| 沈建其： 你始终写不出能够处理初始项的“Lorentz变换”，我就试着写一个给大家参观参观。 x′- xo′＝ k[(x - xo)－ v(t - to)] 、 t′- to′＝ k[（t - to）－ v (x – xo)/cc] ， x – xo ＝ k[（x′- xo′）+ v (t′- to′)] t - to ＝ k[（t′- to′）+ v( x′- xo′)/cc] ； 这是在“Lorentz一世”基础上改造出来的“玩艺”，你研究一下，看看能不能满足四个坐标系共变的要求。如果行，不用再争，OK！如果不行，还要用别的变换，你写出来好了。我们现在的分析不是在庞加莱变换上面，我对庞加莱作出的数学研究完全信任。问题在于爱氏认为庞加莱到死都没有弄懂相对论！如果后人非要把爱氏发明的相对论与庞加莱研究的相对论混为一谈，这显然是在回避错误。 因我马上要换电脑，重新安装电脑，可能在几天内不能上网。你发帖后，我可能在几天后才能来回帖。 Ccxdl 2002年1月2日 |
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物理的东东能在数学中争出什么？ Lorentz变换从何而来，它是从物理上推导出来的，而不是从数学上导出来的。对于这点我们明白了，又何苦与沈争来争去呢。想论应说明Lorentz变换导出的错误根源，仅从数学中是找不到毛病，它的根源是物理上的，就是光速的绝对性，否定光速的绝对性， Lorentz变换就不用我们再去反驳它了，这是不攻自破的道理所在。 ※※※※※※ 逆子 |
| 沈建其： 你始终写不出能够处理初始项的“Lorentz变换”，我就试着写一个给大家参观参观。 x′- xo′＝ k[(x - xo)－ v(t - to)] 、 t′- to′＝ k[（t - to）－ v (x – xo)/cc] ， x – xo ＝ k[（x′- xo′）+ v (t′- to′)] t - to ＝ k[（t′- to′）+ v( x′- xo′)/cc] ； 这是在“Lorentz一世”基础上改造出来的“玩艺”，你研究一下，看看能不能满足四个坐标系共变的要求。如果行，不用再争，OK！如果不行，还要用别的变换，你写出来好了。 {{{{{{{{应该说你很聪明,就是这个形式.不过它还是不算大,庞加莱变换比他还要大一点,但无所谓.你这个变换就是我们说的庞加莱变换! 我因为庞加莱变换是用算符矩阵表示,有上标下标太麻烦,所以一直没有输出来.}}}}}}}} 我们现在的分析不是在庞加莱变换上面，我对庞加莱作出的数学研究完全信任。问题在于爱氏认为庞加莱到死都没有弄懂相对论！如果后人非要把爱氏发明的相对论与庞加莱研究的相对论混为一谈， {{{{{{{这里你错了. 庞加莱承认不承认相对论与庞加莱变换是两回事,不可附会起来.}}}}}}}} 这显然是在回避错误。 因我马上要换电脑，重新安装电脑，可能在几天内不能上网。你发帖后，我可能在几天后才能来回帖。 Ccxdl 2002年1月2日 |
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回复Relativistic quantum gravitational effects Relativistic quantum gravitational effects in weak-gravitational fields Jian Qi Shen, Hong Yi Zhu 1. Zhejiang Institute of Modern Physics & Department of Physics of Zhejiang University, Hangzhou 310027, P.R.China 2.State Key Laboratory of Modern Optical Instrumentation, Center for Optical and Electromagnetic Research, College of Information Science and Engineering, Zhejiang University, Hangzhou 310027, P.R.China On the basis of the theoretical and experimental works concerning spin-rotation coupling by Mashhoon et al., we predict three relativistic quantum gravitational effects associated with gravitomagnetic fields: geometric quantum phase factor of a spinning particle interacting with time-dependent gravitomagnetic field, and non-inertial gravitational wave in time-dependent rotating reference frame as well as the gravitomagnetic Meissner effect. By means of neutron-gravity interferometry experiment, this geometric phase factor due to time-dependent spin-rotation coupling can be applied to obtaining information on the small fluctuations of Earth rotating frequency. Mashhoon spin-rotation coupling is a static case, while the interaction of the intrinsic spin of a particle with the non-inertial gravitational wave is its mobile realization. Utilizing the similarities between gravitational force and electromagnetic force in some aspects, we propose the gravitational analogue of Meissner effect in superconductivity, i.e., gravitational Meissner effect, which gives a valuable insight into the problems of cosmological constant and vacuum gravity. With the improvements in precise measuring instruments, particularly the laser technology, it becomes possible for investigating quantum mechanics in weak-gravitational fields, which provides tests of Einstein theory of General Relativity in quantum regime. According to the equivalence principle in General Relativity, the nature of spin-rotation coupling is merely the interaction between the gravitational spin-magnetic moment and the gravitomagnetic field. By considering the Doppler effect of a light signal in the non-inertial reference frame rotating relative to the fixing reference frame, Mashhoon obtained the Hamiltonian of the intrinsic spin-rotation coupling which is of the form with and denoting the rotating frequency of the rotating frame and the intrinsic spin of a photon, respectively. In the framework of general relativity, however, we transform the Kerr metric from the fixing reference frame to the rotating frame, and calculate the exterior gravitomagnetic potential (one of the metric components ) of the spherically symmetric rotating body as follows (1) which is obtained by using the weak-field approximation, where and is respectively the speed of light and the gravitational constant, is so defined that represents the angular momentum per unit mass of this gravitating body, and stand for the displacements of the spherical coordinate fixed in the rotating reference frame. It follows that the first term on the right handed side in Eq. (1) is related to the gravitational constant and is vanishing when the radial coordinate , whereas the second term does not vanish since it arises from the coordinates transformation in terms of the equivalence principle. It is of interest that the second term in Eq. (1) gives rise to a gravitomagnetic field whose strength is just the rotating frequency of the rotating frame, with respect to the fixing reference system. Magnetic field results in the Lorentz force acting on a charged particle, in the similar fashion, the non-inertial gravitimagnetic field yields the fictitious Coriolis force acting on a moving particle. In view of above discussion, one can also obtain the same Hamiltonian of spin-rotation coupling by using the Dirac eqution with spin connection in curved spacetimes. Essentially, we can draw a conclusion that the interaction of the gravitational magnetic moment and the gravitomagnetic field involves spin-rotation coupling. The spin-rotation coupling leads to the inertial effects of the intrinsic spin of a particle, for instance, although the equivalence principle still holds, the universality of the law of freely falling particles is violated, provided that the spin is polarized vertically up or down in the non-inertial frame. Since there exists observational evidence for the coupling of spin- particle with the rotation of the Earth, we suggest a geometric effect in the coupling of the neutron spin with the time-dependent rotation of the Earth. Since the analogy can be drawn between gravity and electromagnetic force in some aspects, Aharonov and Carmi proposed the geometric effect of the vector potential of gravity, and Anandan, Dresden and Sakurai et al. proposed the quantum-interferometry effect associated with gravity. What they investigated is now termed Aharonov-Carmi effect which is the gravitational analogue of Aharonov-Bohm effect in electrodynamics that appears as a geometric quantum phase factor (namely, Berry phase factor) in the wave function of an electron moving along a closed path surrounding a magnetic flux. Although the spin-rotation coupling and Aharonov-Carmi effect have the sameorigion, namely, both arise from the presence of the Coriolis force (the interaction of the motion of the particle with the non-inertial frame), we argue that the Aharonov-Carmi effect mentioned above does not comprise a new geometric effect due to the time-dependent rotation of the non-inertial frame. It is well known that the geometric phase factor appears in the quantum systems whose Hamiltonian is time-dependent or possesses evolution parameters. Differing from the dynamical phase which is related to the energy, frequency or velocity of a particle or a quantum system, geometric phase depends only on the geometric nature of the pathway along which the system evolves, which reflects the global and topological properties of evolution of the quantum systems. By making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, we compute the geometric phase that results from neutron spin-rotation coupling in which the rotating frequency is time-dependent. The result may be written as follows (2) with being the angle displacements over the parameters space of the conserved invariant, an operator whose eigenvalue is time-independent; corresponding to the neutron spin polarized vertically up and down. For the case of the adiabatic limit in which is a constant, the geometric phase in one cycle over the parameter space is then where is the expression for the solid angle which presents the geometric properties of time evolution of this spin-rotation system. At present, investigation of geometric phase factor is an important direction in atomic and molecular physics, quantum optics, condensed matter physics and molecular reaction chemistry as well. Geometric phase factor has many applications in various branches of physics, say, in the case of spin-rotation coupling, a potential application can be suggested. Since this geometric phase reveals the time evolution of , information on the Earth variations of rotation will be obtained by measuring the geometric phase of the polarized neutrons through the neutron interferometry experiment. Mashhoon spin-rotation or spin-gravity coupling is confined within the static case in which the rotating frequency is independent of time. Here we propose another interaction where the intrinsic spin of a particle is coupled to a propagating gravitomagnetic field. Einstein theory of General Relativity predicts that the accelerated mass produces the propagation of the space-time curvature which is termed gravitational wave. Detecting and investigating these space-time ripples is one of the leading areas in astrophysics and cosmology. Because of the weakness of the gravitational radiation, gravitational wave has not been detected at present even by means of both resonant-mass detectors and laser-interferometric detectors. In this report, however, we suggest the concept of non-inertial gravitational wave which does not relate to the smallness of the gravitational constant. Further detailed reasons are illustrated in the following. It follows from Eq. (1) that the rotation of the frame yields additional space-time curvature (expressed by ) which is independent of the gravitational constant, . If , therefore, the rotating frequency varies with time, the variations of the space-time curvature (the disturbance of the gravitational field) in the rotating reference frame propagates outwards in the form of wave motion, such a propagating disturbance is a non-inertial gravitational wave (NGW). By ignoring some small terms and higher-order terms, the wave equation of motion involving source terms is readily obtained (3) where and denote the amplitudes of gravitational wave and the mettic tensor of the flat Minkowski spacetime, respectively; and are the matrix elements of coordinate transformation frome the fixing frame to the rotating frame; with and being the energy-momentum tensor of matter. Further analysis shows that there exist only two kinds of amplitudes of NGW, i.e., and in the time-dependent rotating reference frame, and the expressions of the source term on the right handed side of Eq. (3) are respectively of the form and . Note, however , that this NGW depends on the non-inertial reference frame and differs from the standard gravitational wave predicted by Einstein. Experimental evidence for spin-rotation coupling exists in the microwave and optical regimes via the phenomenon of frequency shift of polarized radiation. It is believed that with the foreseeable improvements in detecting technology, the interaction between spin and NGW can also be detected. Since the existence of spin-rotation coupling is observed only from the non-inertial frame, NGW is thus defined to be such space-time ripples associated with the non-inertial reference frame. It is therefore apparent that investigation of NGW is of interest since its intensity is no longer dependent on the gravitational wave. Although it possesses the non-inertial properties, this NGW can be coupled to matter. It is shown in what follows that the coupling coefficient is dependent on the gravitational constant, . In London electrodynamics of superconductivity, the velocity of the superconducting electrons and the magnetic potentials satisfies which leads to the self induced charge current and thus provides photons field with an effective mass term in field equation or Lagrangian of electrodynamics. This procedure is equivalent to the mechanism of spontaneous symmetry breaking. In the theory of gravity, the similar phenomenon exists since the momentum density is conserved around the particles scattering, which is in analogy with the case in the superconductor where the electric current density is also conserved around scattering. Note that the Einstein equation of gravitational field under the low-motion weak-field approximation is formally analogous to the Maxwell equation of electromagnetic field, one can arrive at the similar relation between the velocity of particles and the gravitomagnetic vector potentials , where . From the point of view of the low-motion weak-field approximation, the self induced mass current results from this coupling of gravity to matter and then enables the gravitational field to possess an effective mass, , where and denote the Planck constant and the mass density of matter, respectively. Apparently, the NGW is not merely the non-inertial effect, for the effective mass of NGW is related to the gravitational constant, . It is of interest to compare the weak-gravitational theory with London electrodynamics of superconductivity. The formal analogy between the gravitational field equation of weak-field approximation and Maxwell equation results in several similarities in perfect fluid and superconductor (Table 1). Our attentions will focus on the two queries in Table 1. A concept of gravitomagnetic charge which is considered the dual charge of mass is proposed by taking into account the fact that Dirac monopole (magnetic charge) is the dual charge of the electric charge. Since the concept of mass is of no use for the gravitomagnetic charge, it is interesting to establish its relativistic dynamics. The effect in the theory of weak gravity corrresponding to the Meissner effect in superconductivity theory is the gravitational Meissner effect. By combination of the gravitational Meissner effect with gravitomagnetic charge (should such exist), we briefly take into consideration the problems of the smallness of the observed cosmological constant and vacuum gravity. In accordance with quantum field theory, vacuum possesses infinite zero-point energy density due to the vacuum quantum fluctuations; whereas according to Einstein theory of General Relativity, infinite vacuum energy density yields the divergent curvature of spacetime, namely, the spacetime of vacuum is extremely curved. However it is apparently in contradiction with the experimental observations. In the context of quantum field theory a cosmological constant corresponds to the energy density associated with the vacuum. However, a diverse set of observations suggest that the universe possesses a nonzero but very small cosmological constant. How to give a natural interpretation for the above paradox? Here, provided that vacuum matter is perfect fluid, we suggest a potential explanation by using the gravitational Meissner effect: the gravitoelectric field (Newtonian field of gravity) produced by the gravitoelectric charge (mass) of the vacuum quantum fluctuations is exactly canceled by the gravitoelectric field due to the current of the gravitomagnetic charge (dual mass) of the vacuum quantum fluctuations; the gravitomagnetic field produced by the gravitomagnetic charge of the vacuum quantum fluctuations is exactly canceled by the gravitomagnetic field due to the current of the gravitoelectric charge (mass current) of the vacuum quantum fluctuations. Thus, at least in the framework of weak-field approximation, the extreme space-time curvature of vacuum caused by its large energy density does not arise, and the gravitational effects of cosmological constant is eliminated by the contributions of the gravitomagnetic charge (dual mass). If gravitational Meissner effect is of really physical significance, then it is necessary to apply this effect to the early universe. For the present, it is possible to investigate the quantum mechanics in the weak-gravitational field, with the development of measuring technology such as laser technology and so on. These investigations enable physicists to test the validity or universality of fundamental laws and principles of General Relativity in, for instance, the microscopic quantum regimes. The above three effects associated gravitomagnetic field reflect the relativistic quantum gravitational properties of matter-gravity coupling in the weak-gravitational field. It is believed that these effects will give rise to further interest of investigation since there exist many physically potential applications in quantum theory, gravity theory, cosmology, applied physics and some related areas. References and notes |