It is said that time traveling is not possible due to the "cause and effect" problem and the changes that may occur that will negate the main purpose of time travel on the fiorst place
In temporal mechanics, sometimes an effect can supercede the cause. I am curious why you did not mention that . . .
Your reasoning is interesting, but if you were to go back in time and even look at you grand father, you alter history and time. Being in the past, or being the individual you are today, alters your surroundings. Just standing in a park with people taking a walk and children playing alters the past. You are NOT suppose to be there and therefor you contaminate your own history and time.
A stand alone action, as you stated, is but a minor step you could even try to accomplish. That and any action is futile because you are already altering the past time you now stand in.
Do you understand where I am coming from?
(i.e.) I yelled from across my stadium bleachers yesterday (watching my former high school's, girls varsity soccer team play) to the goalie, "great job Delap!!" In reality, her future has now been altered and the choices she makes will be different from the ones she would've taken had I not yelled out to her for an outstanding second half of the game.
Similar in terms of action/reaction, she heard me or someone call out her name nearby, which shifted her mind away for a brief moment, made her think "who might that be" or "how awesome". The end result is . . . I changed her life path because of such a little action. Minor actions, such as this, have a powerful affect on anyone. No matter what people say, an action even so minor such as staring someone in the eyes in the hall way at school, will have an impact on that individuals life in the future.
Believe it, for it is the truth. As you read my post, (and this goes for everyone) I have changed the way you look at things, or at least made you think. Nontheless, you will be a different person after you read it. The individuals who did not know about this thread and did not read my post are unaffected, unless someone informs them otherwise.
Confused?