What are the temporal limits of the auditory system? I would like to know what the time scale is of the human ear. I mean, what is the shortest duration of a sound that a human ear can notice
and what is the longest duration of a sound that a human ear can not track?
As far as I know, auditory clicks are the shortest possible auditory stimuli. The shortest auditory click I was able to find in the literature, and which was used in a psychophysical context (i.e., audible to a human) was 10 microseconds (Leshowitz, 1971).

The longest sound we can hear is pretty much defined as a human's maximum age I guess. While the auditory system definitely adapts to acoustic stimuli at the neurophysiological level (Pérez-González &amp; Malmierca 2014), this neural adaptation does not become evident in gross psychophysical adaptations. In other words, prolonged acoustic stimulation does not lead to sounds becoming less audible, let alone inaudible. That, because tonal stimuli consist of continuously changing air pressure differences. Of course, a continuous pressure applied to the eardrum is not heard, but a stimulus like that is not sound, but simply pressure, as it has no tonal content.

References
- Leshowitz et al. J Acoust Soc Am 1971; 49, Suppl 2:462-6
- Pérez-González &amp; Malmierca, Front Integr Neurosci (2014); 8: 19