Question: Is it possible to survive the Grandfather Paradox? What If…
Since quantum mechanics is governed by probabilities, an unmeasured entity (in this case, your historical grandfather) has numerous probable states. When that entity is measured, the number of its probable states singularities (analogous to a psi wave in a world-history line), resulting in a single outcome; in this case, ultimately, you. Therefore since the outcome of your grandfather is known, killing your grandfather would be incompatible with that outcome. Thus, the outcome of one’s trip backwards in time must be complementary with the state from which one left.
What if the Grandfather paradox only works in a system (a reference frame) that is local to the entropy state of that local reference frame’s state of knowledge, i.e., what if, the information of what happened with say a history of a grandfather relative is lost (or older ancestor), either information becomes dispersed and forgotten with time or information within a short period is being trapped by a black-hole. So lets suppose that if this information is lost and no living person or system state has a record of a grandfather or older relative. If you went back in time and killed them, not knowing that they were your grandfather, you would cease to exist?
Logically you might think so, but the quantum state of knowledge (information) has not changed. Therefore if you kill your grandfather without any system or person within the Universe knowing that they are your grandfather, (or older relative back in time), would you cease to exist or would you continue to exist in a merged paradox as the state of information is then changed and incorporated into a new state? The supposition being that the previous information (on your grandfather) has become lost and therefore logic no paradox would be created? This might be done without the need for a parallel world or a paradox machine to keep the consistency invoked.
The Novikov self-consistency principle holds that if one were to travel back in time, the laws of nature (or other intervening cause) would simply forbid the traveller from doing anything that could later result in their time travel not occurring. For example, a shot fired at the traveller’s grandfather will miss, or the gun will jam, or misfires, or the grandfather will be injured but not killed, or the person killed will turn out to be not their real grandfather, or some other event will occur to prevent the attempt from succeeding. No action the traveller takes to affect change will ever succeed, as there will always be some form of “bad luck” or coincidence preventing the outcome. In effect, the traveller will be unable to change history from the state they left it. Very commonly in fiction, the time traveller does not merely fail to prevent the actions s/he seeks to prevent; s/he in fact precipitates them (see predestination paradox), usually by accident.
The Novikov self-consistency principle theory might lead to concerns about the existence of free will (in this model, free will may be an illusion). This theory also assumes that causality must be constant: i.e. that nothing can occur in the absence of cause, whereas some theories hold that an event may remain constant even if its initial cause was subsequently eliminated.
Closely related but distinct is the notion of the time line as self-healing. The time traveller’s actions are like throwing a stone in a large lake; the ripples spread, but are soon swamped by the effect of the existing waves (interference). For instance, a time traveller could assassinate a politician who led his country into a disastrous war, but the politician’s followers would then use his murder as a pretext for the war, and the emotional effect of that would cancel out the loss of the politician’s charisma. Or the traveller could prevent a car crash from killing a loved one, only to have the loved one killed by a mugger, or fall down the stairs, choke on a meal, killed by a stray bullet, etc.
In some stories it is only the event that precipitated the time traveller’s decision to travel back in time that cannot be substantially changed, in others all attempted changes will be “healed” in this way, and in still others the universe can heal most changes but not sufficiently drastic ones. This is also the explanation advanced by the Dr. Who role-playing game, which supposes that Time is like a stream; you can dam it, divert it, or block it, but the overall direction it is headed will resume after a period of conflict.
An interesting concept in the “The Stone Rose” (Jacqueline Rayner, BBC Books, 2006), but slightly obscure perspective on a temporal paradox. By seeing a statue of yourself in the future, even for a time lord’s companion such as Rose in this case is a paradox in itself, because until they see the statue the Doctor has not taken her to Rome 1900 years ago (give or take 100 or so years). But by doing so he sets up a paradoxical causal loop, so the real question is, where did the knowledge of Rose being in Rome 1900 years ago come from?
After all the Doctor may never have taken her to Rome unless Mickey showed her the stature of Fortuna (Rose) being an exact replica, right down to her ear rings. So where did this state of knowledge of events that put the statue of Rose before he decided to go to Rome come from? If the Doctor had not see the statue of Rose, he may never have gone back to Rome 100 ~ 200 AD with Rose. Did the information of the trip come into existence on its own? And if so, from where did this quantum information come from? A paradox within a paradox or did the information just arise naturally form Rose’s very existence as a complex system in her own right?