# 物理代写|理论力学作业代写Theoretical Mechanics代考|PHYS386

#### Doug I. Jones

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## 物理代写|理论力学作业代写Theoretical Mechanics代考|EPR and conservation laws

A similar “realistic” approach can be adopted to discuss the third counterintuitive quantum phenomenon, the famous EPR “paradox”, whose solution, after the numerous experiments confirming the violation of Bell’s inequalities, can only be expressed by saying that Einstein was wrong in concluding that quantum mechanics is an incomplete theory.

Usually people ask: how is it possible that when the first particle of a pair initially having zero total angular momentum acquires in interaction with its filter a sharp value of a given component of its angular momentum, the far away particle comes to “know” that its own angular momentum component should acquire the same and opposite value? I do not think that a realistic interpretation of this counterintuitive behaviour can be “explained” by minimizing the difference with its classical counterpart, because this difference has its roots, in my opinion, in the “ontological” (or irreducible) – not “epistemical” (or due to imperfect knowledge) – nature of the randomness of quantum events. If this is the case, one has in fact to accept that physical laws do not formulate detailed prescriptions, enforced by concrete physical entities, about what must happen in the world, but only provide constraints and express prohibitions about what may happen. Random events just happen, provided they comply to these constraints and do not violate these prohibitions.

From this point of view, the angular momentum component of the far away particle has to be equal and opposite to the measured value of the first particle’s component, because otherwise the law of conservation of angular momentum would be violated. In fact, the quantity “total angular momentum” is itself, by definition, a non-local quantity. Non locality therefore needs not to be enforced by a mysterious action-at-a-distance. The two filters are not two uncorrelated pieces of matter: they are two rigidly connected parts of one single piece of matter which “measures” this quantity. The non local constraint is therefore provided by the nature of the macroscopic “instrument”. This entails that, once the quantum randomness has produced the first partial sharp result, there is no freedom left for the result of the final stage of the interaction: there is no source of angular momentum available to produce any other result except the equal and opposite sharp value needed to add up to zero for the total momentum.

We arrive to the conclusion that Bohr was right, but Einstein was not wrong in insisting that an uncritical acceptance of the current interpretation of QM would lead to absurd statements about the physical nature of the world we live in.

## 物理代写|理论力学作业代写Theoretical Mechanics代考|The randomness of quantum reality in phase space

After eighty years of Quantum Mechanics $(Q M)$ we have learned to live with wave functions without worrying about their physical nature. This attitude is certainly justified by the extraordinary success of the theory in predicting and explaining not only all the phenomena encountered in the domain of microphysics, but also some spectacular nonclassical macroscopic behaviours of matter. Nevertheless one cannot ignore that the wave-particle duality of quantum objects not only still raises conceptual problems among the members of the small community of physicists who are still interested in the foundations of our basic theory of matter, but also induces thousands and thousands of physics students all around the world to ask each year, at their first impact with Quantum Mechanics, embarassing questions to their teachers without receiving really convincing answers.

We have seen that typical examples of this insatisfaction are the nonseparable character of long distance correlated two-particle systems and the dubious meaning of the superposition of state vectors of measuring instruments, and in general of all macroscopic objects (Schrödinger 1935). In the former case experiments have definitely established that Einstein was wrong in claiming that QM has to be completed by introducing extra “hidden” variables, but have shed no light on the nature of the entangled two-particle state vector responsible for the peculiar quantum correlation between them, a correlation which exceeds the classical one expected from the constraints of conservation laws.

In the latter case, generations of theoretical physicists in neoplatonist mood have insisted in claiming that the realistic aspect of macroscopic objects is only an illusion valid For All Practical Purposes (in jargon FAPP). The common core of their views is the belief that the only entity existing behind any object, be it small or large, is its wave function, which rules the random occurrence of the object’s potential physical properties. The most extravagant and bold version of this approach is undoubtedly the one known as the Many Worlds Interpretation of QM Everett E.(1973), which goes a step further by eliminating the very founding stone on which QM has been built, namely the essential randomness of quantum events. Chance disappears: the evolution of the whole Universe is written – a curious revival of Laplace – in the deterministic evolution of its wave function. “The Many-Worlds Interpretation (MWI) – in the words of Lev Vaidman, one of its most eminent supporters (Vaidman 2007) – is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same time and in the same space. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.”

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## 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。

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