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Others provide mathematical models for the optimization of growth process parameters and a control procedure for the shape of a Nd, anomalous Langrangians, the lifetime asymmetry of polarized fermions in flight, and world-line observables and clocks in general relativity.
6) and the world-line equations for interacting particles (2.
alpha]]/ds from the world-line equation of a particle moved by a non-gravitational force [[PHI].
The world-lines deviation equation for two free particles (the Synge equation) is deduced and that for two force-interacting particles (the Synge-Weber equation) in the terms of chronometric invariants --physical observable quantities in the General Theory of Relativity.
The basis for all the experiments is the Synge-Weber equation (the world-lines deviation equation), which sets up a relation between relative oscillations of test-particles and the Riemann-Christoffel curvature tensor.
0], are moved along non-geodesic world-lines, determined by the equation
In this case the world-lines deviation equation takes the form
Two different particles can not occupy the same world-line, so they are in absolutely separated states--they are disentangled particles.
In our statement the world-line of a particle, being entangled to itself by definition, splits into two different world-lines under teleportation conditions.
In the classical problem statement accepted in General Relativity [17, 18, 19], two mass-bearing particles are considered which are moved along neighbour world-lines, a signal is transferred between them by a photon.
This classical statement has been developed a few years later by Weber , who has obtained the world-lines deviation equation (Synge-Weber's equation).
1) moving along neighbour geodesic world-lines [GAMMA](v) and [GAMMA](v + dv), where v is a parameter along the direction orthogonal to the geodesics (it is taken in the plane normal to the geodesics).
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