Surveys in Mathematics and Mathematical Sciences
Volume 1, Issue 2, Pages 89 - 104
(May 2012)
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THE HISTORY OF QUANTUM MECHANICS REVISITED: TOWARD A NEW ALGEBRAIC TOPOLOGICAL PERSPECTIVE
Evert Jan Post, Stan Sholar, Hooman Rahimizadeh and Michael Berg
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Abstract: In this article, we propose to take another look at an old theme in quantum mechanics, viz. the assumption that Schrödinger’s function describes a single quantum mechanical system, and analyze a number of subsequent postulations in quantum physics as it emerged in history, culminating in the Copenhagen interpretation of quantum mechanics. It is our position that these postulations need to be re-examined carefully from two perspectives. First, there is a great deal of benefit to be derived from a historical analysis of the evolution of these ideas, given our present state of knowledge and the availability of alternatives, primarily mathematical, which conspire to a delineation of four epistemological choices made by some of the trailblazers which we propose are in need of revision. Second, these four wrong moves provide us with opportunities to propose alternatives, some historically documented but jettisoned for the wrong reasons, others making for alternative mathematical constructs pointing toward rather different physical positions than those prevalent in the Copenhagen interpretation. We begin in what follows with the indicated exercises in historical criticism and point toward certain physical alternatives and the mathematical formalism, we propose to rectify the four missteps mentioned above. In our subsequent paper on this theme, we proceed to the details of these novel mathematical maneuvers which we only outline here. We refer also to our separate publications [23-25] in the latter connection. |
Keywords and phrases: a new algebraic topological perspective on QM. |
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