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- Title
Entangled Harmonic Oscillators and Space-Time Entanglement.
- Authors
Başkal, Sibel; Kim, Young S.; Noz, Marilyn E.
- Abstract
The mathematical basis for the Gassing entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gassing entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorenz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorenz-covariant picture of the bound state, which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. AM. Direct in 1963, the system of two oscillators contains the symmetries of the O(3, 2) de Sitter group containing two O(3, 1) Lorenz groups as its subgroups. Direct noted also that the system contains the symmetry of the ESP(4) group, which serves as the basic language for two-mode squeezed states. Since the ESP(4) symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified.
- Subjects
HARMONIC oscillators; GAUSSIAN processes; LORENTZ groups; DIRAC function; DIRAC, P. A. M. (Paul Adrien Maurice), 1902-1984; SPACE-time mathematical models
- Publication
Symmetry (20738994), 2016, Vol 8, Issue 7, p55
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym8070055