Comparing ontologies, under the growing block universe concept it is not possible for a person to change his or her future composite world-line because it does not exist; in this view, the future is made in the objectively advancing present.
When particle movements are graphed, four-dimensional world-lines are traced out .
So, within eternalism, the composite world-lines of human beings are complete from birth to death in every physical and behavioral detail.
So, in this instance of pastward time travel, the composite world-lines of time travelers are necessarily embedded in "the past" as judged with respect to the date of their journey's origin.
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.
Then, to obtain formulae for the velocity [U.sup.[alpha]] it is necessarily to solve the geodesic equations for free particles (2.6) and the world-line equations for interacting particles (2.11).
Using formulae (7.17) and (7.18), and the quantity d[U.sup.[alpha]]/ds from the world-line equation of a particle moved by a non-gravitational force [[PHI].sup.[alpha]] (2.11), we obtain
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.
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.
If these are two particles connected by a non-gravitational force (for instance, by a spring), they are moved along neighbour non-geodesic world-lines. This classical statement has been developed a few years later by Weber , who has obtained the world-lines deviation equation (Synge-Weber's equation).