Time travel is one of the core components of the Terminator movie franchise, but despite the relatively simplistic fashion in which this age-old science fiction trope is used within the movies there is a degree of debate within the fandom as to how it is implemented within the overarching narrative of the franchise.
Alternate Timelines vs Temporal Causality
Despite being established in all of the Terminator movies (except Terminator: Genisys) that the nature of time travel adheres to the underlying rule of causality (cause precedes effect), some fans believe that time travel in the Terminator movies is only possible through the use of alternate realities.
As with the many-worlds interpretation of quantum mechanics, whereby decisions taken result in alternate realities, with alternate timelines whenever something or someone travels from one point in time to another they arrive in a reality parallel to, though separate from the one they previously existed in. As such the use of alternate realities avoids the possibility of paradoxes, whereby one could theoretically impact and change their past, such as a time traveler traveling back in time to kill their parents before they were conceived.
Using time travel adhering to the underlying rule of causality, the paradox of such a situation would mean the time traveler would, therefore, have never existed, and thus never traveled back in time to kill their father who would go on to conceive the time traveler, creating a causality loop known as a grandfather paradox (see Paradoxes below).
However, using time travel adhering to the rules of alternate realities, the aforementioned paradox would be negated by having the time traveler not actually kill their parents but the parents of another realities version of themselves, thus not undoing their own existence, but merely the existence of the other realities version of themselves.
By their very nature, alternate realities make time travel free of consequence, ultimately meaning that there would be no repercussions for one's actions. Conversely, causality infers that with time travel comes repercussions, which will alter the timeline by creating a series of previously unexplored or unavailable events.
Consequence, fate, and destiny are central themes of the Terminator franchise, as exemplified in the franchise's motto "there is no fate, but what we make", which is shared by this website accordingly. Furthermore, with the exception of Terminator Genisys (which does not adhere to the canon timeline of The Terminator and Terminator 2: Judgment Day), there is absolutely no evidence in the Terminator movies that any of those that have traveled through time have also traveled from another reality.
When discussing the concept and theoretical impacts of time travel paradoxes are introduced, chiefly to highlight the improbable nature of time travel. The two most common paradoxes mentioned alongside the concept of time travel are predestination paradoxes and the grandfather paradox.
A predestination paradox is an example of a causality loop, where once instigated in a previous iteration of events a loop of perpetuating events is established. This is how time travel was depicted to have occurred in The Terminator. This is evidenced by the movies closing scene, in which Sarah Connor has her photograph taken, the same photograph that Kyle Reese will pine over in the post-apocalyptic future war, and from which he will be able to recognize Sarah when he is sent back to protect her.
However with Terminator 2: Judgment Day, the narrative offered the possibility that the predestined future events could be changed, possibly even canceled. This could potentially result in a grandfather paradox. A simplified version of the grandfather paradox (as already explained above) is as follows - A man travels back in time and murders his father before his father met his mother. As a result, the man is not conceived and therefore never existed, and thus never traveled back in time to kill their father who would go on to conceive the time traveler.
This is used as a narrative in The Terminator, whereby Skynet sends the Terminator back in time to murder Sarah Connor before her son John, the future leader of the Human Resistance is born, but in its attempts to create a grandfather paradox and change past events in its favor Skynet inadvertently creates the perfect opportunity for the resistance to create a predestination paradox, thus changing past events in their favor. Because of the events later depicted in Terminator 2, the predetermined date of Judgment day is changed, and the future events that made up Kyle Reeses past have been changed, rewritten.
In Terminator 3: Rise of the Machines and Terminator Salvation Judgment Day was revealed to have been merely delayed, reinstating the predestination paradox narrative of the original movie, but with the new Terminator movie, there is a possibility that the narrative may result in the future war between Skynet and the Human Resistance having never occurred - again creating a grandfather paradox (see The Cameron Paradox).