The intellectual merit of this proposal is to argue for a new solution to the measurement problem (MP): a solution under the idealization of macroscopic limit (ML). MP is one of the main problems, if not the problem, at the foundations of physics. Because this is the last, and the most important, part of my multi-stage effort that in the past six or so years has produced works on the nature of idealization and approximation, of model-building, of thermodynamic limit, of phase transitions and critical phenomena, of laws of nature, and of classical and quantum spontaneous symmetry 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 of science. The difficulty of MP centers on an apparent contradiction between what theories hypothesize happens at the micro-level and what happens at the macro-level. All existing attempts to solve the problem make what seems to be an inescapable assumption that all systems involved are of finite number of degrees of freedom (or finite). But finite quantum systems harbor ineliminatable superpositional effects, just as all finite thermo-systems harbor fluctuations; and such effects seem to make a rigorous solution of MP impossible. I propose that we drop the assumption. There is a sound 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, SSB is only possible under ML, and it can be used to replace the notion of the 'collapse' of wave functions in 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 to audiences of both experts and general public interested in philosophy and physics. Because the project tackles MP, the arguably single most important problems in the foundations of physics, the reverberation of its results is far-reaching. Historians of quantum physics and of the revolution of modern physics will find the spirit of the proposed solution closer to the views of the founders of quantum physics (Bohr et al and the Copenhagen school). Researchers interested in the symbiotic relationships between disciplines of science will find it interesting to see how a recalcitrant orthodox position in quantum physics -- the Hilbert-space approach -- is unseated (if I am right) by results in solid state physics; or how the 'foundation' of quantum physics is shaken by models in solid state (a much less fundamental and hence neglected area in foundational studies). A solution to MP that challenges the prevailing bias in the conception of quantum physics should open the door for new possibilities 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 community college at Jacksonville and at nearby universities of north and central Florida, as well as at professional meetings and colloquia here and abroad.
