Artificial time travel
Timeline A developed their time travel technology independently based on an accidental experiment in 2055. The time machine is shaped like a spherical orb, with a frame connected with two rotating rings, not unlike a gyroscope. Inside the orb is a chair placed in the center.
Mental time travel
In the late 1990s within Timeline B, Dr. Lloyd Carpenter experimented with hundreds of children and young adults for the application of using the mind to initiate travel through time. It is not known, if the experiment was successful. (See Pilot)
Natural time travel
It was postulated in the Timeline A that there are random and inexplicable sections of disconnected space-time. Which would in theory be able to replace large portions of a known geography to other parts of space-time anywhere in the universe, if encountered.
Alternate timelines, pardoxes, and time loops
The three alternate timelines are parallel and do not intersect or affect the only in any fashion and thus "time travel" to any of these timelines pasts will simply spin-off a new timeline. Thus, paradoxes and time loops are inherently impossible. However, it is possible to maintain contact between two seperate timelines. An cause in one timeline, will not effect the other timeline. For example, if someone traveled from 2050A to 2000A, and murdered their grandfather before they met their grandmother in 2000A, the timeline would thus change into 2000B but no significant change would effect 2050A.
(also check out: TIME TRAVEL on RationalWiki)