“People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.” – Albert Einstein.

It’s a worry of physics enthusiasts who believe in the notion of “Time Travel” everywhere. What if they go back in time and alter the course of time, like preventing one's parents from meeting or killing their grandfather? Such a time-traveling act could prevent them from ever being born or divert them from ever attempting to go back in time. Therefore, they would have never existed or gotten the opportunity to travel back in time in the first place. This is called a Paradox...The solution you ask for?? Well, there is none, that's why it’s a Paradox. Before diving deep into the various Paradoxes in Time Travel and their possible solutions let's look at the two broad categories of Time Travel Paradoxes:

1. Closed Causal Loops, such as the Predestination Paradox and the Bootstrap Paradox, involve a self-existing time loop in which cause and effect run in a repeating circle but is also internally consistent with the timeline’s history. Assuming the one in the show “Dark” where each character goes into the past with the intent of stopping an action from happening but ends up being a part of why that was caused.
2. Consistency Paradoxes, such as the Grandfather Paradox, and other similar variants such as The Hitler paradox, and Polchinski’s Paradox, generate several timeline inconsistencies related to the possibility of altering the past. Take the example of the movie “Back to the Future” where the protagonists repeatedly travel to the past and the future to alter the course of time and actions made by certain people at certain points in time and can return to their new future.

One way to solve a paradox is by stating “Time travel isn’t possible at all”. Although the very notion of traveling to the past violates one of the most fundamental premises of physics, and that of causality, there is still nothing in Einstein’s Theories to rule out the possibility of Time Travel. So why not ponder over such a reality as an exercise in logical reasoning?

1. The Predestination Paradox occurs when the actions of a person traveling back in time become part of past events, and may ultimately cause the event he is trying to prevent to take place........ This results in a ‘temporal causality loop’ wherein assuming there is an Event 1 in the past which influences Event 2 in the future (time travel to the past) which then causes Event 1 to occur, with this circular loop of events ensuring that history is not altered by the time traveler proving our previously stated point that any attempts to stop something from happening in the past will simply lead to the cause itself, instead of preventing it from happening. This paradox inferences that things are always destined to turn out the same way and that whatever has happened must happen. But this also raises questions as to can there be Free Will when it comes to becoming a Time Travel or if you are just a part of an enormous predetermined Time Loop.
2. The Bootstrap Paradox is when an object, person, or piece of information sent back in time results in an infinite loop where the object has no discernible origin and exists without ever being created. A materialistic thing may degrade post several cycles or Time Loops and may wither off the loop but a piece of information is always an excellent constant to picture a scenario like this. It is also known as an Ontological Paradox, as ontology is a branch of philosophy that deals with the nature of being, or existence. Now Assume A Scientist traveling back in time and giving himself the knowledge of how to build a machine that can allow him to travel through time and space which he then goes on to use to return to the past and pass on the information to himself again for would create a bootstrap paradox involving information, as the information would have no true point of creation or origin.
3. Now the Paradox you’ve been waiting for: The Grandfather Paradox concerns ‘self-inconsistent solutions’ to a timeline’s history caused by traveling back in time. For example, if you traveled to the past and killed your grandfather, you would never have been born and would not have been able to travel to the past –That is a paradox. Assuming you did decide to kill your grandfather because he created a dynasty that destroyed the world. You figure if you ended his life before he meets your grandmother then the whole family line .including you. will cease to exist and the world will be saved from the heinous acts of tyranny but that wouldn’t work considering you wouldn’t have been born to travel back in time to commit the murder.

Now Solution: Assuming You go back in time, walk up to your Grandfather before he met your grandmother, and point a revolver at his head and pull the trigger......and Boom! The deed is done. You return to what you think is "The Present" but you never existed here. Everything about you has been erased, including your family, friends, home, possessions, bank account, and history. You’ve entered a timeline where you never existed. Scientists put forward the possibility that you have now created an alternate timeline or entered a parallel universe.

The Parallel Universe Theory states that every time you attempt to Travel forwards or backward in time you are not really traveling to a reality on your earth but a parallel reality where things are absolutely identical to actions taken on your world. This can answer a lot many questions and rule out the later mentioned Butterfly effect from the equation. Consider it’s a parallel universe and it can open up the possibility of Coexistence where you can live in a world where your parents or any memory of you doesn't exist or in other words the effect lives on even after removing the cause.

Butterfly Effect: Perhaps the most important theory in time travel states that a small change in one state of a deterministic nonlinear system can result in large differences in a later state. Let's see the story of one Paleontologist:

A Paleontologist, with the help of a Time Machine, travels back to the Jurassic Period to get photographs of the various dinosaurs and species. He knows he can’t take samples so he just takes magnificent pictures from the fixed platform that is positioned precisely to not change anything about the environment. His assistant is about to pick a long blade of grass, but he stops him and explains how nothing must change because of their presence. They finish what they are doing and return to the present, but everything is gone. They reappear in a wild world with no humans, and no signs that they ever existed. They fall to the floor of their platform, the only man-made thing in the whole world, and lament “Why? We didn’t change anything!” And there on the heel of the scientist’s shoe is a crushed butterfly.

Thus, Even changing anything as small as moving a leaf or killing one small butterfly can cause drastic ripples in the fabric of time and the overall effect of decision it has on the lives of the people let alone be the action of killing one's Grandparents before their parents are conceived.