 10.1007/s10702-006-1850-3
Abstract: 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 the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars.
Perspectives on the quantum Zeno paradox  [PDF]
W. M. Itano
Physics , 2006,
Abstract: As of October 2006, there were approximately 535 citations to the seminal 1977 paper of Misra and Sudarshan that pointed out the quantum Zeno paradox (more often called the quantum Zeno effect). In simple terms, the quantum Zeno effect refers to a slowing down of the evolution of a quantum state in the limit that the state is observed continuously. There has been much disagreement as to how the quantum Zeno effect should be defined and as to whether it is really a paradox, requiring new physics, or merely a consequence of "ordinary" quantum mechanics. The experiment of Itano, Heinzen, Bollinger, and Wineland, published in 1990, has been cited around 347 times and seems to be the one most often called a demonstration of the quantum Zeno effect. Given that there is disagreement as to what the quantum Zeno effect is, there naturally is disagreement as to whether that experiment demonstrated the quantum Zeno effect. Some differing perspectives regarding the quantum Zeno effect and what would constitute an experimental demonstration are discussed.
Inertial Frames and Clock Rates  [PDF]
Subhash Kak
Physics , 2012,
Abstract: This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If inertial frames are explicitly identified by motion with respect to the large scale structure of the universe, it makes it possible to consider the relative inertiality of different frames.
Mass, Time, and Clock (Twin) Paradox in Relativity Theory  [PDF]
Anatoli Vankov
Physics , 2006,
Abstract: The paper is intended to clarify operational meaning of mass and time quantities as main characteristics of an atomic clock, which is considered a quantum oscillator in association with the de Broglie wave concept. The specification of the concept of clock in quantum terms reflects the idea of relativistic mass and time complementarity, which is important for avoiding ambiguity of such notions as ``time rate'', ``time record'', and ``elapsed time'' under relativistic conditions. We used this approach in SRT Kinematics to conduct a detailed analysis of the clock paradox; results are discussed. It is also shown that in SRT Dynamics the proper mass must be acted by Minkowski force, what results in a clock rate variation.
History and Physics of the Klein Paradox  [PDF]
A Calogeracos,N Dombey
Physics , 1999, DOI: 10.1080/001075199181387
Abstract: The early papers by Klein, Sauter and Hund which investigate scattering off a high step potential in the context of the Dirac equation are discussed to derive the 'paradox' first obtained by Klein. The explanation of this effect in terms of electron-positron production is reassessed. It is shown that a potential well or barrier in the Dirac equation can become supercritical and emit positrons or electrons spontaneously if the potential is strong enough. If the well or barrier is wide enough, a seemingly constant current is emitted. This phenomenon is transient whereas the tunnelling first calculated by Klein is time-independent. It is shown that tunnelling without exponential suppression occurs when an electron is incident on a high barrier, even when the barrier is not high enough to radiate. Klein tunnelling is therefore a property of relativistic wave equations and is not necessarily connected to particle emission. The Coulomb potential is investigated and it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, as $Z$ increases the Coulomb barrier should become increasingly transparent to positrons. This is an example of Klein tunnelling. Phenomena akin to supercritical positron emission may be studied experimentally in superfluid $^3$He
An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity  [PDF]
Lorenzo Iorio
Physics , 2004, DOI: 10.1007/s10702-005-2466-8
Abstract: In 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 direction of its motion assumed to be rectilinear. No inertial motion steps are considered. The rest clock is denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: I) What is the effect of the finite force acting on (2) on the proper time intervals measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The Special Theory of Relativity is used in order to describe the hyperbolic motion of (2) in the frame I II) Is this effect an absolute one, i.e. does the accelerated observer A comoving with (2) obtain the same results as that in I, both qualitatively and quantitatively, as it is expected? We use the General Theory of Relativity in order to answer this question.
A tale of two twins  [PDF]
Lucien Benguigui
Physics , 2012,
Abstract: The thought experiment (called the clock paradox or the twin paradox)proposed by Langevin in 1911 of two observers, one staying on Earth and the other making a trip toward a star with a velocity near the light velocity is very well known for its surprising result. When the traveler comes back, he is younger that the stay on Earth. This astonishing situation deduced from the theory of Special relativity sparked a huge amount of articles, discussions and controversies such it remains a particular phenomenon probably unique in Physics. We propose to study it. First we looked for the simplest solutions when one can observe that the published solutions correspond in fact to two different versions of the experiment. It appears that the complete and simple solution of Moller is neglected for complicated methods with dubious validity. We propose to interpret this avalanche of works by the difficulty to accept the conclusions of the Special Relativity, in particular the difference in times indicated by two clocks, one immobile and the second moving and finally stopping. We also suggest that the name "twin paradox" is maybe related to some subconscious idea concerning conflict between twins as it can be found in the Bible and in several mythologies
A variation of the clock paradox and a distinguishing feature of an inertial frame  [PDF]
Chandru Iyer,G. M. Prabhu
Physics , 2008,
Abstract: The clock paradox is analyzed for the case when the onward and return trips cover the same <> (as observed by the traveling twin) but at unequal velocities. In this case the stationary twin observes the distances covered by her sister during the onward and return trips to be different. The analysis is presented using formulations of special relativity and the only requirement for consistency is that all observations are made from any one chosen inertial frame. The analysis suggests that a defining feature of an inertial frame should be based on the continued maintenance of the distinctive synchronicity of the clocks co-moving with it. Published in Journal of Physical and Natural Sciences Volume 1, Issue 1, 2007 http://www.scientificjournals.org/journals2007/articles/1102.pdf
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