As this is a topic many people have delved into before, I present to you my version, which I came to on my own without having previously read or seen any information directly relating to this subject (the closest being the absurdities of time travel regarding the Grandfather Paradox, which you can read about here http://www.daviddarling.info/encyclopedia/G/Grandfather_Paradox.html).
The past does not exist in the way that you or I exist. You cannot hold or touch the past or, for that matter, re-experience the past in the way you experienced it the first time, as a recreation or reenactment is only that, a replaying of the past where you already know the outcomes. The past only exists as memory and testament based on our interpretation, implying that what we know as truth is only considered truth if we all agree yet is not necessarily true, as fact is fact regardless of democratic opinion. For example, the sky is blue only because the color of the sky is of a hue we have all agreed upon as being called “blue.” If I objectively see the sky as what everyone else calls “orange” it does not change the fact that we all have agreed to objectively call that hue “blue” and, as such, it would not change no matter what hue we looked at as we see it with the same name regardless.
This arbitrariness of our words, and as such our knowledge, implies that our knowledge of the past is just as arbitrary. Say, for example,
To take this one step further and thus disprove time travel, imagine, for example, the common idea some people enjoy entertaining should they have a time machine, for some strange reason. Given the opportunity, most people claim they would use it to kill Hitler before he had the opportunity to commit the atrocities of the Holocaust (never mind that many would most like actually use it for personal monetary gain).
Let’s assume you were one of these people and you actually did make it back in time. Time exists as a function of traveling from point A to point B so it is easiest to represent time for this purpose as a single straight line (Fig.1).
As shown in Figure 2, there are points along this timeline, for example, your birth and the assumed point at which you were to “travel” to the past from, with history representing the entire line which has already happened and the “X” representing your “period of learning” wherein you learned about history, through school for example.
Now, let’s assume, you actually did make it before Hitler (at whichever age you chose to find him) and were able to pull the trigger (Fig. 3).
From there, should you pull the trigger and successfully kill Hitler you would create a new alternate timeline (Fig. 4).
This new alternate timeline would immediately become the original timeline and the original timeline would cease to exist (Fig 5).
What this would mean is that history would become dependent on this new moment, that is to say, the point at which you “traveled” to would become the focal point wherein the original timeline and the alternate timeline switched. What this means, then, is that there can be no alternate timeline since the timeline is always the original; this means that altered events alter the original timeline, thus replacing it.
By this logic, it means that it would be impossible to go back in time and kill Hitler. The area represented by “X,” what I referred to as your “period of learning,” was where you had initially learned of Hitler and the atrocities he committed during the Holocaust. “Traveling” to the past and killing him would remove him from existence, thus removing him from any history you may hear about thereby giving you no compelling reason to travel back in time to kill Hitler, which means you would never go back in time to kill Hitler and the atrocities would still happen. This is why the desire to travel back in time for any purpose will never be fulfilled. The purpose happening gives you the reason to initially travel back in time; should you go back in time and prevent it from happening you would lose your reason to travel back in time in the first place.
It is this paradox which makes idea of time travel completely impossible, regardless of whether you had attained some machine or ability to defy physics and travel through time.
(all pictures created by me for the purpose of this discussion)