Time is constantly branching. Every single time a decision is made or chance operates to produce one of several distinct outcomes, a different timeline – a parallel world, if you like – is created for each of the possible outcomes. If time travel is possible, the only one of these realities accessible to the traveler is the one resulting from conditions at the point where he leaves ordinary time to move through the time-stream. In other words, if our hypothetical time-traveler went back in time and murdered his own grandfather before he could reproduce, he could then only travel forward to the timeline resulting from that action, in other words one in which he himself did not exist. But he himself originated in a diferent timeline; though he could never return to that world, and there would be no official record or living memory of him in the world where he was trapped, those he left behind in his own reality would remember him just fine. They would simply perceive him as having vanished without a trace from the moment he activated his time machine, never to return. If time travel is even possible, it must work this way in order to avoid a nonsensical paradox: if the version of himself which broke the timeline ceased to exist when he did so, then he never existed to travel in time to break the timeline in the first place. He wouldn’t fade out of a photograph he carried from his own world, nor would his body fade away; he would be just as real and solid as ever, albeit stranded in a world of his own creation where he never existed. Both worlds are equally real, but our traveler is an alien marooned in one to which he is not native and does not belong. The worlds of causality are completely countless, infinity raised to the power of infinity, but though vast numbers of them may be so alike as to be indistinguishable, the gulf between them – delineated as it is by a dimension of existence we are powerless to bridge – is even more impassable than the void between the galaxies. 
All Possible Worlds
November 9, 2020 by Maggie McNeill
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A neat fantasy, but it would have consequences. Are you familiar with Niven’s All the Myriad Ways?
I’ve seen this same basic idea presented lots of times. If time travel were actually possible, it’s always seemed to me that this is the most logical way it could work.
However, there is so much we don’t understand about time, and physics in general, that I suspect that if time travel really were to actually work that it would work in some fashion that nobody has ever thought of, and the problems of causality would actually be handled some other way.
This is the “many worlds” hypothesis in quantum mechanics.
Here is an explanation of the “many worlds” hypothesis, and its historical background.
And Physics Girl even makes an appearance.
This is really an interesting topic. Your view of time travel is much the same as my view; that that’s how it must work. There are physical structures like wormholes that could function as time machines, and postulating that there’s some law of physics that controls your actions so you don’t alter the timeline just seems to me like a much more complicated solution than branching.
Take into account the (in my view) compelling arguments for the many-worlds interpretation of quantum mechanics, and I think it becomes highly likely. New worlds split all the time as all possibilities are realized; going into the past and altering it is just another choice that produces a split in the world. No special consideration of “altering the past” is even needed; it all becomes much the same thing no matter if you come from the past or the future.
Just one possible model. It comes with a host of problematic implications, hence I have pretty much discounted it. I think the main origin is that some theoretical Physicists see this as a convenient way to plug some rather glaring holes in their theory.
Yes, every model is just one possible model. As the video narrator explains about the many worlds interpretation:
The many worlds model is derived from the mathematics of the wave function, as is the Copenhagen interpretation which collapses the wave function. Countless physically unrealizable things derive from mathematics, eg: Alexander’s horned sphere, or Antoine’s necklace.
But the Copenhagen and the many worlds interpretations of Schrodinger’s wave function are the two we know of so far that deal mathematically self-consistently with it. A third, string theory interpretation, may, or may not. But string theory is far above my pay grade.
The best statement of the nature of the universe I’ve heard is often attributed to the late Douglas Adams (The Hitchhiker’s Guide to the Galaxy), approximately this:
“queerer than we can imagine” is usually attributed to J.B.S.Haldane, before Adams was born; along with “[God must have] an inordinate fondness for beetles.”
Given quantum uncertainty, I can imagine timelines re-merging (rarely) if their differences are small enough.