### 物理代写|广义相对论代写General relativity代考|PHY475

statistics-lab™ 为您的留学生涯保驾护航 在代写广义相对论General relativity方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义相对论General relativity代写方面经验极为丰富，各种代写广义相对论General relativity相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|广义相对论代写General relativity代考|Physics Consequences

First, consider simultaneity. $\mathrm{O}$ and $\mathrm{O}^{\prime}$ are coincident. $\mathrm{O}^{\prime}$ says two events occur at the same time so $d t^{\prime}=0$, but at positions from the origin $\pm d z^{\prime}$. $\mathrm{O}$ says that the time differences from zero of the two events are,
$$d t_{\pm}=\pm \gamma V d z^{\prime}, \quad d t_{+}-d t_{-} \neq 0 .$$
In general, observers in relative motion do not agree on simultaneity. Only if events are spatially coincident will observers so agree. Thus, to compare times, clocks at the same spatial position have to be compared. Also note, the present position of $\mathrm{O}^{\prime}$, when all clocks are synchronized, is connected with all points in the past, present, and future of $\mathrm{O}$. In spacetime, all space and time points are available. Time isn’t a special quantity, it’s just a one-dimensional projection of spacetime.

Next consider causality. In the unprimed frame, observer $\mathrm{O}$ fires a bullet at $t=0$ from the origin. It hits a target at time $d t$ and position $d z=v_{b} d t$, where $v_{b}$ is the speed of the bullet. $\mathrm{O}^{\prime}$ also says the bullet was fired from the origin at $t^{\prime}=0$, as that’s where the clocks were synchronized. $\mathrm{O}^{\prime}$ says the target was hit at
$$d t^{\prime}=\gamma\left(d t-V\left[v_{b} d t\right]\right)=d t \gamma\left(1-V v_{b}\right)$$
According to $\mathrm{O}^{\prime}$, if $d t^{\prime}<0$, the target is hit before the bullet is fired. That would violate causality, and can happen only if $v_{b}>1$. Thus, $c=1$ is the limiting speed.

## 物理代写|广义相对论代写General relativity代考|Spacetime Diagrams

Many GR texts stress the concept of spacetime diagrams. Analytic calculations are favored by this author. However, for completeness, the former are briefly discussed in this section. One draws on a flat sheet, and must be concerned with four coordinates. Thus, one-dimensional motion, in the $z$-direction, is considered.

Draw a set of axes for frame $\mathrm{O}$ as shown on the top of Fig. 1.5. The upward vertical axis represents increasing time $t$, while the rightward horizontal axis represents increasing $z$. At some time $t_{1}$, particle $\mathrm{A}$ is at $z_{1}$. If particle A has rest mass, it can remain at rest with respect to O. Its world line is just a vertical line upward from $\left(z_{1}, t_{1}\right)$. On the clock attached to $\mathrm{A}$, the coordinate time duration $d t$ is just the proper-time duration $d \tau$. Photons $\mathrm{B}$ and $\mathrm{C}$, starting from the same position and time, must move with unit speed $\left|\frac{d z}{d t}\right|=1$. Events outside of the triangle, defined by world lines $\mathrm{B}$ and $\mathrm{C}$, are inaccessible starting from $\left(z_{1}, t_{1}\right)$. This triangle is called the future triangle. If motion in two spatial directions is considered, the triangle becomes a cone.

A massive particle $\mathrm{D}$, that moves with constant speed $V<1$ relative to $\mathrm{O}$, has a world line with $\left|\frac{d z}{d t}\right|<1$. Its proper-time duration, measured relative to $t_{1}$, is $d \tau=d t / \gamma$. Here, $d t$ is the time on a clock at rest with respect to $\mathrm{A}$ that, according to $\mathrm{D}$, is coincident with D’s position. Let twins $\mathrm{O}$ and $\mathrm{O}^{\prime \prime}$ start at this spacetime point. O notes that her twin, moving with accelerated motion, always stays within the future triangle, at first moving away from $\mathrm{O}$, but later returning. The gist of the twin “paradox” is that it is only $\mathrm{O}^{\prime \prime}$ that experiences acceleration. If not created at $\left(z_{1}, t_{1}\right)$, then $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$, and $\mathrm{O}^{\prime \prime}$ can get there only from the past triangle, obtained by extending $\mathrm{B}$ and $\mathrm{C}$ backwards in time.

## 物理代写|广义相对论代写General relativity代考|Physics Consequences

$$d t_{\pm}=\pm \gamma V d z^{\prime}, \quad d t_{+}-d t_{-} \neq 0 .$$

$$d t^{\prime}=\gamma\left(d t-V\left[v_{b} d t\right]\right)=d t \gamma\left(1-V v_{b}\right)$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。