From Farsight's source:
Having already rocked the mathematical world with is incompleteness theorem, Gödel now took aim at Einstein and relativity. Wasting no time, he announced in short order his discovery of new and unsuspected cosmological solutions to the field equations of general relativity, solutions in which time would undergo a shocking transformation. The mathematics, the physics and the philosophy of Gödel's results were all new. In the possible worlds governed by these new cosmological solutions, the so called rotating or Godel universes, it turned out that space-time structure is so greatly warped or curved by the distribution of matter that there exist timelike future directed paths by which a spaceship, if it travels fast enough - and Gödel worked out the precise speed and fuel requirements, omitting only the lunch menu - can penetrate into any region of the Past, present, or future.
Gödel, the union of Einstein and Kafka, had for the first time in human history proved, from the equations of relativity, that time travel was not a philosopher's fantasy but a scientific possibility.
...
Gödel was quick to point out that if we can revisit the past, then it never really "passed." But a time that fails to pass is no time at all. Einstein saw at once that if Gödel was right, he had not merely domesticated time: he had killed it.
So here we have, it seems, Farsight's source explicitly stating that Gödel's solutions seem to suggest that time travelling into the past or the future could be as simple as heading in the right direction at the right speed, and then, seemingly, going on to demolish Farsight's entire premise by stating that the implication is that the past exist as a tangible thing somewhere (which no longer requires us to move everything back to where it was), and that the implication of that is that if these solutions mirror reality then time, as we think of it, is essentially another direction in space.