Quantum Measurement at the Mimit? Idealization, Emergence, and Spontaneous Symmetry Breaking

本提案的智力价值在于为测量问题（MP）提出了一种新的解决方案：宏观极限理想化（ML）下的解决方案。MP是物理学基础上的主要问题之一，如果不是问题的话。因为这是我在过去六年多的努力中最后的，也是最重要的一部分，我在理想化和近似的性质，模型建立，热力学极限，相变和临界现象，自然定律，以及经典和量子自发对称性破缺（SSB）方面的工作，其中一些得到了以前的NSF资助（No. 5）。SES-9910889)，其结果，除了其自身的优点，将验证和改进这些领域的结果。这个期末项目可以看作是对我以前在科学哲学方面的贡献的测试和展示。MP的困难集中在理论假设发生在微观层面和发生在宏观层面之间的明显矛盾。所有解决这个问题的现有尝试似乎都有一个不可避免的假设，即所有涉及的系统都有无限个自由度（或有限）。但是有限量子系统有不可消除的叠加效应，就像所有有限热系统都有波动一样；这样的影响似乎使MP的严格解决方案变得不可能。我建议我们放弃这个假设。有一种合理而严格的数学方法（代数方法）可以想象，在适当的限制下，所涉及的系统具有无限的自由度（或无限）。此外，ssb仅在ML下是可能的，并且它可以用来取代正统公式中波函数的“坍缩”概念。这个项目的广泛影响是多方面的。鉴于其性质，该项目将主要为对哲学和物理学感兴趣的专家和公众提供研究论文（可能还有专著）和讲座或演讲。因为这个项目处理的是MP，可以说是物理学基础中最重要的一个问题，因此它的结果影响深远。研究量子物理学和现代物理学革命的历史学家会发现，提出的解决方案的精神更接近量子物理学的创始人（玻尔等人和哥本哈根学派）的观点。对科学学科之间的共生关系感兴趣的研究人员会发现，量子物理学中顽固的正统学说——希尔伯特空间方法——是如何被固态物理学的结果所取代的（如果我是对的），这是很有趣的；或者量子物理学的“基础”是如何被固态模型动摇的（在基础研究中，这一领域不那么基础，因此被忽视了）。一个挑战量子物理概念中普遍存在的偏见的MP解决方案应该为该领域的新可能性打开大门，这应该引起理论物理学家和数学家的注意。我将尽一切努力把这些成果融入到我的教学中，在杰克逊维尔的社区学院和附近佛罗里达北部和中部的大学，以及国内外的专业会议和座谈会上发表演讲。

Project Summary The intellectual merit of this proposal is to argue for a new solution to the measurementproblem (MP): a solution under the idealization of macroscopic limit (ML). MP is one of the mainproblems, if not the problem, at the foundations of physics. Because this is the last, and the mostimportant, part of my multi-stage effort that in the past six or so years has produced works on thenature of idealization and approximation, of model-building, of thermodynamic limit, of phasetransitions and critical phenomena, of laws of nature, and of classical and quantum spontaneoussymmetry breaking (SSB), some of which are supported by a previous NSF grant (No. SES-9910889), its results, apart from their own merit, will validate and improve on results in those areas.This final project may be seen as a test and showcase of my previous contributions to philosophy ofscience. The difficulty of MP centers on an apparent contradiction between what theorieshypothesize happens at the micro-level and what happens at the macro-level. All existing attempts tosolve the problem make what seems to be an inescapable assumption that all systems involved are offinite number of degrees of freedom (or finite). But finite quantum systems harbor ineliminatablesuperpositional effects, just as all finite thermo-systems harbor fluctuations; and such effects seem tomake a rigorous solution of MP impossible. I propose that we drop the assumption. There is asound and rigorous mathematical way (the algebraic approach) to imagine, with properly taken limits,that the systems involved are of infinite number of degrees of freedom (or infinite). Moreover, SSBis only possible under ML, and it can be used to replace the notion of the 'collapse' of wave functionsin the orthodox formulation. The broader impacts of this project are many-fold. Given its nature,this project will mainly produce research papers (and possibly a monograph) and lectures or talks toaudiences of both experts and general public interested in philosophy and physics. Because theproject tackles MP, the arguably single most important problems in the foundations of physics, thereverberation of its results is far-reaching. Historians of quantum physics and of the revolution ofmodern physics will find the spirit of the proposed solution closer to the views of the founders ofquantum physics (Bohr et al and the Copenhagen school). Researchers interested in the symbioticrelationships between disciplines of science will find it interesting to see how a recalcitrant orthodoxposition in quantum physics -- the Hilbert-space approach -- is unseated (if I am right) by results insolid state physics; or how the 'foundation' of quantum physics is shaken by models in solid state (amuch less fundamental and hence neglected area in foundational studies). A solution to MP thatchallenges the prevailing bias in the conception of quantum physics should open the door for newpossibilities in the field, which should get the attention of theoretical physicists and mathematicians.Every effort will be made to incorporate the results into my teaching, to give talks at the communitycollege at Jacksonville and at nearby universities of north and central Florida, as well as atprofessional meetings and colloquia here and abroad.