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 & 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.
In terms of the shortest stimuli, the auditory system can process acoustic impulses, but defining the duration of an impulse is problematic. As the duration of the impulse gets shorter, the bandwidth gets broader. A 25 us impulse has frequencies between 0 and 20 kHz, as you decrease the duration of the impulse you add higher frequency components such that a 10 us impulse has a maximum frequency of 50 kHz. The upper edge of human hearing is 20 kHz so it is unlikely that we could detect a difference between a 25 us impulse and a 10 us impulse (or even a 1 us impulse), but assuming sufficient energy, all would be detectable. Making really short sounds with sufficient levels of energy is technically challenging and requires good transducers, but ultrasonic transducers exist.
The upper limit depends on what you consider the human ear. Durlach and Braida (1969) introduced the concepts of sensory‐trace mode and context‐coding mode to separate sensory limitations from memory limitations. The 15 papers in the series, written over 25 years, delve into the details (and then some), but basically after about 250 ms, listener switch from trace mode to context coding, suggesting this is the upper limit of processing by the ear.
That said, my recollection is that echolocating bats need precise temporal tuning (so sensory mode) over the time course of 10s of seconds. As humans are also able to echolocate, to an extent, there may be some aspects of the auditory system for which the neural trace degrades much more slowly.