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我们提供的理论力学Theoretical Mechanics及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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|理论力学作业代写Theoretical Mechanics代考|PHY306

物理代写|理论力学作业代写Theoretical Mechanics代考|The two slits experiment

In order to introduce the reader to the issues at stake I will briefly recall the essence of the debate between Bohr and Einstein which took place after the Fifth Solvay Conference (1927) where for the first time the different independent formulations of the new theory were presented by Heisenberg, Dirac, Born and Schrödinger, together with their common interpretation by Bohr – the socalled “Copenhagen interpretation” of Quantum Mechanics which won since then a practically unanimous acceptance by the community.

This acceptance remained unquestioned for thirty years until when the books by Max Jammer (Jammer a1966, b1974) presented again to the new generation of physicists the ambiguities which still remained unsolved, and stimulated a renewed interest on those conceptual foundations of the theory which had been set aside under the impact of the the extraordinary experimental and theoretical boom of physics triggered at the end of World War 2 by the opening of the Nuclear Era.

The central issue of the debate, according to Jammer’s reconstruction (Jammer b1974 p.127), was “whether the existing quantum mechanical description of microphysical phenomena should and could be carried further to provide a more detailed account, as Einstein suggested, or whether it already exhausted all possibilities of accounting for observable phenomena, as Bohr maintained. To decide on this issue, Bohr and Einstein agreed on the necessity of reexamining more closely those thought-experiments by which Heisenberg vindicated the indeterminacy relations and by which Bohr illustrated the mutual exclusion of simultaneous space-time and causal descriptions.”

The thought experiment which both agreed to discuss was the diffraction of a beam of particles of momentum $p$ impinging perpendicularly on a screen $\mathrm{D}$ with two slits $\mathrm{S}{1}$ and $\mathrm{S}{2}$ at a distace $d$ from each other. Each particle, which passes through, falls, deviating at random from its initial direction, on a photographic plate $P$ located after the screen. When a sufficiently high number of particles has been detected, a distribution of diffraction fringes typical of a wave with a central maximum and adjacent minima and less pronounced maxima appears. Each particle is detected locally, but seems to propagate as a wave.

物理代写|理论力学作业代写Theoretical Mechanics代考|The EPR paradox

The second phase of the debate sees a change in Einstein’s strategy of proving that the description of reality given by Quantum Mechanics is incomplete. This phase is based on the formulation of the EPR (Einstein, Podolski, Rosen) paradox (Einstein et al 1935).. I will briefly sketch its main argument, even if it is not essential for the further development of the argument of this Chapter.

This is how the authors formulate the basic assumption of their argument: “If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”
Consider a system of two particles in a state in which the relative distance $\mathrm{x}{1}-\mathrm{x}{2}=\mathrm{a}$ and their total momentum $\mathrm{p}{1}+\mathrm{p}{2}=\mathrm{p} \quad$ are fixed. This is possible because these quantities are not complementary. Then EPR argue as follows. By measuring the position $\mathrm{x}{1}$ of the first particle it is possible, without interfering directly with the second particle, determine its position $\mathrm{x}{2}=$ $a+x_{1}$. This means that, according the initial definition, that $x_{2}$ is an element of reality. However, we might have chosen to measure, instead of $x_{1}$ the momentum $p_{1}$ of the first particle. This measurement would have allowed us to assess, without interfering in any way with the second particle, that its momentum $\mathrm{p}{2}=\mathrm{p}{2} \mathrm{p}{1}$ is an element of reality. This would have allowed to conclude that $\mathrm{p}{2}$ is an element of reality. Therefore, Einstein sums up, Quantum Mechanics is incomplete.

Bohr’s answer stresses once more that one cannot speak of quantities existing independently of the actual procedure of measuring them: “From our point of view we now see that the wording of the above mentioned criterion of physical reality proposed by EPR contains an ambiguity as regards the meaning of the expression “without in any way disturbing a system”. Of course there is, in a case like that just considered, no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term “physical reality” can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantummechanical description is essentially incomplete.”

物理代写|理论力学作业代写Theoretical Mechanics代考|PHY306


物理代写|理论力学作业代写Theoretical Mechanics代考|The two slits experiment

为了向读者介绍所涉及的问题,我将简要回顾一下在第五次索尔维会议(1927 年)之后发生的玻尔和爱因斯坦之间辩论的本质,该会议首次提出了新理论的不同独立表述海森堡、狄拉克、玻恩和薛定谔,以及他们对玻尔的共同解释——量子力学的所谓“哥本哈根解释”,从那时起,几乎得到了社会的一致认可。

三十年来,这种接受一直没有受到质疑,直到 Max Jammer (Jammer a1966, b1974) 的著作再次向新一代物理学家展示了仍未解决的模棱两可的问题,并激发了人们对该理论的概念基础的新兴趣。在第二次世界大战结束时核时代的开启引发了非凡的物理学实验和理论热潮的影响下被搁置了。

根据 Jammer 的重建(Jammer b1974 p.127),辩论的核心问题是“是否应该并且可以进一步推进现有的对微观物理现象的量子力学描述,以提供更详细的解释,正如爱因斯坦所建议的那样,或者正如玻尔所坚持的那样,已经用尽了解释可观察现象的所有可能性。为了决定这个问题,玻尔和爱因斯坦同意有必要更仔细地重新检查那些海森堡证明不确定性关系的思想实验,以及玻尔说明同时时空和因果描述的相互排斥的思想实验。”


物理代写|理论力学作业代写Theoretical Mechanics代考|The EPR paradox

辩论的第二阶段看到爱因斯坦证明量子力学对现实的描述不完整的策略发生了变化。这一阶段基于 EPR(爱因斯坦、波多尔斯基、罗森) 悖论 (Einstein et al 1935) 的表述。我将简要概述它的主要论点,即使它对于本章论点的进一步发展不是必需的.
这就是作者如何制定他们论证的基本假设的方式:“如果我们可以在不以任何方式干扰系统的情况下确定地预测一个物理量的值,那么就 存在与该物理量相对应的物理现实元素。
考虑一个由两个粒子组成的系统,其相对距离为 $\mathrm{x} 1-\mathrm{x} 2=\mathrm{al}$ 以及它们的总动量 $\mathrm{p} 1+\mathrm{p} 2=\mathrm{p}$ 是固定的。这是可能的,因为这些数量不 是互补的。然后EPR争论如下。通过测量位置x1对于第一个粒子,可以在不直接干扰第二个粒子的情况下确定其位置 $x=a+x_{1}$. 这意味 着,根据最初的定义, $x_{2}$ 是现实的一个元素。然而,我们可能选择测量,而不是 $x_{1}$ 势头 $p_{1}$ 的第一个粒子。这种测量将使我们能够在不以 任何方式干扰第二个粒子的情况下评估它的动量 $\mathrm{p} 2=\mathrm{p} 2 \mathrm{p} 1$ 是现实的一个元素。这本来可以得出这样的结论 $\mathrm{p} 2$ 是现实的一个元素。因 此,爱因斯坦总结道,量子力学是不完整的。
玻尔的回答再次强调,人们不能独立于测量它们的实际程序来谈论存在的量: “从我们的观点来看,我们现在看到,EPR 提出的上述物理 现实标准的措辞包含关于”不以任何方式干扰系统”一词的含义。当然,在刚刚考虑的这种情况下,在测量过程的最后一个关键阶段,所研 究的系统不会出现机械干扰的问题。但即使在这个阶段,本质上也存在对定义有关系统末来行为的可能预测类型的条件的影响的问题。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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