"Definitely" vs. "absolutely"

What's the difference between absolutely and definitely? Actually which of the following sentences is correct?

You are definitely right.

You are absolutely right.

Solution 1:

They can mean almost the same thing, although I perceive a slight difference.

You are definitely right.

means that it is certain that you are right.

You are absolutely right.

means that you are completely right. One couldn't be "more right", as it were.

So, grammatically, I'd say that in the first sentence, definitely modifies the whole sentence (the verb), whereas in the second absolutely modifies right.

Solution 2:

When the question is about something you or somebody has a control over, it is answered with 'definitely'.

Can you look into this problem? Definitely.

When referring to something outside one's jurisdiction, like natural laws, absoluteness can be attributed.

Are you sure Jim is here? Absolutely.

Here, Jim's presence has an absolute nature, that can not be influenced by anybody else's willingness to keep it one way or the other.

(Disclaimer: this answer is from the statistics in my brain that has a model for 'English Usage'. A trustworthy authority, like OALD, takes always precedence.)

Solution 3:

Definitely : without doubt

Absolutely : completely