2003/09/24 by Inge S. Helland, Helland, Inge S.
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.quant-ph/0309178
openalex publication_date 2003/09/24 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28
The aim of the paper is to derive essential elements of quantum mechanics\nfrom a parametric structure extending that of traditional mathematical\nstatistics. The main extensions, which also can be motivated from an applied\nstatistics point of view, relate to symmetry, the choice between complementary\nexperiments and hence complementary parametric models, and use of the fact that\nthere for simple systems always is a limited experimental basis that is common\nto all potential experiments. Concepts related to transformation groups\ntogether with the statistical concept of sufficiency are used in the\nconstruction of the quantummechanical Hilbert space. The Born formula is\nmotivated through recent analysis by Deutsch and Gill, and is shown to imply\nthe formulae of elementary quantum probability/ quantum inference theory in the\nsimple case. Planck's constant, and the Schroedinger equation are also derived\nfrom this conceptual framework. The theory is illustrated by one and by two\nspin 1/2 particles; in particular, a statistical discussion of Bell's\ninequality is given. Several paradoxes and related themes of conventional\nquantum mechanics are briefly discussed in the setting introduced here.\n