We are now ready to give the world lines of the particles according to Camilla.
This straightforwardly leads us to the description given by observer D of the world lines of the soft particle and of the hard particle:
Notice that these equations for the world lines show in particular that the soft particle goes through the origin of observer D but the hard particle does not.
Therefore according to observer D' the world lines of the soft particle and of the hard particle are described by
Notice that these equations for the world lines show in particular that the hard particle goes through the origin of observer D but the soft particle does not.
With the choice of coordinates made in this section one has that Alice's description of the relevant two world lines is
On the surface of the strip lies the trajectory traveled by a current time pointer as it changes between its bindings in the initial and final world lines. Figure 2(a) shows the picture that is appropriate to the wait on C statement, and Figure 2(b) shows the picture for a signal assignment.
The whole sequence comprises a world line, borrowing a term from general relativity.
During or after a process run, the world line that a process sees may differ in two ways from the initial world line that it saw:
(1) the historical part of the world line will be conserved and extended;
(2) the "future" (i.e., scheduled) part of the world line may have changed, and it will be shorter, in the sense of now extending over a smaller time range.
In this case, the world line
of [p.sub.1] would not be continuous at t = 3 because, if we take as f(t) the function defined by the x coordinate of [p.sub.1], then [lim.sub.t[right arrow]3-] f(t) = -[infinity] while f(3) = r.