狭义相对论解决双生子佯谬之不可能

详细地阐明了狭义相对论解决双生子佯谬之不可能，对一种很有影响的狭义相对论解进行了深入细致的分析     

Special Relativity over the Field of Rational Numbers

We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of special relativity. We show that there is a natural axiom system of special relativity which can be modeled even over the field of rational numbers.     

自由质点测地线仿射参量时空坐标系

以时序t为自变量,可给出自由质点空间测地线的参数方程组{Xⁱ(t)},借助于仿射参量R(t)变换实现测地线微分方程的齐次化, 推导出仿射参量R满足的一阶微分方程、获得以有理数C_u为标志的序列解析解R.基于R定义平直四维坐标系{t,r,θ,φ}的空间距离单位,建立自由质点测地线仿射参量时空坐标系{t,ξ,θ,φ}.研究{t,ξ,θ,φ}中狭义相对论时空间隔模型度规张量g的对角化过程, 发现与对角化度规对应的特征量t₁(t,ξ), τ₁(τ,ξ),t_t(t,τ,ξ),τ_τ1(t,τ,ξ); 从而推出时空坐标系{t,ξ,θ,φ}维数小于4.     

Simultaneity on the Rotating Disk

The disk that rotates in an inertial frame in special relativity has long been analysed by assuming a Lorentz contraction of its peripheral elements in that frame, which has produced widely varying views in the literature. We show that this assumption is unnecessary for a disk that corresponds to the simplest form of rotation in special relativity. After constructing such a disk and showing that observers at rest on it do not constitute a true rotating frame, we choose a “master” observer and calculate a set of disk coordinates and spacetime metric pertinent to that observer. We use this formalism to resolve the “circular twin paradox”, then calculate the speed of light sent around the periphery as measured by the master observer, to show that this speed is a function of sent-direction and disk angle traversed. This result is consistent with the Sagnac Effect, but constitutes a finer analysis of that effect, which is normally expressed using an average speed for a full trip of the periphery. We also use the formalism to give a resolution of “Selleri’s paradox”.     

On Diagonal P-Representation of Superposition Field of Two Light Modes

For the superposition field a₁^†+a₂^† of two light modes we introduce an appropriate diagonal P-representation which is constructed on the common eigenvectors |z,x〉of (X₁-X₂) and a₁+a₂, where X_i=(a_i+ a_i^†)/√(2), [a_i,a_i^†] =δ_ij. It is remarkable that |z,x〉make up a new quantum mechanical representation.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.     

On the Ingredients of the Twin Paradox

If M is a 4-dimensional connected, orientable flat spacetime manifold endowed with a time-arrow, and if the existence of a finite speed limit to energy/information transfers over M can be assessed, then the “twin paradox” necessarily follows (and indeed, the full special relativity theory). Two other implicit ingredients of the paradox are also identified.     

Conventionality of Simultaneity and the Tippe Top Paradox in Relativity

In this paper we critically examine a recently posed paradox (tippe top paradox in relativity) and its suggested resolution. A tippe top when spun on a table, tips over after a few rotations and eventually stands spinning on its stem. The ability of the top to demonstrate this charming feat depends on its geometry (all tops are not tippe tops). To a rocket-bound observer the top geometry should change because of the Lorentz contraction. This gives rise to the possibility that for a sufficiently fast observer the geometry of the top may get altered to such an extent that the top may not tip over! This is certainly paradoxical since a mere change of the observer cannot alter the fact that the top tips over on the table. In an effort to resolve the issue the authors of the paradox compare the equations of motion of the particles of the top from the perspective of the inertial frames of the rocket and the table and observe among other things that (1) the relativity of simultaneity plays an essential role in resolving the paradox and (2) the puzzle in some way is connected with one of the corrolaries of special relativity that the notion of rigidity is inconsistent with the theory. We show here that the question of the incompatibility of the notion of rigidity with special relativity has nothing to do with the current paradox and the role of the lack of synchronization of clocks in the context of the paradox is grossly over-emphasized. The conventionality of simultaneity of special relativity and the notion of the standard (Einstein) synchrony in the Galilean world have been used to throw light on some subtle issues concerning the paradox.     

Number-Difference-Phase Uncertainty Relationship for Complex Scalar Fields

For the complex scalar fields we introduce unitary phase operators which obey the definite number-difference-phase uncertainty relation. The behavior of phase operators can be demonstrated clearly in the common eigenvector representation of fields φ(x) and φ⁺(x).     

On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Explicit Relations of Physical Potentials Through Generalized Hypervirial and Kramers' Recurrence Relations

Based on a Hamiltonian identity,we study one-dimensional generalized hypervirial theorem,Blanchardlike(non-diagonal case) and Kramers'(diagonal case) recurrence relations for arbitrary x~κ which is independent of the central potential V(x).Some significant results in diagonal case are obtained for special κ in x~κ(κ≥ 2).In particular,we find the orthogonal relation(n_1|n_2) = δ_(n_1n_2)(κ = 0),(n_1|V'(x)\n_2) =(E_(n_1)-E_(n_2))~2〈n_1x|n_2)(κ = 1),E_n =(n/V'(x)x/2|n) +(n|V(x)|n)(κ = 2) and-4E_n(n|x|n) +(n|V'(x)x~2\n〉 +4〈n|V(x)x|n〉 = 0(κ = 3).The latter two formulas can be used directly to calculate the energy levels.We present useful explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.     

Conservation Laws and Bianchi Identities in R+R2+Q2 Theories

We investigate the conscrvalion Jaws in the class of R+R²+Q² theory with torsion. We prove that the conservation Jaws may be dcrived Born the Bianchi identities of the curvature and torsion tensors. In particular the conservation law for matter is showed to be a result of the Dianchi identities and gravitational ficld equations just as it does for T^uv=0 in general relativity.     

Gluonia and Charmonium Decays

We discuss the search for a 1^-- gluonium state, 0, in connection with a possible solution for the so-called ρπ, K^*K puzzle in the J/φ and φ' decays. Some issues are examined. In particular, we argue that the expected most favorable process φ → ππO can have an appreciable branching ratio (say 10^-3 ~ 10^-4) only if the O has a very narrow partial decay width to ρπ (say 1 ~ 10 MeV). For the 0^-+ system we deduce a relation that BR(η'_c → h) ≈ BR (η_c → h), where h denotes an exclusive light hadronic channel. This relation may be useful for the experimental search of the yet to be confirmed q: state, for which the branching ratios of φ' → η'_c → γKKπ, γηππ, γη'ππ are estimated to be about 1 × 10^-4 if the mass of η'_c is around 3600 MeV, and this relation may also serve as a criterion to determine whether there exist anomalous decays in the η_c and η'_c system, in particular in the VV decay channels, which might be related to the 0^-+ glueball-charmonium mixing. We emphasize that the bigluonium and the trigluonium may have very different effects on these decays.     

Influence of Nd substitution on the superconducting properties of ceramics in the 2212 system Bi2−wPbwSr2−xCa1−yNdx+yCu2O8+z

In the system Bi_2−wPb_wSr_2−xCa_1−yNd_x+yCu₂O_8+z different fractions of Nd are substituted on either Sr of Ca sites in order to introduce intrinsic insulating pinning centres. It is shown that a Nd concentration around x or y = 0.2 is likewise favourable with an average Nd---Nd distance in the range of the coherence length in the a, b-plane. However, clear evidence of flux pinning is only present for charge compensation with Pb²⁺. A simultaneous substitution of the Bi-based 2212 superconductor with moderate amounts of Nd³⁺ and Pb²⁺ improves the superconducting properties by strengthening the flux pinning forces.     

Theoretical calculations of hyperfine splitting,Zeeman shifts,and isotope shifts of 27Al+ and logical ions in Al+ clocks

Based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, similar models are employed to simultaneously calculate the first-order and second-order Zeeman coefficients as well as the hyperfine interaction constants of the related energy levels of ²⁷Al⁺ and its logical ions ⁹Be⁺ and ²⁵Mg⁺ in the ²⁷Al⁺ optical clock. With less than 0.34% deviations from experimental values in Zeeman coefficients of ²⁷Al⁺, these calculated parameters will be of great help for better evaluation of the systematic uncertainty. We also calculate the isotope shift parameters of the related energy levels, which could extend our knowledge and understanding of nuclear properties of these ions.     

Ionic Charge State Distribution of Au Plasma for 7-Ion System

The present work extends the previous work on 5-ion system to consider 7-ion system (i.e., Au⁴⁷⁺～Au⁵³⁺. It is found that more highly charged ions, e.g., Au⁵³⁺, Au⁵⁴⁺ etc., could be able to be neglected, however, less highly charged ions, e.g., Au⁴⁷⁺, Au⁴⁶⁺ etc., are rather important. Therefore, a new idea to consider 8-ion system, i.e., Au⁴⁶⁺～Au⁵³⁺, is under way. As a supplement, we discuss the simultaneous reaction, which would be important in this sort of works.     

相对论多组态相互作用方法计算Mg~+离子同位素位移

采用相对论多组态相互作用方法研究了Mg~+离子3s~2S_(1/2)—3s~2P_(1/2)和3s~2S_(1/2)—3s~2P_(3/2)两条跃迁谱线的特殊质量位移系数和场位移因子,并计算了中子数8≤N≤20的Mg~+离子的同位素位移.计算结果与其他理论的计算值符合得比较好,与最新的实验测量结果比较,相对误差在0.13%到0.28%范围,是目前最接近Mg~+离子同位素位移实验测量的理论计算结果.该计算结果可为Mg~+离子同位素位移实验和理论研究提供参考,能够用于Mg~+离子的短寿命同位素的光谱测量实验以及利用Mg~+离子开展幻中子数N=8和N=20附近的奇异原子核特性研究等.所用的计算方法和电子激发模式也可以推广到其他核外电子数为11的多电子体系,用于开展相应的原子光谱结构计算和同位素位移的理论研究.     

ENERGY AND LIFETIME OF CORE-EXCITED Be+ RESONANCES

The energies, shifts, widths, and radiative rates of double excited Be⁺ resonances are calculated using the saddle point and saddle-point complex-rotation methods. A restricted variational method is used to extrapolate a better nonrelativistic energy. Relativistic effects are included using first-order perturbation theory. These results are used to make a better understanding of observed Be⁺ spectra.     

Effect of ultrasound on the dissolution kinetics of phosphate rock in HNO3

Ultrasound is known to enhance solid/liquid reactions. This paper deals with the investigation of the dissolution of phosphate rock in nitric acid, in the absence and presence of ultrasound. The reaction is first-order with respect to H⁺ and activation energy equal to 16 kJ/mol in both cases. The effect of ultrasound is on the pre-exponential factor A. An empirical relation is given, which relates rate constant to ultrasound power.     

Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.