I used to have a simular question of this paradox. What if I solved time travel went back and somehow convinced my self not to pursue time travel. In that instance I might not create a time machine because I talked my self out it. But, I believe that the world is more than phyisical. There is also a Spritual
Realm that is the next plane. These are perhaps the visions of what a person remember seeing in afterlife experiences that they believe to be a classic vision of heaven.
But, on this plane time is irrelevent. There is but one time the Here and Now everything else is speculative. And, I believe that the coexistence of these two planes is for the purpose of third dimentional experiences which is impossible in the fourth dimention. But, for this experience to be practical and efficient it would have to extract every possiblity in every instance. Other wise our Subconscience selves would be rolling dice whice I believe would be inefficient and not worthy of the effort.
So say the Man goes to his 10th birthday party and meets his younger self. Now the 10 year old boy has memory of meeting his older self. But, unless you yourself had this same memory you would not. There would be two alternatives. As it should be. Something to note in this instance is that you may be surprised to find that in this reality your 10th birthday party might be different than you remember it being. Or it could be exactly the same, the only difference being that an older you is present. Something that I try to observe is that there is nothing a person can do or not do, that I would be incapable given the same situation there in. Therefore when another person is in joy or in saddness, is dancing on stage or is a seashore hermet, I feel that experience through a higher conscience that is not only shared, but, by the most accurate definition is one and the same. But, this is not time travel it's dimention travel which would also be a fasinating experience. Getting back might be a problem. But, by the time you journeyed to hand full of other worlds your entire thinking of your own world might change. And, you might not want to find your way back because of the infinite possibilities. Who knows the experience might change you more than you change it. You might have been destined to have met yourself at the party which would mean that we could throw free will out the window. But, I believe that in a functional universe free will is really an illusion determined by your reletive position. But then everyone would have to accept there existence as something more than it is. Are we ready?