Extension of Quantum Mechanics to Individual Systems
| dc.creator | Ax, James | |
| dc.creator | Kochen, Simon | |
| dc.date | 1999-05-24 | |
| dc.date | 1999-06-14 | |
| dc.date.accessioned | 2026-07-07T06:16:34Z | |
| dc.date.available | 2026-07-07T06:16:34Z | |
| dc.description | 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. | |
| dc.description | 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: jimax@Princeton.EDU or kochen@math.Princeton.EDU | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9905077 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9905077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94100 | |
| dc.subject | Quantum Physics | |
| dc.subject | Mathematical Physics | |
| dc.title | Extension of Quantum Mechanics to Individual Systems | |
| dc.type | text |