The clock paradox in the relativity theory

A systemS (rocket) starts from rest in an inertial systemS, and after a series of accelerated, uniform and decelerated motions, comes back to rest at its initial position inS. An exact calculation is carried out, from the standpoint ofS, of the time intervals for the arrivals atS of light signals sent back byS. From the standpoint ofS, S has made a round trip after undergoing a series of free falls in gravitational fields and coasting motions. An exact calculation is carried out for the proper time intervals inS from the standpoint ofS. It is shown that there is exact agreement betweenS andS in their reckonings of the total time intervals for the two frames, namely, bothS andS agree quantitatively, to them, the time interval is longer forS than forS.The accelerated motion ofS relative toS explicitly used in the treatment of the problem in the present work is that under time-independent field and subject to the condition oflocal Lorentz contraction and dilation; the resulting motion turns out to be that obtained earlier by Møller on entirely different considerations. The result of the present treatment is, however, more general than this particular motion seems to imply, since by an arbitrary coordinate transformation, it can be made to include an infinite number of accelerated frames including time-dependent fields, all within the framework of flat space-time. General remarks are given for the clock problem in the general theory of relativity in the sense of Einstein's curved space.     

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.     

Limitations of the geometrodynamic clock

We examine sources of error in the geometrodynamic (or Marzke-Wheeler) clock, and choose parameters to minimize the total error. In theories with time-varying masses, there is an unavoidable minimum error. For a human-scale clock, the dominant error is from quantum uncertainty in the photon location.     

The physics of the Einstein-Podolsky-Rosen paradox

The Einstein-Podolsky-Rosen paradox as formulated in their original paper is critically examined. Their argument that quantum mechanics is incomplete is shown to be unsatisfactory on two important grounds. (i) The gedanken experiment proposed by Einstein, Podolsky, and Rosen is physically unrealizable, and consequently their argument is invalid as it stands. (ii) The basic assumptions of their argument are equivalent to the assumption that quantum mechanical systems are in fact describable by unique eigenfunctions of the operators corresponding to physical observables, independent of any observation or measurement. Following an argument due to Furry, it is shown that this interpretation of quantum mechanics must lead to some physical predictions at variance with those of conventional quantum mechanics. A decisive experiment has been performed by Freedman and Clauser, which rules out this interpretation, and imposes severe restrictions on any alternative theory which incorporates the Einstein, Podolsky, and Rosen concept of physical reality.     

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.     

Clarification of the bootstrap percolation paradox

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.     

Origin of the blackhole information paradox

It is argued that the blackhole information paradox originates from treating the blackhole geometry as strictly classical. It is further argued that the theory of quantum fields in a classical curved space with a horizon is an ill posed problem. If the geometry is allowed to fluctuate quantum mechanically, then the horizon effectively disappears. The sharp horizon emerges only in the classical limit when the ratio of the Compton wavelength of the black hole to its Schwarzschild radius vanishes. The region of strong gravity that develops when matter collapses to form the blackhole remains visible to the whole of spacetime and has to be described by a microscopic theory of strong gravity. The arguments imply that the information paradox is demoted from a paradox involving fundamental principles of physics to the problem of describing how matter at the highest densities gravitates.     

光钟

时间标准的研究在人类生活和科学探索中有着举足轻重的地位.文章简要介绍了时间的基本单位“秒”定义的几次重要发展与变迁,重点介绍了光钟的工作原理、关键部件、研究进展和光钟对“秒”定义未来发展的重要性.     

Noncommutative geometry of the quantum clock

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.     

A new explanation of the extinction paradox

This work presents a new explanation for the extinction paradox and shows that the canonical explanations are incorrect. This paradox refers to the large size limit of a particle's extinction cross section. It is called a paradox because the geometrical optics approximation, which should be valid in this limit, predicts a cross section that is half of the true value. The new explanation is achieved by formulating the scattered wave in terms of an integral over the particle's surface where the seemingly unrelated Ewald-Oseen theorem appears in the formulation. By expressing the cross section in terms of this surface integral, the Ewald-Oseen theorem is analytically connected to the cross section. Several illustrations are used to reveal the significance of this connection: The paradox is seen to be a consequence of the requirement that the incident wave be canceled within the particle by secondary radiation from its own internal field. Following this, the canonical explanations are examined to reveal serious problems. In the process, the same asymptotic extinction behavior is shown to occur for small highly refractive dielectric particles, and thus is not just a large particle size or small wavelength effect as is often stated. The traditional explanations cannot account for this behavior while the new one actually predicts it. All in all, this work constitutes a fundamental reworking of 60 years of accepted understanding for the cause of the asymptotic behavior of the extinction cross section.     

New loophole for the Einstein-Podolsky-Rosen paradox

Using the new concept of "stochastic gauge system", we describe a novel loophole to circumvent the Einstein-Podolsky-Rosen (EPR) paradox. We derive a "realistic" (i.e., classical) model, free from any paradox, which exactly emulates the spin EPR experiment. We conclude that Bell's inequalities are violated in classical physics as well, or, conversely that quantum mechanical theory is logically consistent with relativity.     

Quantum anti-zeno paradox

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator E(t) = U(t)EUdagger(t) is measured continuously from t = 0 to T, where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If U(t) not equal1, the watched kettle is sure to "boil."     

The quark-parton paradox

We heuristically discuss the paradox that quarks are seldom produced and show semiclassical parton features while at the same time they interact strongly and are deeply bound inside hadrons. Rising total cross sections are interpreted as partially due to the production of massive free quarks through “pionization” graphs.     

A relativistic formulation of the Einstein-Podolsky-Rosen paradox

The Einstein-Podolsky-Rosen (EPR) paradox and the correlated states it introduced comprise one of the central interpretive problems of quantum mechanics. Because of the apparent nonlocal character of this paradox, it should be given a relativistic treatment. The purpose of this paper is to provide such a treatment.     

Klein paradox in the Breit equation

We demonstrate that in the Breit equation with a central potentialV(r) having the propertyV(r ₀)=E there appears a Klein paradox atr=r ₀. This phenomenon, besides the previously found Klein paradox arr→∞ appearing ifV(r)→∞ atr→∞, seems to indicate that in the Breit equation valid in the singleparticle theory the sea of particle-antiparticle pairs is not well separated from the considered two-body configuration. We conjecture that both phenomena should be absent from the Salpeter equation which is consistent with the hole theory. We prove this conjecture in the limit ofm ⁽¹⁾→∞ andm ⁽²⁾→∞, where we neglect the terms ～1/m ⁽¹⁾ and 1/m ⁽²⁾. In Appendix I we show that in the Breit equation the oscillations accumulating atr=r ₀ in the case ofm ⁽¹⁾≠m ⁽²⁾ are normalizable to the Dirac δ-function. In Appendix II the analogical statement is justified for the nonoscillating singular behaviour appearing atr=r ₀ in the case ofm ⁽¹⁾=m ⁽²⁾.     

锶原子光晶格钟自旋极化谱线的探测

87Sr原子存在核自旋,在磁场作用下原子能级会分裂成不同塞曼子能级.通过光抽运对原子进行自旋极化,其自旋极化谱线的探测为锶光钟系统的闭环锁定提供精确的频率参考.本文对~(87)Sr原子钟跃迁能级5s~2~1S_0→5s5p~3P_0中的m_F=+9/2和m_F=-9/2的塞曼磁子能级自旋极化谱线进行了探测.经过一级宽带冷却和二级窄线宽冷却与俘获后,锶冷原子温度为3.9μK,原子数目为3.5×10~6.利用邻近"魔术波长"的813.426 nm半导体激光光源实现水平方向的一维光晶格装载.采用归一化探测方法用线宽为Hz量级的698 nm钟激光对~1S_0→~3P_0偶极禁戒跃迁进行探测,在150 ms的探测时间下获得线宽为6.7 Hz的钟跃迁简并谱.在磁光阱竖直方向施加一个300 mGs的偏置磁场获得塞曼分裂谱,并通过689 nm的圆偏振自旋极化光进行光抽运,最终在探测时间为150 ms时,获得左右旋极化谱线线宽分别为6.2 Hz和6.8 Hz.