Using "so that" without modal verbs
I know that usually with "so that" there is a modal verb. However, I do not know if this is correct because there is not a modal verb.
I will wake him up so that he does not (will not) miss the train.
I woke him up so that he did not miss the train.
Solution 1:
The first one is correct. You can use either "won't" or "doesn't."
The second example isn't Ok because "so that" talks about a cause and its intended effect. In other words, "so that" is used for purpose or reason.
This is why your alternative is better (why did you erase it?):
Ex. I woke him up so that he wouldn't miss the train.
You can use "would" here as the Past Tense of "will." The Past Tense of "I'm going to wake him up so he won't miss the train."
If you really want to keep "did not" in your second example, you have to change "so that" into "so."
"So" just means the continuation of the first action.
Like this:
I woke him up, so he didn't miss the train.
Solution 2:
First of all so that is a conjunction and is not tied to modals. It means in order that. Your examples are fine. Here is another example.
He must die so that others might live. 1900, L. Frank Baum, The Wonderful Wizard of Oz. He seized his axe, which he had made very sharp, and as the leader of the wolves came on the Tin Woodman swung his arm and chopped the wolf's head from its body, so that it immediately died.
Solution 3:
So and that are independent Complementizers -- words or phrases that identify (and often delimit) various types of subordinate clauses -- with separate syntactic trajectories. They happen to come together in this construction, but there is a lot of variation.
That is the same that that (optionally) appears introducing the tensed Object Complement clause the Earth is a rhomboid cylinder in
- She believes (that) the Earth is a rhomboid cylinder.
and that used to appear before other kinds of tensed clauses as well
- Whan that Aprille with his shoures soote / The droghte of Marche hath perced to the roote
Nowadays we can't say
- *Tell him when that you will see him again.
but we can say
- Tell him so that you will see him again.
So is a frequent and quite general complementizer, a "pro-adverb", if you will, marking pretty much any clause or reduced clause (i.e, phrase) with implied causation, intention, or responsibility -- human, natural, logical, accidental, or conversational -- such as might be expressed more precisely with adverbial clause conjunctions like
because, anyway, therefore, as I was saying, hence, now, regrettably, surprisingly, thus, ...
So that can therefore introduce any such tensed clause and thus means the same as in order that (unlike so, in order can appear also with the infinitive complementizer to, as in order to).
Order has a variety of deontic modal meanings -- orders are imperatives, and Imperative is a Mood, after all -- and therefore the OP's intuition that modal verbs are involved is correct. Like many constructions in English and other languages, there are often presupposed modal meanings that show up in lexical choices.
For instance, English relative infinitives almost always imply some kind of weak deontic modality, like the modal auxiliaries should or ought to:
- Bill is the man to see about that. = Bill is the man whom one ought to see about that.
- Bill is the man to do that. = Bill is the man who should do that.
Since so is so non-specific, the details of precisely what kind of purpose, result, causative, or summatory clause relationship obtains is left, like so much else, to the listener or reader to guess at, from what they believe about the context.