In "A Rose for Emily" what details from the story lead some people to believe that this is a "meditation on the nature of time"?

The time-frame was from after the civil-war until the 1920's or 30's, and this was a time where a lot of old cities in the south were reeling from the after-effects of war and the abolition of slavery.  What used to be wealthy, upper-class families with a lot of money were left without anything but the legacy of their name.  Because of the notoriety of being from a wealthy southern family, these people (the Griersons in the story) were like the Hollywood celebrities of the time; we love to watch them, analzye their lives, and gloat a bit in their downfalls.  This celebrity gossip is what allows the narrator to represent the townsfolk as a whole, and what allows us to get such a complete picture, considering we never really go beyond the townspeople's perspectives.

As time goes on, the townspeople forget, eventually about Emily, until the scandalous news of the surprising discovery comes about.  She is no more than a curiosity to people; they go to her house like it is a viewing of an ancient museum, which emphasizes how times have really changed, and how people like Emily Grierson, with all of her elite background, have become obsolete.  From the beginning with her father in a more relevant and prominent position, to the end where Emily is no more than a museum relic, the story covers the deterioration and disappearance of a certain era in Southern history.