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abstract: '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 $O(3,2)$ 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 