# Entangled Harmonic Oscillators and Space-Time Entanglement

2016-6-28
Başkal, Sibel
Kim, Young S.
Noz, Marilyn E.
The mathematical basis for the Gaussian 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 Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-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. M. Dirac in 1963, the system of two oscillators contains the symmetries of the O (3, 2) de Sitter group containing two O (3, 1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of the Sp (4) group, which serves as the basic language for two-mode squeezed states. Since the Sp (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.
Symmetry

# Suggestions

 Neutrino oscillations induced by spacetime torsion Adak, M; Dereli, T; Ryder, LH (IOP Publishing, 2001-04-21) The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan spacetime and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass eigenstates are found. These effects are of the order of Planck scales.
 RELATIVELY COMPLETELY HAPPY Parkan, Barış (2007-06-22) This paper tries to formulate a link between a phenomenological description of certain experiences of the co-presence of the past, present and future with the scientific theory of the block model of the universe that is based on the Einstein-Minkovski conception of spacetime. The argument that is constructed to this end utilizes Whitehead's process metaphysics. Using Whiteheads attack on the bifurcation of nature problem as my springboard, I argue that even though the passage of time as described in the blo...
 Autoparallel orbits in Kerr Brans-Dicke spacetimes Cebeci, H; Dereli, T; Tucker, RW (2004-01-01) The bounded orbital motion of a massive spinless test particle in the background of a Kerr Brans-Dicke geometry is analysed in terms of worldlines that are auto-parallels of different metric compatible spacetime connections. In one case the connection is that of Levi-Civita with zero-torsion. In the second case the connection has torsion determined by the gradient of the Brans-Dicke background scalar field. The calculations permit one in principle to discriminate between these possibilities.
 Equivariant Reduction of Gauge Theories over Fuzzy Extra Dimensions Kürkcüoğlu, Seçkin (IOP Publishing, 2012-2-8) In SU(N) Yang-Mills theories on a manifold M, which are suitably coupled to a set of scalars, fuzzy spheres may be generated as extra dimensions by spontaneous symmetry breaking. This process results in gauge theories over the product space of the manifold M and the fuzzy spheres with smaller gauge groups. Here we present the SU(2)- and SU(2) x SU(2)-equivariant parametrization of U(2) and U(4) gauge fields on S-F(2), and S-F(2), x S-F(2), respectively and outline the dimensional reduction of these theories...
 RELATIVISTIC DESCRIPTION OF HEAVY Q(Q)OVER-BAR BOUND-STATES ZAKOUT, I; Sever, Ramazan (1994-10-01) We study the relativistic description of heavy qqBAR bound states in the context of the relativistic wave equation. We used some attractive QCD based potentials where the vector part incorporates in the two loop perturbation QCD effects at short distances while the scalar part approaches the linear confining potential at large distances. We calculate the energy levels, leptonic and hadronic decay widths, as well as the E1 rate transition for ccBAR and bbBAR. Results are compared with their experimental v...
Citation Formats
S. Başkal, Y. S. Kim, and M. E. Noz, “Entangled Harmonic Oscillators and Space-Time Entanglement,” Symmetry, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51226. 