اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Faraday induction law in relativity theory
156
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of four-velocity, defined on a circuit under its deforming motion. The obtained equations show one more facet of the physical meaning of electromagnetic potentials, where the motional and transformer parts of the flux rule are incorporated into a common phenomenon, reflecting the dependence of four-potential on spatial and time coordinates, correspondingly. It has been explicitly shown that for filamentary closed deforming circuit the flux rule is Lorentz-invariant. At the same time, analyzing a transformation of e.m.f., we revealed a controversy: due to causal requirements, the e.m.f. should be the value of fixed sign, whereas the Lorentz invariance of flux rule admits the cases, where the e.m.f. might change its sign for different inertial observers. Possible resolutions of this controversy are discussed.
قيم البحث
اقرأ أيضاً
Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newtons third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall show here t
hat to demonstrate the equivalence, we require the explicit use of the principle of superposition contained in Newtons second law. On the other hand, under some additional conditions the combined laws of conservation of linear and angular momentum, are equivalent to Newtons third law with central forces. The conditions for such equivalence apply in many scenarios of classical mechanics; once again the principle of superposition contained in Newtons second law is the clue.
Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all g
enerations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Baths law. Our theory shows that Baths law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +- 0.1 for Baths constant value around 1.2, our exact analytical treatment of Baths law provides new constraints on the productivity exponent alpha and the branching ratio n: $0.9 <= alpha <= 1$ and 0.8 <= n <= 1. We propose a novel method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the ``second Baths law for foreshocks: the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude.
The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wires magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only th
e particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher order post-adiabatic corrections make the orbits precess, but recent analysis of this `vector Kepler problem has shown that the effective Hamiltonian incorporating a post-adiabatic scalar potential (`geometric electromagnetism) fails to predict the precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the post-adiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a $1/r^3$ singularity which is an artifact of the adiabatic approximation.
Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these particles fro
m the exponential form of the decay law, that is the transition times region between exponential and non-expo-nen-tial form of the survival amplitude, occur much earlier than it follows from the classical standard approach boiled down to replace time $t$ by $t/gamma_{L}$ (where $gamma_{L}$ is the relativistic Lorentz factor) in the formula for the survival probability. The consequence is that fluctuations of the corresponding decay curves can appear much earlier and much more unstable particles have a chance to survive up to these times or later. It is also shown that fluctuations of the instantaneous energy of the moving unstable particles has a similar form as the fluctuations in the particle rest frame but they are seen by the observer in his rest system much earlier than one could expect replacing $t$ by $t/gamma_{L}$ in the corresponding expressions for this energy and that the amplitude of these fluctuations can be even larger than it follows from the standard approach. All these effects seems to be important when interpreting some accelerator experiments with high energy unstable particles and the like (possible connections of these effects with GSI anomaly are analyzed) and some results of astrophysical observations.
The existence of an internal frequency associated to any elementary particle conjectured by de Broglie is compared with a classical description of the electron, where this internal structure corresponds to the motion of the centre of charge around th
e centre of mass of the particle. This internal motion has a frequency twice de Broglies frequency, which corresponds to the frequency found by Dirac when analysing the electron structure. To get evidence of this internal electron clock a kind of experiment as the one performed by Gouanere et al. cite{Gouanere} will show a discrete set of momenta at which a resonant scattering effect, appears. The resonant momenta of the electron beam are given by $p_k=161.748/k$ MeV$/c$, $k=1,2,3,...$, where only, the corresponding to $k=2$, was within the range of Gouanere et al. experiment. The extension of the experiment to other values of $p_k$, would show the existence of this phenomenon.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
