Time within the Matrix was designed to be perceived at the same rate as in the Real World. This allowed the real-world bodies to age at the same rate as the mind and the RSI. This also allowed operators to communicate with crew members jacked into the Matrix while simultaneously observing the events from both worlds.
Time is also mentioned in relation to the precognitive abilities that the Oracle and Neo shared, specifically, while talking about the dreams Neo had about Trinity getting shot with a bullet through the heart:
You have the sight now, Neo. You are looking at the world without time.
Then why can't I see what happens to her?
The Matrix could, to a point, be accurately predicted by both the Oracle, who specialized in human psychology, and by Neo, who closely knew Trinity and predicted her future in a dream. The slowed perception of time and "looking at the world without time" both played at the concepts of:
- Time dilation - commonly experienced while dreaming i.e. a second in reality feels longer while dreaming.
- Accelerated brain functions - the illusion of time slowing down due to increased brain power i.e. time did not slow down but, instead, the mind was more quickly processing the information and, as a result, was reacting much faster.
Thanks to his knowledge and sight of the inner workings of the Matrix, Neo was able to understand and predict the chains of cause and effects made by his choices by effectively tracing and simulating the path his choices would make. So long as he understood his choices then he could predict the future, and the quicker he could simulate the path, a process helped by time dilation and increased brain functions, then the further he was able to see into the future.
The entirety of the Matrix, at one point, was also altered to accelerate time such that every mind connected to it were able to live out years in a matter of real-world minutes, by accelerating all minds connected to the Matrix. The pilot, for example, experienced fifteen years inside the Matrix while only actually expending less than an hour in the Real World. This was possible because the mind was processing within the Matrix at a much more rapid rate but, instead of the individual alone moving at hyper speeds (like in the case of an Agent dodging bullets), the entire Matrix and all of the minds connected to it were also all adjusted to process at the same higher speed i.e. if everyone and everything within the Matrix moved, thought, and acted at twice the speed then no discernible change was really ever noticed by any singular mind.
Time is relative. And although the relativity of time was never explored inside the Matrix, it can be assumed that time within the Matrix followed the same principles of relativity that governed reality. Interestingly, this theory supposes that the unnamed Goliath of a pilot was bound to experience time dilation while moving incredibly fast when piloting planes.
- Goliath, the story contains accounts of the human mind being used as processors or computers more than just mere batteries