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物理代写|电动力学代考Electrodynamics代写|FYS2016 Relativistic kinematics and four-vectors

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物理代写|电动力学代考Electrodynamics代写|Relativistic kinematics and four-vectors

The general kinematic idea is arranging all physical variables into such groups, that each of them presents a tensor in Minkowski’s space. Basic coordinates in spacetime $\left(x_{0}=c t, x_{1}=x, x_{2}=y, x_{3}=z\right)$ include the fourth (we call it zero) constituent ct and create the first order tensor – the vector with respect to Lorentz group. For the set of velocity components $v_{i}=\frac{d x_{i}}{d t}$ we naturally add the speed of light $c=\frac{d x_{0}}{d t}$. An important question arises: what is the temporal component $p_{0}$ of the momentum $p_{i}$ ? The sense of this additional component can be explained also by the invariant of a similar combination equation (4.19):
$$m_{0}^{2} c^{2}=p_{0}^{2}-p_{1}^{2}-p_{2}^{2}-p_{3}^{2},$$
marked on the right side with the inclusion, therefore the coefficient $c^{2}$ has been entered. In the rest system $p_{i}=0$, so the zero-component of the quadrupole momentum $p_{0}$ is proportional to the invariant lhs $p_{0}=m_{0} c$. The parameter $m_{0}$ is named as invariant mass.

物理代写|电动力学代考Electrodynamics代写|Relativistic mechanics

A fundamental physical postulate is that a transition to a different reference frame should not break the sense of the Maxwell equations. Here, in electrodynamics, let us stress, that the complete set of Maxwell’s equations includes not only field components but, as well, the charge and current density, that, for a charged particle is proportional to its velocity j ⃗= qv⃗. It means that the components of velocity, that enters the mechanics, should transform as the vector components in the space–time[14]. As was mentioned in the previous section 4.3; the fourth component of the fourvector of velocity is the velocity of light. Next, it is important to note that the complete (closed) system of equations (Maxwell ones + Newtons) should include also the Lorentz force [7]. So, we arrive at the main principle of the modern theoretical physics: it is the principle of general covariance [2]. It reads as The basic equations of physics should have the tensor form, each side of equation would have to be a some rank tensor with respect to the Lorentz group.

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物理代写|电动力学代考Electrodynamics代写|Relativistic kinematics and fourvectors

$\left(x_{0}=c t, x_{1}=x, x_{2}=y, x_{3}=z\right)$ 包括第四个 (我们称之为零) 成分 $\mathrm{ct}$ 并创建一阶张量 – 关于洛伦兹群的向量。对于速度分量 类似的组合方程 (4.19) 的不变量来解释:
$$m_{0}^{2} c^{2}=p_{0}^{2}-p_{1}^{2}-p_{2}^{2}-p_{3}^{2}$$

物理代写|电动力学代考Electrodynamics代写|Relativistic mechanics

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