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

这一建议的理论价值在于为测量问题(MP)提供了一种新的解决方案：宏观极限(ML)理想化下的解决方案。如果不是问题的话，MP是物理学基础上的主要问题之一。因为这是最后的，也是最重要的，我的多阶段努力的一部分，在过去的六年左右的时间里，我已经产生了关于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，自然规律，以及经典和量子自发对称破缺(SSB)的工作，其中一些得到了以前的NSF拨款(No.它的成果，除了它们本身的优点外，还将验证和改进这些领域的成果。这个最后的项目可以被视为对我以前对科学哲学贡献的检验和展示。MP的困难在于微观层面上的理论假设和宏观层面上发生的事情之间存在明显的矛盾。所有现有的解决问题的尝试都建立了一个似乎不可避免的假设，即所有涉及的系统都是有限的(或有限的)自由度。但是有限的量子系统有不可消除的叠加效应，就像所有有限的热系统都有波动一样；而这种效应似乎使MP的严格解变得不可能。我建议我们放弃这个假设。有一种合理而严格的数学方法(代数法)，可以想象所涉及的系统具有无限多个自由度(或无限)，并采用适当的限制。此外，SSB只有在ML下才是可能的，它可以用来取代正统公式中波函数“崩溃”的概念。这个项目的广泛影响是多方面的。鉴于它的性质，这个项目将主要产生研究论文(可能还有一本专著)，并向对哲学和物理学感兴趣的专家和普通公众的听众进行演讲或演讲。由于该项目解决的是物理学基础中可以说是最重要的单一问题--MP，因此其结果的混响是深远的。研究量子物理学和现代物理学革命的历史学家将发现，提出的解决方案的精神更接近量子物理学创始人(玻尔等人和哥本哈根学派)的观点。对科学各学科之间的共生关系感兴趣的研究人员将会发现有趣的是，量子物理学中一个顽固的正统观点--希尔伯特空间方法--如何被固态物理的结果推翻(如果我是正确的)；或者量子物理的“基础”如何被固态模型动摇(在基础研究中，这是一个不那么基础的领域，因此被忽视了)。下院议员挑战量子物理概念中普遍存在的偏见的解决方案应该会为该领域的新可能性打开大门，这应该会引起理论物理学家和数学家的注意。我将尽一切努力将结果纳入我的教学，在杰克逊维尔社区学院和附近的佛罗里达州北部和中部的大学发表演讲，以及在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.