Elves leaving for Aman by the Fourth Age, while bound to the world and its fate

Question

Aman was detached from the world itself by Eru Ilúvatar after the Númenóreans tried to invade it, and, in a sense, it is a place in another dimension; so elves moving there permanently while still bound to the world confuses me. Does that mean that Aman is still part of the world, in some multi-layered sense?

Answer 1

There are two things called "the world" in the Legendarium:

Arda - the realm of land and sea where much of the action takes place. This is the "world" from which Aman was removed, when it was reshaped into a globe (i.e. planet Earth).

Eä - the whole created universe given being by the Music of the Ainur. This is the "world" to which immortal spirits† are bound.

Aman is part of Eä, but no longer part of Arda.

†it's unclear whether Ainur are able to leave. Gandalf possibly did when he died, being sent back by Eru. Morgoth was also forcibly ejected from Eä. Sauron and Saruman, however, appear to be forever bound, similarly to Elves.

Answer 2

As you say, Aman was not properly part of the world anymore, but it was still possible for Elves to travel there by the Straight Road. Essentially, even though Aman was not part of the world, the Valar allowed Elves to sail there along the path that would have existed had the world not been made curved.

Thus in after days, what by the voyages of ships, what by lore and star-craft, the kings of Men knew that the world was indeed made round, and yet the Eldar were permitted still to depart and to come to the Ancient West and to Avallónë, if they would. Therefore the loremasters of Men said that a Straight Road must still be, for those that were permitted to find it. And they taught that, while the new world fell away, the old road and the path of the memory of the West still went on, as it were a mighty bridge invisible that passed through the air of breath and of flight (which were bent now as the world was bent), and traversed Ilmen which flesh unaided cannot endure, until it came to Tol Eressëa, the Lonely Isle, and maybe even beyond, to Valinor, where the Valar still dwell and watch the unfolding of the story of the world. And tales and rumours arose along the shores of the sea concerning mariners and men forlorn upon the water who, by some fate or grace or favour of the Valar, had entered in upon the Straight Way and seen the face of the world sink below them, and so had come to the lamplit quays of Avallónë, or verily to the last beaches on the margin of Aman, and there had looked upon the White Mountain, dreadful and beautiful, before they died.

_{The Silmarillion, "Akallabêth: The Downfall of Númenor"}

Answer 3

While Aman was no longer attached to the (now-spherical) world of Arda, it remained physically present and accessible by traveling through space. There are several pieces of evidence for this. One, already mentioned, is that the Eldar could still leave Middle-earth by taking the Straight Road—this is, by flying their ships to the Undying Lands.

A second key piece of evidence is found in the last revised version Tolkien created of the Second Prophecy of Mandos, telling of the end of the world. In the aftermath of Morgoth's return, Aman will be visible from Middle-earth.

Thus spake Mandos in prophecy, when the Gods sat in judgement in Valinor, and the rumour of his words was whispered among all the Elves of the West. When the world is old and the Powers grow weary, then Morgoth, seeing that the guard sleepeth, shall come back through the Door of Night out of the Timeless Void; and destroy the Sun and Moon. But Eärendil shall descend upon him as a white and searing flame and drive him from the airs. Then shall the Last Battle be gathered on the fields of Valinor. In that day Tulkas shall strive with Morgoth, and on his right hand shall be Eönwë, and on his left Túrin Turambar, son of Húrin, returning from the Doom of Men at the ending of the world; and the black sword of Túrin shall deal unto Morgoth his death and final end; and so shall the children of Húrin and all Men be avenged.

Thereafter shall Earth be broken and re-made, and the Silmarils shall be recovered out of Air and Earth and Sea; for Eärendil shall descend and surrender that flame which he hath had in keeping. Then Fëanor shall take the Three Jewels and he will break them and with their fire Yavanna will rekindle the Two Trees, and a great light shall come forth. And the Mountains of Valinor shall be levelled, so that the Light shall go out over all the world.

After Fëanor finally repents his sins and reveals how the Silmarils were made, so that they may be broken open and the pure light of the Two Trees revealed, Yavanna may recreate the Trees. Because the mountains that the Valar raised to block their light have been destroyed in the violence of the Dagor Dagorath, the Trees' light will be visible everywhere, even in Middle-earth.