A Theory on the Grandfather Paradox

The grandfather paradox

The grandfather paradox is a pafradox about time travel that, what would happen if one were to travel back in time and kill his grandfather before the time travler's parants were born? The time traveler's father will not be born because his father, who has been killed, didn't had any children before. This leads to that the time travler himself cannotbe born. This is a paradox because if not born, how would the time traveler kill his own grandparent? But if he didn't, because he wasn't born, his grandfather would not have been kiled and the time traveler will exist in the future.

An idea on the grandfather paradox

My first idea was based on the concept that the flow of time was what we experience as we / our 'now', moving upwards(towards the future) in the direction of the time axis. Displayed in 3D, this can be thought as planes of universes exist piled up in the time axis direction, and we move in one direction(the future), perceiving it as the flow of time. If one were to travel back in time and come back immediately after killing his/her ancestor, the changing past and the proceding present will always keep a distance in the time axis, never affecting each other.

 

Light cones

I developed my previous idea after reading about light cones. A ight cone is a curved suface made by light moving from a point in Minkowski space. There are two light cones spreading from a point(event) - the future light cone and the past light cone. Events or signals at point E can only affect future events in the volume of the future light cone, and can only be affected by past events in the voume of the future light cone. This is because everything we encounter in the universe(except for light) can only have its worldline in the time-like interval, which is the inner volume of a light cone. The border area is called a light-like interval, and the positions outside the light cone are called space-like intervals. A light cone will face towards a heavy object with stong gravity.

[image 2_ light cone]    https://en.wiktionary.org/wiki/light_cone

Another idea on the grandfather paradox

Based on what I knew of light cones, I upgraded my initial idea. Instead thinking the universe as stacks of now, I decided to imagine it as light cones. If a time traveler went to the past and killed his own grandfather and immediately came back, what would happen? A new series of events will happpen, represented as a future light cone from point D, which is the event of the time traveler's grandfather's death. Meanwhile, a future light cone will also form from point P, the time traveler's actual present. Were the future light cone from point D reaches, history will set path in another way. But since information of the changing events can only b experienced when the worldline of the time traveler meets with that of one of the following events due to his grandfather's death, and the light cones spead in the same speed, the none of the time traveler's present possibilities(the base plane of his future light cone) will intersect with the light cone of changing past from his grandfather's death. This means that the two light cones will never have any interactions with one another.