Why do 'wonder' and 'think' act differently in wh-movement?

Question

For instance:

Object moving:

1. Who do you think that John saw t? (correct)
2. *Who do you wonder that John saw t? (incorrect)

Subject moving:

1. Who do you think t saw John? (correct)
2. *Who do you wonder t saw John? (incorrect)

Adjunct moving:

1. Why do you think that I left t? (correct)
2. *Why do you wonder that I left t? (incorrect)

Answer 1

Wonder takes an embedded interrogative complement with its own internal trace:

You wonder who John saw t.
You wonder who t saw John.
You wonder why I left t.

When you front that wh- you're asking it to do double duty, in both an external interrogative and the embedded interrogative: in effect it's standing for itself rather than for the trace!

ADDED:
It's the interrogative role of the wh- complement which prohibits this movement. Note that this pair sustains the movement, because the original wh- clause is deployed not as an interrogative but as a pronominal:

I know who saw John. ⇒ ^okWho do you know saw John?

But this pair doesn't, because the original wh- clause is interrogative:

I'd like to know who saw John. ⇏ ^∗Who would you like to know saw John?

Some grammarians distinguish these two uses of the wh- clause as 'embedded questions' and 'free' or 'fused relatives'. I don't, because the internal structure of the wh- clause is identical; but the difference in the external syntactic roles justifies a distinction at that level.