Relationship between time and events, Poisson process

I have a question,
For the Poisson process, the relationship between the C.D.F of the continuous random variable Tk and the C.D.F of the discrete random variable N(t) is a consequence of the equivalence of the events Tk<=t and N(t)>=k.
Tk- A random variable, the length of wait to the k'th occurrence.
N(t)- The number of occurrences when a temporally homogeneous Poisson process is observed for a fixed length of time t.
Does this mean that without events their is no time?
Thank you