1999/05/24 by James Ax, Simon Kochen, Ax, James +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9905077
Latex+pb-diagram, 77 pages + 10 figures. Many minor corrections, more and better figures. IQM.ps may be more inter-system reliable than IQM.pdf. Additional and animated graphics are available at: http://www.princeton.edu/~jimax/iqm.html This site also contains and invites informal discussion of related ideas to be sent to the CORRECTED email address: [email protected] or [email protected]
openalex publication_date 1999/05/24 · arxiv created 1999/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Copenhagen Interpretation describes individual systems, using the same Hilbert space formalism as does the statistical ensemble interpretation (SQM). This leads to the well-known paradoxes surrounding the Measurement Problem. We extend this common mathematical structure to encompass certain natural bundles with connections over the Hilbert sphere S. This permits a consistent extension of the statistical interpretation to interacting individual systems, thereby resolving these paradoxes. Suppose V is a physical system in interaction with another system W. The state vector of V+W has a set of polar decompositions with a vector q of complex coefficients. These are parameterized by the right toroid T of amplitudes q, and comprise a singular toroidal bundle over S, which comprises the enlarged state space of V+W. We prove that each T has a unique natural convex partition yielding the correct SQM probabilities. In the extended theory V and W synchronously assume pure spectral states according to which member of the partition contains q. The apparent indeterminism of SQM is thus attributable to the effectively random distribution of initial phases.