How does time work in The Matrix?

Question

I'm somewhat confused about the nature of Time in the Matrix, but I have 3 different possibilities, all of which are neither confirmed nor denied in the trilogy as far as I can see.

1. Possibility 1: Time is fixed. By saying time is fixed, I don't mean it's constantly one specific point in time, but it is always the 90s (as I know the Architect stated that the 90s were the optimum time). The way I envisage this possibility, it goes from Jan 1 1990 to Dec 30 1999, then the next day is Jan 1 1990 again (an infinite loop). The people of the Matrix, however, are oblivious of this. In this possibility, humanity is in stagnation - no development of new ideas beyond those attained by 30 Dec 1999. (This would be denied if we see that the date in number 3 exceeds 1999, as the film itself was made post 1999).
2. Possibility 2: Time repeats itself. Similar to Possibility 2, but instead of limiting it to the 90s, the Matrix runs from some point near the beginning of humanity (perhaps the year 0? Your guess is as good as mine here) and runs until the war between the machines and humans erupts, then goes back to the beginning again. Supported perhaps by Smith's statement in the first movie about Decartes being an evil genius or something.
3. Possibility 3: Alternate timeline. Similar to the above possibility in that time for those in the Matrix begins from some point (an unknown point in time), but continues without the war between humanity and the machines erupting - a completely alternate timeline.

I'm not claiming to be an expert on The Matrix, but I'm looking for evidence within the movies to explain how time works for those in the Matrix itself - something that I've overlooked. (Note however: if this proves to be impossible i.e. there is no evidence to support one of these possibilities (or another one for that matter), I am willing to accept materials external to the trilogy).

Answer 1

In the film, we learn that the date is sometime after July 1998 but before December 1999. That date appears on Neo's Security file and Morpheus specifically references "the world as it was at the end of the Twentieth Century" in his 'desert of the real' speech.

I think we can be reasonably certain that your hypothesis 1 is the closest;

• Time in The Matrix advances normally until it reaches late 1999.
• The inhabitants are then memory-wiped and reset to an earlier date, say January 1st 1990.
• Repeat ad infinitum

This loop has presumably happened at least 40 times since creation of The Matrix, factoring in the time between the end of the Machine War, the creation of the Paradise Matrix and the Nightmare Matrix and the present day.