Was it Gollum who untied Sam's Elf-rope?

Question

When Frodo and Sam are safely down on the ground after having climbed down using the Elf-rope, Sam pulls it and, to the surprise of both Hobbits, it comes back down.

Frodo assumes that Sam had been sloppy tying it, whereas Sam thinks that the rope is magical and knowingly aided them by untying itself for their benefit.

Is not a plausible -- likely, even -- alternative explanation that it was simply Gollum who had caught up with them, a bit too late for his liking, and tried to wound the Hobbits by untying the rope for at least one of them to fall down and get hurt, so that he could more easily snatch back the illegally stolen Preciousssss from the nasty, cruel Hobbitses?

As far as I can remember, this is never explained, but to me, it seems quite possible. While this is "fantasy", and literal magic exists in their world, it seems a bit far-fetched to me that a rope would be able to think and "untie itself" in that manner, even if it was made by Galadriel herself. Sentient ropes that think and act on their own seems to go a bit far even considering the context, while acknowledging that the Ring is indeed another "dead object" that appears to have a will on its own...

Answer 1

In the novel the rope is noted to have been secured tightly

He took up the rope and made it fast over the stump nearest to the brink.

_{^{LOTR: The Two Towers}}

and it does indeed fall down when tugged, just as occurs in the film.

"Noodles! My beautiful rope! There it is tied to a stump, and we're at the bottom. Just as nice a little stair for that slinking Gollum as we could leave. Better put up a signpost to say which way we've gone! I thought it seemed a bit too easy." "If you can think of any way we could have both used the rope and yet brought it down with us, then you can pass on to me ninnyhammer, or any other name your Gaffer gave you," said Frodo. "Climb up and untie it and let yourself down, if you want to!" Sam scratched his head. "No, I can't think how, begging your pardon," he said. "But I don't like leaving it, and that's a fact." He stroked the rope's end and shook it gently. "It goes hard parting with anything I brought out of the Elf-country. Made by Galadriel herself, too, maybe. Galadriel," he murmured nodding his head mournfully. He looked up and gave one last pull to the rope as if in farewell. To the complete surprise of both the hobbits it came loose. Sam fell over, and the long grey coils slithered silently down on top of him. Frodo laughed. "Who tied the rope? " he said. "A good thing it held as long as it did! To think that I trusted all my weight to your knot!" Sam did not laugh. "I may not be much good at climbing, Mr. Frodo," he said in injured tones, "but I do know something about rope and about knots. It's in the family, as you might say. Why, my grand-dad, and my uncle Andy after him, him that was the Gaffer's eldest brother he had a rope-walk over by Tighfield many a year. And I put as fast a hitch over the stump as any one could have done, in the Shire or out of it." "Then the rope must have broken - frayed on the rock-edge, I expect," said Frodo. "I bet it didn't! " said Sam in an even more injured voice. He stooped and examined the ends. "Nor it hasn't neither. Not a strand!" "Then I'm afraid it must have been the knot," said Frodo. Sam shook his head and did not answer. He was passing the rope through his fingers thoughtfully. "Have it your own way, Mr. Frodo," he said at last, "but I think the rope came off itself - when I called." He coiled it up and stowed it lovingly in his pack. "It certainly came," said Frodo, "and that's the chief thing".

Noting that the rope burns Gollum's skin when he touches it and Sam's proclivity with knots, it seems most likely that the rope is imbued with Elven magic (it glows, for example) rather than that Gollum untied it or that Sam tied a duff knot.

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In the film script, the order of events is even clearer. The rope "unties itself".

SAM tugs on the rope - hard.

ANGLE ON: The ELVISH ROPE unties itself and plummets.

ANGLE ON: The ROPE lands at SAM’S FEET...SAM stands speechless for a moment, and then he looks at FRODO who shrugs.

FRODO: Real Elvish rope.

Answer 2

Elves—or at least, those of Lothlórien—have some funny ideas about what is and isn’t magic.

‘Are these magic cloaks?’ asked Pippin, looking at them with wonder.

‘I do not know what you mean by that,’ answered the leader of the Elves. ‘…we put the thought of all that we love into all that we make. Yet they are garments, not armour, and they will not turn shaft or blade. But they should serve you well: they are light to wear, and warm enough or cool enough at need. And you will find them a great aid in keeping out of the sight of unfriendly eyes, whether you walk among the stones or the trees.’

— Book Two, Chapter VIII, ‘Farewell to Lórien’

(Paraphrase: ‘They’re not magic, they’re just your ordinary, everyday, temperature-controlled colour-changing camouflage cloaks imbued with their makers’ thoughts. Everybody has those, right?’)

To my mind, the bolded part means more than just ‘we think of nice things while making stuff’. Some part of the maker’s thought is literally in the things Elves make. They think of light and shade and trees and earth while making cloaks, and the cloaks then adapt to the wearer’s environment and need. The cloaks don’t have to be sentient, deciding how best to blend into a particular environment; they just do it. The thought is the maker’s, not the item’s.

Likewise, the rope doesn’t need to be sentient to have the helpful trait of coming untied when desired. While spinning the rope, the maker thinks of all the useful things a rope can do, and the result is a rope that does useful things for its owner.