Time for even more real language examples. And as usual, I have dug deep in the grammar of my native language to find a belated hannukah-gift to you, my dear readers.
In syntax, a that-trace effect is a kind of blocking, where a complementizer cannot be followed by a trace. This effect is present in English, and causes this system of sentences with various transformations to hold:
I didn't think he could sing
He, I didn't know sings in that choir (arguably not grammatical)
Unlike English, Scandinavian languages permit topicalizing elements of subclauses rather freely. In English, this seems mainly to occur with interrogative pronouns. A __ will be inserted where the moved element originally stood in example sentences:
who did you think __ would finish this?
Compare this with Swedish clauses such as these:
Evert tror jag inte __ äter fisk.
Evert think I not __ eats fish.
Evert, I don't think eats fish.
I don't think Evert eats fish.
Other constituents can also be moved around:
Fisk tror jag inte Evert äter __.
Fish I don't think Evert eats.
I don't think Evert eats fish.
Here, it would be fun if we could do this to verbs as well, but alas, this is not permissible:
Äter tror jag inte Evert __ fisk.
Eats I don't think Evert fish
I don't think Evert eats fish (think this as contrasting to what he does do with fish: farm, cut fillets, cure, smoke, put in brine, make fish fingers, mong, etc, them)
Let's return to our English example "who did you think would finish this?" Let us consider two possible rewordings of this where it's "he" instead of "who", and it's just a statement.
You did think he would finish this?
You did think that he would finish this?
We find an interesting difference here, with regards to the permissibility of "that":
The hypothesis is that "that" cannot be followed by a trace of the element that has been moved left. (In essence, this means we can't have "that" and a move at the same time.) The subclause must be introduced by a null-element instead if there is a trace.
Anyways, Standard Swedish as spoken in Sweden has the same that-trace effect as English, whereas Standard Swedish as spoken in Finland lacks it. Norwegian seems also to have geographical splits on this, and Icelandic, I am happy to tell, solidly sides with my variety of Swedish. Since left-moved elements seem to be more common in Scandinavian in general, these phenomena are much more visible than in English.
han tror jag kan simma
he thinks I can swim
As it happens, standard Swedish has V2, so this can actually correspond to _two_ different English orders. Notice that Swedish does not have person congruence on the verb:
he think (that) I can swim (remove (that))
he think I that can swim
he I think that can swim
The reason this particular difference between the two Swedish varieties has not been squashed by the education system is probably the fact that it's kind of difficult to explain something as abstract as this rule to kids.
I am kinda at awe at the level of hypocrisy "grammar nazis" reach on this thing. With one side of their face say we should make sure the language is as unambiguous as possible and with the other side of face teach that this trait of F-Swedish should be eliminated - despite the fact that it objectively reduces the amount of ambiguity. Fuck them. Seriously.