It's Impossible!

Duncan Reid thinks:

"I'm almost at the machine.
"The time machine?
"Nonsense. A bilgeful of crap. Physical, mathematical, logical impossibility. I proved it once, for a term paper in the philosophy of science."
-Poul Anderson, The Dancer From Atlantis, CHAPTER THREE, p. 27.

Of course. Before he is accidentally pulled into the past, Reid inhabits a world like ours where it can be proved that time travel is impossible. Physically, mathematically and logically? I can comment only on the logic. Physics changes, in any case.

This is logically impossible: a single timeline in which an event, e.g., Hitler's birth, both occurs and is prevented from occurring. However, several other time travel scenarios seem to me to be logically possible:

a later event, e.g., the departure of a time machine, causing an earlier event, e.g., the arrival of a time machine;

an effect causing its cause;

a single discontinuous timeline in which the arrival of a time machine prevents the later departure of that time machine;

a timeline in which Hitler was born and a timeline in which Hitler's birth was prevented, these two timelines being related to each other as earlier and later along a second temporal dimension.

But these scenarios probably are physically impossible.

Jack Havig says:

"'All theory says that what I do is totally impossible. It starts by violating the conservation of energy and goes on from there.'"
-Poul Anderson, There Will Be Time, V, p. 46.

The conservation of energy is a physical law.

In Robert Heinlein's "By His Bootstraps," when the older Bob Wilson steps out of the Time Gate behind him, the younger Bob Wilson is typing:

"'- nor is it valid to assume that a conceivable proposition is necessarily a possible proposition, even when it is possible to formulate mathematics which describes the proposition with exactness. A case in point is the concept "Time Travel." Time travel may be imagined and its necessities may be formulated under any and all theories of time, formulae which resolve the paradoxes of each theory. Nevertheless, we know certain things about the empirical nature of time which preclude the possibility of the conceivable proposition. Duration is an attribute of consciousness and not of the plenum. It has no Ding an Sicht. Therefore -'"
-Robert Heinlein, "By His Bootstraps" IN Heinlein, The Menace From Earth (London, 1983), pp. 40-87 AT p. 40.

Wilson seems to mean that a logical possibility is not necessarily a physical possibility but how is the psychological nature of duration relevant?