If time were to be infinite in both the past and the future, does that mean that every event must occur an infinite number of times?
If time is only infinite in one direction, it is easy to see how this isn't necessarily the case. For example, a wave propagating. It can propagate infinitely in one direction, but still only be in one location once. It is also easy to assign a time to this event; t=0 at the "start" of this time, and t continues into infinity.
However, does this translate into time infinite in both directions? If we use the wave propagation example, the wave will never start propagating in a single direction (no start to an infinite past), and it seems that after an infinite time (without the future even existing yet), the wave will already have propagated fully into infinity. Secondly, does it make sense to assign a time to a single event? If an event only occurs once in this infinite time, in what sense can we say that this event is unique, in terms of the time at which it occurs?
Sorry if this is in the wrong site, it might be more of a physics question, as I'm wondering about whether infinite time in both directions, as implied by eternal inflation, means every event must be recurrent.