A comment on the twin paradox and the Hafele-Keating experiment

We show that a theoretical and experimental analysis of the twin paradox and the Hafele-Keating experiment recently presented in this journal is non sequitur from the epistemological point of view and wrong according to the mathematical structure of relativity theory.     

A quantum mechanical twin paradox

When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schrödinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that theory and classical physics.     

The twin paradox and the hafele and keating experiment

We review the twin paradox from a theoretical and experimental point of view in the cases of rectilinear and rotational motions and we comment on the interpretation of the Hafele and Keating experiment.     

On Einstein's later view of the twin paradox

It is shown that Einstein abandoned his earlier view that there are material consequences, such as asymmetric aging, implied by the space-time transformations of transformations of relativity theory.     

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 worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.     

Experimental approaches to the quantum measurement paradox

I examine the question of how far experiments that look for the effects of superposition of macroscopically distinct states are relevant to the classic measurement paradox of quantum mechanics. Existing experiments on superconducting devices confirm the predictions of the quantum formalism extrapolated to the macroscopic level, and to that extent provide strong circumstantial evidence for its validity at this level, but do not directly test the principle of superposition of macrostates. A more ambitious experiment, not obviously infeasible with current technology, could provide a direct test between quantum mechanics and a whole class of theories embodying the postulate of realism at the macroscopic level.     

A new approach to the Einstein-Podolsky-Rosen paradox

Some new aspects of the EPR paradox are considered. We first show that the authors' argument, leading to the conclusion that quantum theory is incomplete, is based on a tacit assumption that may be questioned. We then investigate the non-local features of the EPR setup and point out an interesting connection between the nonlocality involved in the quantum correlations of pairs of particles and that of a single particle in quantum theory.     

"广义芝诺悖论"的探讨

两辆相向匀速运动的车之间有一只小鸟,在两车间来回飞行.小鸟运动速率比车的要大,其初始位置是x0.当两车最终相遇时,相遇位置就是小鸟的最终位置.现在逆向演示(回放)该过程,即小鸟从两辆车相遇位置出发而两车作相背运动.当两车回到它们的初始位置时,小鸟将回到x0点.然而,在正过程中,由于两车相遇位置(即小鸟的最终位置)实际上和小鸟的初始位置无关,因此在逆过程中,小鸟最终可以处在任意位置而未必回到x0点.由此产生悖论,称做“广义芝诺悖论”.通过建立适当的物理模型,利用运动定律,分析并最终解决了这个悖论问题.     

Einstein's paradox and a new mixing paradox

A study is made of Einstein's paradox for the isothermal mixing of ideal quantum gases and also of a new paradox when such gases are mixed adiabatically. Both paradoxes are resolved.     

Nonlocality and the Kochen-Specker paradox

A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics.     

"广义芝诺悖论"的再探讨

在第25卷第5期的《大学物理》上,一篇文章对"广义芝诺悖论"进行了探讨,但他们分析的并不是"悖论"中的匀速率的理想运动,而且还存在推导错误.本文通过对"广义芝诺悖论"物理情境的分析,抽象建立起VPV模型,并由此得出:从运动学角度考虑,"广义芝诺悖论"正过程的初态和末态是"多对一"的关系,"广义芝诺悖论"并不为悖论.     

Solution to the twin image problem in holography

While holography truly constitutes an ingenious concept, ever since its invention by Gabor it has been troubled by the so-called twin-image problem limiting the information that can be obtained from a holographic record. For symmetry reasons there are always two images appearing in the reconstruction of a hologram and the unwanted out of focus twin-image obscures the object. Here we show a universal method of reconstructing a hologram completely free of twin-image disturbances while no assumptions about absorbing or phase shifting properties of the object need to be imposed. Thus, truthful amplitude and phase distributions are retrieved.     

A Krein quantization approach to Klein paradox

In this paper we first introduce the famous Klein tization approach and taking the negative modes into account densities could be achieved without confronting any paradox. paradox. Afterwards by proposing the Krein quan- , we will show that the expected and exact current     

Numerical studies on boundary effects on the FPU paradox

We study numerically the dynamics of a chain of particles subjected to an on site restoring nonlinear force and a first neighbor harmonic coupling. We excite the first linear mode and investigate the distribution of the average harmonic energies at metastable regime, in the spirit of Fermi Pasta Ulam experiment. The limit distribution turns out to strongly depend on the boundary conditions. A theoretical discussion of the phenomenon is also given.     

Solution to causality paradox upon total reflection

A dispute about the existence of an additional time (named as the Goos-H?nchen time) associated with the Goos-H?nchen shift in total reflection has recently arisen. At the same time, an inconsistency between the optical ray model and the electromagnetic theory also appears in the optical planar waveguide. By analyzing light propagation in an optical planar waveguide with both the zigzag-ray model and the electromagnetic theory, this paper shows that the Goos-H?nchen time really exists, and the total time delay upon total reflection upon an ideal nonabsorbing plasma mirror is the sum of the group-delay time and the Goos-H?nchen time. The causality paradox of total reflection of a TM wave upon an ideal nonabsorbing plasma mirror is also solved taking into consideration the negative Goos-H?nchen shift. Finally, the expression of the group velocity of the guided mode in optical planar waveguide was obtained, which clearly shows that the time delay upon total reflection is the sum of the group-delay time and the Goos-H?nchen time at given any time.     

Sub- and super-diffusion on Cantor sets: Beyond the paradox

There is no way to build a nontrivial Markov process having continuous trajectories on a totally disconnected fractal embedded in the Euclidean space. Accordingly, in order to delineate the diffusion process on the totally disconnected fractal, one needs to relax the continuum requirement. Consequently, a diffusion process depends on how the continuum requirement is handled. This explains the emergence of different types of anomalous diffusion on the same totally disconnected set. In this regard, we argue that the number of effective spatial degrees of freedom of a random walker on the totally disconnected Cantor set is equal to $n_{sp}=[D]+1$, where $[D]$ is the integer part of the Hausdorff dimension of the Cantor set. Conversely, the number of effective dynamical degrees of freedom $(d_s)$ depends on the definition of a Markov process on the totally disconnected Cantor set embedded in the Euclidean space $E^n$$(n\ge n_{sp})$. This allows us to deduce the equation of diffusion by employing the local differential operators on the $F^{\alpha }$-support. The exact solutions of this equation are obtained on the middle-? Cantor sets for different kinds of the Markovian random processes. The relation of our findings to physical phenomena observed in complex systems is highlighted.     

Notes on the quantum-mechanical discussion of the Gibbs paradox

Starting from the deductive development of quantum theory as worked out byNeumann and making use of the quantum-theoretical propositional calculus it will be shown that the quantum theoretical entropy of any physical property increases if the property is replaced by a logically weaker one.

     

Effect of dislocation distribution in twin boundaries on the nucleation of microcracks at the twin tip

The effect of dislocation distribution in the boundaries of an arrested twin on the nucleation of microcracks at its tip is investigated. The twin is simulated by a double step pileup (cluster) of twinning dislocations located in adjacent slip planes. The equilibrium equations for dislocations are solved numerically. Clusters with different total numbers of dislocations and with different ratios of the numbers of dislocations at the upper and lower twin boundaries are considered. The formation of microcracks as a result of coalescence of head dislocations according to the force and thermally activated mechanisms is analyzed. The equilibrium configurations of a single twin boundary and of the twin are calculated. It is found that the condition for microcrack formation at the twin tip considerably depends on the ratio of the numbers of dislocations in twin boundaries. In the limit, this condition coincides with the condition of crack formation at the tip of a single twin boundary with the same total number of dislocations. It is shown that thermally activated formation of a microrack corresponds to lower values of the critical stress.