Detection By Time Travel

In Catching Up, see Stieg Larsson's reference to time travel. A girl disappears from an island that is connected to the mainland by a bridge which is temporarily blocked by a serious traffic accident. It is known who was on the island. Also, the girl was photographed on the mainland shortly before going to the island and it is important to find out who or what she might have been looking at while being photographed.

How would Manse Everard, whose timeline is mutable, or Jack Havig, whose timeline is immutable, have investigated Harriet's disappearance? In a mutable timeline, it is necessary to avoid changing the events being investigated. In an immutable timeline, it is necessary for the investigator to insert himself into known events, e.g., it is known who was on the island so how can a time traveler also have been there?

Everard would hover above on a timecycle and observe events with a telescopic camera. Havig would be able, while time traveling, and therefore both invisible and intangible to everyone else, to stand behind Harriet while she was being photographed and to follow her onto the island. He would also be able, if necessary, either to pass through the overturned oil tanker or to travel to a time before or after the accident and safely cross the bridge then.

Thus, Time Patrolmen and mutant time travelers would easily investigate the disappearance whereas other kinds of time travelers might experience difficulties.