I have been thinking about an argument between the Rashbam and the Ramban [Nachmanides] if a divorce document needs to have the time of its writing put into it. [In Rav Shach, Laws of Divorce perek I chapter 25]

The Rashbam [Shmuel ben Meir,  a grandson of Rashi] holds it never needs the time in it. The only opinion that holds it needs the time is R. Meir who holds the witnesses on the document cause the divorce to become valid. But the law goes like R. Elazar that the witnesses that see the giving of the document to the woman cause the validity of the divorce.  So he would hold there is no worry about the daughter of his brother.  [The opinion that holds the reason the time is in the document is because of the fact that he might have married the daughter of his brother, and then she might have committed adultery. Then, since she is his relative, he might write a divorce document, and put in a time before the time of the adultery to save her from the death penalty.] But to R. Elazar there is no worry about that because if there is not time in the document, then we would assume she was married until right now and thus there is not worry about the daughters of his brother.  

What occurred to me today was this question. Why does this have to do specially with the opinion of R Elazar?  I think the idea is that R Meir not have the same idea--that we would assume the divorce did not happen until the last minute. So the time needs to be put in so that he does not put in a latter time. But would not the same go for R. Elazar? He could have a divorce now and have no time in it and later put in a time? That is to say I am not really clear about what the explanation of Rav Shach is here.