Eldest, that's what I am. Mark my words, my friends: Tom was here before the river and the trees; Tom remembers the first raindrop and the first acorn. He made paths before the Big People, and saw the Little People arriving. He was here before the Kings and the graves and the Barrow-wights. When the Elves passed westward, Tom was here already, before the seas were bent. He knew the dark under the stars when it was fearless -- before the Dark Lord came from Outside.
In this passage, Tom goes back in time, until he reveals that he was present in Arda even before Melkor, who was the first of the Valar to arrive. As far as I know, the only "entity" that arrived in Arda before Melkor was the Secret Fire that brought the inert planet to life. From the Ainulindale in The Silmarillion:
. . . but Iluvatar called to them [the Ainur], and said: "I know the desire of your minds that what ye have seen should verily be, not only in your thoughts, but even as ye yourselves are, and yet other. Therefore I say: Ea! Let these things Be! And I will send forth into the Void the Flame Imperishable, and it shall be at the heart of the World, and the World shall Be; and those of you that will may go down into it." And suddenly the Ainur saw afar off a light, as it were a cloud with a living heart of flame; and they knew that this was no vision only, but that Iluvatar had made a new thing: Ea, the World that Is.
Thus, if Tom is a manifestation of the Flame Imperishable, then Tom's imperative is "to be" not "to change" or "to defy," which might help explain the paradox of his undeniable power juxtaposed with his seeming inability to be of help against Sauron. As Goldberry says, "He is." He can influence a living creature's state of being -- i.e., he can influence Old Man Willow to go back to sleep and release his prisoners -- but he cannot change their nature -- i.e., he cannot remove the evil that gnaws at the heart of Old Man Willow. He also has no sway over the weather -- it "is." This is why the Ring has no effect on him, and he can see through its magic (Frodo remains visible to him, even when the Ring is on Frodo's finger), but he cannot negate its evil.
Consider these statements about Bombadil from the Council of Elrond:
"But within those bounds nothing seems to dismay him [Bombadil]," said Erestor. "Would he not take the Ring and keep it there, for ever harmless?"
"No," said Gandalf, "not willingly. He might do so, if all the free folk of the world begged him, but he would not understand the need. And if he were given the Ring, he would soon forget it, or most likely throw it away. Such things have no hold on his mind. He would be a most unsafe guardian; and that alone is answer enough."
"But in any case," said Glorfindel, "to send the Ring to him would only postpone the day of evil. He is far away. We could not now take it back to him, unguessed, unmarked by any spy. And even if we could, soon or late the Lord of the Rings would learn of its hiding place and would bend all his power towards it. Could that power be defied by Bombadil alone? I think not. I think that in the end, if all else is conquered, Bombadil will fall, Last as he was First: and then Night will come."
"I know little of Iarwain save the name," said, Galdor; "but Glorfindel, I think, is right. Power to defy our Enemy is not in him, unless such power is in the earth itself. And yet we see that Sauron can torture and destroy the very hills . . . ."
This theory also suggests an interesting development, should Sauron have recovered the Ring and succeeded in conquering all of Middle-Earth. What would happen to Arda when Sauron and his forces finally overcome the last remaining power in Middle-Earth -- Tom Bombadil? I would postulate that the Dark Lord would suddenly find himself the master of a dead, inert planet. With the destruction of the living incarnation of the Flame Imperishable, the Secret Fire would return to Eru Iluvatar, and Sauron would be left with nothing.
Here's another interesting bit to consider along with my theory, also from the Ainulindale in The Silmarillion:
To Melkor among the Ainur had been given the greatest gifts of power and knowledge, and he had a share in all the gifts of his brethren. He had gone often alone into the void places seeking the Imperishable Flame; for desire grew hot within him to bring into Being things of his own, and it seemed to him that Iluvatar took no thought for the Void, and he was impatient of its emptiness. Yet he found not the Fire, for it is with Iluvatar.
Would it not be the height of ironies if Melkor's greatest lieutenant Sauron could have succeeded in "conquering" Arda, only to have the Flame Imperishable -- his ultimate desire -- return to Iluvatar, leaving him with an empty, dead world -- yet another Void?
This is where my original theory ended. I would like to add one last bit, based on a question from our new friend Per -- If Tom is a manifestation of Eru's Secret Fire, then who is Goldberry?
I think Goldberry is exactly who Tom says she is and who she says she is. She is the River-woman's daughter -- a water elemental who has taken physical shape as Tom's companion.
"Come dear folk . . . . Laugh and be merry! I am Goldberry, daughter of the River."
The hobbits, Frodo in particular, are moved with "a joy that he did not understand. He stood as he had at times stood enchanted by fair elven-voices; but the spell that was now laid upon him was different: less keen and lofty was the delight, but deeper and nearer to mortal heart; marvellous and yet not strange." Frodo KNOWS her because her essence has been around him all his life. She "is" water. Every living creature would experience an immediate intimacy with her.
I certainly do not see her as Yavanna in disguise, the muse/protector of plant and animal life. Goldberry is all about water and its cycle of being -- from raindrop to running stream to melting snow to evaporating water vapor and back to raindrop. She "is" water. Tolkien's descriptions of her always allude to water -- falling, rippling, glinting, shimmering, flashing. Her voice is described "as young and as ancient as Spring, like the song of a glad water flowing down into the night from a bring morning in the hills." The sound of her footsteps "was like a stream falling gently away downhill over cool stones in the quiet of the night."
Later Tom names the autumn rainstorm that settles over his house and land as "Goldberry's washing day and her autumn-cleaning." They hear her singing but do not see her all day -- she "is" the rain. That evening she returns to declare, "The rain has ended and new waters are running downhill, under the stars. Let us now laugh and be glad!"
Later she sings for the hobbits, "songs that began merrily in the hills and fell softly down into silence; and in the silences they saw in their minds pools and waters wider than any they had known, and looking into them they saw the sky below them and the stars like jewels in the depths."
When the hobbits bid her goodbye, she is the epitome of water evaporating in the sun: "There on the hill-brow she stood beckoning to them: her hair was flying loose, and as it caught the sun it shone and shimmered. A light like the glint of water on dewy grass flashed from under her feet as she danced." Isn't that the very picture of dew evanescing in the morning light?
I think Tom's description of his first "meeting" with Goldberry is very interesting:
By that pool long ago I found the River-daughter,
fair young Goldberry sitting in the rushes.
Sweet was her singing then, and her heart was beating!
So very enigmatic! When Tom "found" Goldberry, was he in fact meeting another existing being, or did his appreciation of the beauty of the sound of the water cause her to manifest as a physical entity? To arise from the running water and take form as a creature with a beating heart? I ask this because to me, Goldberry seems to be both a separate entity and a part of Tom. In fact, Goldberry acknowledges Tom as being "the Master of wood, water, and hill." Did Tom so delight in the water that he asked it to take shape, with the result being Goldberry -- "my pretty lady"?
I see Tom and Goldberry as a Yin-Yang relationship; opposites attracting each other; the everlasting creative Fire and the never-ending cycle of Water living in perfect harmony.