Final answer:
In a physics context, if the smallest meaningful time interval is greater than zero, two lines representing relationships over time may never meet due to discrete time intervals and potential quantum effects. This implies a departure from a continuous to a discrete model of time.
Step-by-step explanation:
If we consider a scenario in a physics problem where the smallest meaningful time interval is greater than zero, it has implications on whether two lines on a graph will meet. Lines on a graph typically represent the path of an object over time or some other relationship between two variables. If the smallest time interval is nonzero, it is implied that there is a minimum quantization in time. This means that time is not continuous, but rather discrete, with the smallest possible step being the nonzero interval mentioned.
If lines represent motions or behaviors that are dependent on time incrementing in a continuous fashion, introducing a discrete time interval could mean that paths that seem to converge may actually not intersect when considered at these discrete intervals. In physics, this could be analogous to phenomena observed at quantum scales where classical assumptions do not always hold true. Therefore, with a nonzero smallest time interval, two lines that appear to converge continuously may never actually meet due to these quantum effects.
However, without additional context, such as the specific nature of the lines in Figure 34.9 or the scale of the system being analyzed, it is difficult to provide a definitive answer. It would require more detailed information from the graph and the conditions of the scenario to give a precise response as to whether the lines would ever meet.