Human Statues
I always assumed a time machine kind of just disappears once it's travelling through time, such as is demonstrated here initially with his time machine model - a poof and it's gone.
But he's travelling through time from a fixed location, which is what is unique about this particular situation, and I believe the source of the paradox that follows. He travels forward slowly at first and can look out the window, seeing a fast-forwarded version of life. That's when it occurred to me; if he can see them, they can see him.
Say a man travels 50 years looking out that window. He has seen a fast-forwarded version of all of the events occurring out that window during those 50 years. The moment he starts to travel is A, the destination 50 years in the future is Z. He exists in that space every moment from A to Z, except the experience for him is much shorter.
The trip took 50 years for those outside the window, and only a few minutes for him inside the time machine, but he was physically in that chair for every point in time between A and Z.
To me, this seems to suggest the time machine wouldn't appear to vanish. Instead it and its traveler should appear as fixed statues: present and detectable at all times, but outside of our spheres of influence because of the difference in our respective speeds of travel.
There's something about this train of thought that seems paradoxical and worth following. Any thoughts?