I know I have read this somewhere and I wonder if it is correct. When the Fellowship comes out of Lothlórien it is implied that, during the time it has taken for them to be in Lothlórien, a lot more time has passed in the world outside. The Fellowship don't realize this themselves, it is supposed to be implied by mentions of the moon cycle. Link to timeline for tLotR.
I believe that any references to the passing of time in the book are merely meant to show that the peacefulness and isolation of Lórien made them forget their task and their urgency (not to mention ease the hurt of losing Gandalf).
"They remained some days in Lothlórien, so far as they could tell or remember." (Book II, Chapter 7)
And as they are leaving:
"Their hearts were heavy; for it was a fair place, and it had become like home to them, though they could not count the days and nights that they had passed there." (Book II, Chapter 8)
Although there is a slightly longer and more specific passage between Legolas and Frodo the night before attempting the rapids. Sam is trying to figure out how many days they stayed in the company of the Elves, but is having trouble reconciling his memory with the phase of the moon:
"Legolas stirred in his boat. 'Nay, time does not tarry ever,' he said; 'but change and growth is not in all things and places alike. For the Elves the world moves, and it moves both very swift and very slow. Swift, because they themselves change little, and all else fleets by: it is a grief to them. Slow, because they do not count the running years, not for themselves. The passing seasons are but ripples ever repeated in the long long stream. Yet beneath the Sun all things must wear to an end at last.'
"'But the wearing is slow in Lórien,' said Frodo. 'The power of the Lady is on it. Rich are the hours, though short they seem, in Caras Galadhon, where Galadriel wields the Elven-ring.'" (Book II, Chapter 9)
It's hard to figure out what the truth is here. Legolas seems to believe that the trouble is simply one of memory in such a place. Frodo, who knows Galadriel possesses the ring Nenya, seems to think there's actual magic somehow changing the passage of days within Lothlórien. As far as I can tell, it's left unresolved (especially since the person who would probably know best, Gandalf, the bearer of Narya, was unavailable to give his opinion).
This is a holdover from earlier drafts
Originally, Tolkien was planning to have time inside Lothlórien either move slower or come to a complete halt. He later decided it was more effort than it was worth, and so removed the idea, but left in a conversation about how the time still "felt different".
Verlyn Flieger summarizes this as such:
As with space, so with time. The relation of Lórien to the outside world gave Tolkien the opportunity to experiment with Faërie time. Yet it also gave him some trouble. Notes, diagrams and rough drafts show that he seriously considered placing Lórien in a different mode labelled ‘Lórien time’, which could intersect with, yet remain different from, an interlocking ‘Mortal time’." But this was hampered by his own requirement of inner consistency and his careful chronology of days and nights and seasons, lunar phases changes of weather. The fairy tale time—warp did not Tale of Years chronology in The Lord of the Rings’ Appendix B, which charts the progress of the Fellowship month by month, and often day by day. After juggling vainly to stretch or shrink Lórien time without disturbing the rest of Middle-earth, he finally abandoned the effort altogether. ‘Better to have no time difference’ he wrote, and left it at that.
Yet, not quite. He inserted a conversation into ‘The Great River’ chapter in which Frodo, Sam, Aragorn and Legolas discuss the length of their stay in Lórien, and whether time slowed down, speeded up or stopped while they were there. That they disagree is as far as Tolkien allowed himself to go with Faërie time. Sam has lost track of the phases of the moon, and speculates that time doesn’t ‘count’ in Lórien; Frodo attributes the apparent slowdown to Galadriel’s Elven ring; Aragorn seems unaware of any discrepancy; and the Elf Legolas explains that since Elves are immortal, time, while it does not pause, passes both faster and slower for them than for Men. As with Frodo’s vision of Lórien, Tolkien uses indirection to convey the indescribable. "His conversation concludes with Aragorn telling Sam he has lost his count until the travellers return to the river and ‘the time that flows through mortal lands’.
Verlyn Flieger, "Faerie: Tolkien’s Perilous Land", Tolkien: Maker of Middle-earth page 40
Tolkien's drafts and notes of this earlier idea can be found in The Treason of Isengard, in various places on pages 285-6, 354-5, 358, 363, 366, and 367-9. Many of the places in the narrative are still found in the published book, but in the earlier drafts it was a lot more explicit, while in the published book it's more of left as an open-ended question, or all has rational explanations when one looks at the chronology in the back and sees that time was indeed passing.
Tolkien's notes show that he was working on a chronology where the time actually stopped.
Jan. 14 Over Silverlode
Jan. 15 Leave Lórien
The Treason of Isengard
Compare this to the published chronology in Appendix B, in which a whole month passes:
Jan. 17 The Company comes to Caras Galadhon at evening.
Feb. 15 The Mirror of Galadriel.
Feb. 16 Farewell to Lórien.
The Lord of the Rings - Appendix B - The Tale of Years
So in the original draft, Sam noticed the Moon doesn't change because no time had passed. In the published book Sam notices the Moon didn't change because exactly one month had passed and he simply lost track of the time.
Tolkien also worked on an idea of time passing by, just at a slower rate. He produced three diagrams showing how the two time frames of reference intersected, which sort of look like Minkowski space-time diagrams (I know that they're not, but they have a similar look.)
For more information and analysis of Tolkien's changing ideas about the concept of Time, see the book A Question of Time: J.R.R. Tolkien's Road to Faërie by Verlyn Flieger.
Time in Lothlórien passes differently than in Middle-earth.
Quote from The History of Middle-earth - "The Tale of Years":
The Coy. [Company] stays in Lórien for many days. They cannot count the time, for they do not age in that time, but outside in fact 30 days goes by.
They cannot count the time, for they themselves do not age or only very slowly. Outside in fact about 30 days passes.