How did Galadriel knew that Gandalf was back?

[Legolas]

The Mirror is a possibility, as well as this:

At the end of the Lammas Pengolodh discusses briefly direct thought-transmission (sanwe-latya "thought-opening"), making several assertions about it, which are evidently dependent upon theories and observations of the Eldar elsewhere treated at length by Elvish loremasters. They are concerned primarily with the Eldar and the Valar (including the lesser Maiar of the same order).

A mind by its nature perceives another mind directly. But it cannot perceive more than the existence of another mind (as something other than itself, though of the same order) except by the will of both parties.

Osanwe - 'communication or interchange of thought'

Power of mind (or fëa) to detect another (and in the event of both giving consent, communication between the two entities). This was a power among the Eldar and Ainur (as noted in the first quote). Men are excluded because of the strength of the hröa (or body) over which they have little control.

[ November 24, 2003: Message edited by: Legolas ]