Unless of course, regardless of the possibility of time travel, events conspire to prevent the invention of your time-travelling machine. I'm no theoretical physicist, which renders my musings technically moot, but I have envisioned a "tree of time," an image of the time line that splits every time a quantum event occurs, and both/all outcomes of that event play out, meaning that there is an exponential growth in the number of parallel universes (this is the "many worlds" interpretation of quantum theory).
A time machine would essentially mean that an element of this tree, a twig, has been bent backwards and grows back into the time line. If you imagine the way a tree grows, which I think models this idea of a time line rather well, you can see why the time line would never have "grown" that way in the first place.
Particularly since events are affected after the twig fuses again, essentially meaning that events in the future are affecting the events in the past that lead to them in the first place (I am aware that this is a re-imagining of all the same paradoxes and problems of time travel, but I think a visual model is very helpful).
So there is a loop through which events are played over and over, different each time. It is not unreasonable to suggest that, unless all events line up perfectly (which they probably wouldn't, given the quantum events making new universes during this process, leading to new futures with the same loops. The whole period would be incredibly tangled) eventually events will occur whereby the loop never occurred at all. It has been "pruned" from existence.
This would of course be fertile ground for the first loop to occur, so it is no more stable than the loops ever were. What effect this would have on history (time is in flux? Thank you Doctor Who, very informative) I can't say. I would conclude that there must one of two outcomes:
1: Events conspire so that the time machine was never invented.
2: Events conspire so that the time machine is never used.
Another possibility that come to mind is that the invention or activation of a time machine would cause your universe to be pruned from the rest of the tree of time. It would continue to growth naturally, but you could not go further back in time. If it is the invention that causes this, there won't be any paradoxes about inventing time machines, but others may become available as the tree grows and matures. If activation causes this, then despite your fully functional time machine, there is no past you can get back to.
The future, it it exists yet (and there is no reason to suggest that it does not), is actually an infinite number of possible futures, each created every time there is a quantum event in one of them. The effect on the human-scale world is inestimable, but going to the future would not be as enlightening as one would hope. Who knows which one you will get to, whether or not that branch of the future will be ruined by your arrival, and if you do not return to your own time at the moment you left, no doubt more quantum events would have occured during your brief absence, leaving a number of time lines/universe devoid of your presence. Although you would never notice it, your family in those universes would suffer emotional distress from our disappearance.
Then again, if human affairs are affected by or are quantum in nature, there are a large number of universes where you went missing anyway, or have died, were never borne, the human race never evolved etc, assuming that there were a sequence of quantum events that could have led up to such incidents.
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