Posted on Categories:General Relativity, 广义相对论, 物理代写

# 物理代写|广义相对论代写General Relativity代考|PHYS515 The Geodesic Hypothesis

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|广义相对论代写General Relativity代考|The Geodesic Hypothesis

The Geodesic Hypothesis. The first step toward this explanation involves recognizing that if $m_{G}$ were really equal to $m_{l}$, then equation $1.3$ would imply that all objects in a given gravitational field experience the same acceleration, and thus that all objects would follow the same trajectory in a given gravitational field if launched from the same position with the same initial velocity, even if they differ in mass and/or other characteristics. Note that such a statement is not true in electrostatics: objects with different charges follow different trajectories in a given electric field, even if their initial positions and velocities are the same. But in the gravitational case, it is as if the trajectory were determined by the space through which the objects move rather than by anything about the objects.

But how can empty space determine a trajectory? In the two-dimensional space represented by a flat piece of paper, there is a unique path between any two points that has the shortest pathlength: that path is a straight line. In the two-dimensional space corresponding to the surface of a globe, the analogous paths are “great circles.” Indeed, in the two-dimensional space corresponding to the surface of any smooth convex threedimensional object, we can find the shortest path between two points by stretching a string tightly between those points. In a general space, we call the paths that represent the shortest (more technically, the extremal) distance between two points a geodesic. A space’s geometric characteristics therefore define unique geodesic paths in that space.’

The geodesic hypothesis of general relativity asserts simply that A free particle follows a geodesic in spacetime.
(where “a free particle” is one free of non-gravitational interactions). According to this hypothesis, a gravitational field shapes spacetime, which in turn specifies the geodesics that particles must follow.

The geodesic hypothesis makes sense only in spacetime, not in three-dimensional space. To see this, consider a thrown ball moving in a parabolic trajectory from point $A$ to point $B$ in the space near the earth’s surface. But I could also fire a bullet from point $A$ in such a way that it passes through point $B$ : because of its greater speed, such a bullet would follow a much shallower parabola between the points (see figure 1.1). But the definition of a geodesic implies that there should be a unique geodesic between points $A$ and $B$. Therefore the ball and bullet, even though both are “free,” cannot both be following a geodesic, contrary to the hypothesis!

## 物理代写|广义相对论代写General Relativity代考|Why Gravitational Mass Is Inertial Mass

Why Gravitational Mass Is Inertial Mass. If we accept the geodesic hypothesis, then gravitational and inertial mass are the same thing, as I will now argue. Note that near the earth’s surface, the geodesic for an object released from rest is a trajectory where the object accelerates downward at a rate of $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$. According to the geodesic hypothesis, this is the “natural” path for a free object to follow, analogous to the straight-line geodesic an object would “naturally” follow in deep space (far from any gravitating objects). Now in deep space, accelerating an object away from a straightline geodesic requires one to exert a force on the object. Analogously, if I hold an object at rest near the earth, I must exert an upward force on the object sufficient to accelerate it at a rate of $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ relative to the downward geodesic it naturally wants to follow. The magnitude of force required, according to Newton’s second law, is simply $m_{l} g$, where $m_{l}$ is the object’s inertial mass.

However, it is precisely the magnitude of the upward force required to hold an object at rest that scales and balances measure when we “weigh” an object. In Newtonian mechanics, we imagine this upward force to be balanced by (and equal in magnitude to) a “gravitational force” $m_{G} g$ acting on the object, and thus we imagine the scale to register the object’s “weight,” which (after division by $g$ ) yields the object’s gravitational mass $m_{G}$. But from the perspective of general relativity, the only real force acting on the object is the upward force (since a net force is required to accelerate an object relative to its geodesic), and that net force has a magnitude of $m_{l} g$. Therefore, when we think we are measuring an object’s gravitational mass using a scale, what we are really measuring its resistance to acceleration. So of course $m_{G}=m_{f}$ : they are really the same thing!

## 物理代写|广义相对论代写General Relativity代考|The Geodesic Hypothesis

（其中“自由粒子”是没有非引力相互作用的粒子）。根据这一假设，引力场塑造了时空，而时空又指定了粒子必须遵循的测地线。

## 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。