I have the following sentence: "The swimmer next to Cavic arrives just before he." My question is why can't we write "The swimmer next to Cavic arrives just before him"? Isn't "just before..." an prepositional phrase that modifies "arrives"? Thus, wouldn't what follows be the object of the preposition, and thus one would have to use the objective case "him"? I know that "he" is correct, but why is it correct, and why can we not use "him"?
Both "he" and "him" are valid; the meaning is the same; "he" would be much less common, and it would mark the expression as formal.
The object of the preposition could be either the whole clause he arrives/does (with the predicate implied), or just the pronoun.
Viewing just the pronoun as the object may seem sloppy when before isn't used in the meanings "literally in front of" or "before the age of", but it was good enough for Shakespeare, which is usually enough to overturn that kind of objection. (E.g. "Spur post, and get before him to the King" from King Richard the Second.)
Anyway, if the before is governing only the pronoun, then the only acceptable form is "him".
If it's governing the whole clause, then a traditional view of grammar would insist on "he", but even in that case, since the predicate here happens to be elided, and if the context is not markedly formal, the modern language prefers "him".
It's not necessary in this case to pick only one of those two analyses of the use of before as the one being actually used, because they have the same meaning. That wouldn't be the case with e.g. "I met Cavic before him/he". (Before he met Cavic? Before I met him?)
In conclusion, "him" is the nearly-neutral formulation which also places no additional strong limitation on the sentence analysis; "he" works only with the object of before being a whole implied clause, and even then marks the expression as formal.