I think that before we can understand the passage of time in dreams we need to reflect upon the passage of time in our daily lives. Time intervals, or the passage of time, seem to be directly related to our activities and perceptions. Albert Einstein responded to questions about his theory of relativity by saying, "Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That's relativity."
Age is a factor as well. When I was a boy, I frequently passed a house where a retired man lived. He would often be sitting on his porch, and I would stop and talk with him. I can still vividly recall a conversation one day when he told me that his days were flying by. He said that as he got older, the days passed more quickly. Now in the later years of his life, he said the days were racing by.
His comments about age and the passage of time are not unique. Many have observed this effect, and I too sense time as moving faster as I have aged. So what is happening here? No one seems to know for certain, but there are theories that involve memory, metabolism changes, and the percentage of life remaining.
At the other end of the age scale, we find that children often think an hour’s trip is an eternity. For them, time is often moving at a snail’s pace. In my own life, I have noticed that my time in elementary school seemed very long compared to my time in junior high and high school. And my time in college seemed to pass much faster than my high school years. Perhaps because everything is new to the young, they focus on every detail, while adults tune out much that has become routine.
Whatever the cause, our perceptions of the passage of time do seem to be related to our current activities, our degrees of focus, and the amounts of pleasure we get from those activities. This concept of psychological time is measured by our senses and brain. This type of time is contrasted with physical time as measured by some external device such as a clock.
What type of time do we experience in dreams? The film industry has much to say about this with movies like Inception. But does this movie or other similar interpretations have any real relationship to actual dreams. The answer is probably not. Studies have been conducted to try to determine how real time and dreamtime differ. The consensus opinion seems to be that they don’t. See http://indianapublicmedia.org/amomentofscience/time-passes-dreams/ and http://filmschoolrejects.com/features/inception-time-passes-slower.php
The passage of time in dreams is similar to actual waking life. Possibly, the explanation given by Christopher Nolan who made the film Inception is correct. He suggests that because in dreams we can change locations and focus in an instant, we think that a greater amount of time is involved. Suppose in a dream we walk out to our car to drive to work. The scene can abruptly shift from walking to the car to arriving at work. Similarly, once we arrive, the next scene may have us in our office. We have a perception that a certain amount of time has passed because we associate the drive to work and walk into the building with the passage of a certain amount of time. In fact, only a few minutes may have passed because of the way the mind can rapidly shift scenes and focus, and roughly corresponds with actual time spent dreaming.
However, one effect is real and can be measured. I have written about the lengthening of dreams in a previous post. Dreams increase in length as the night progresses, with the last dream being the longest. The last dream can last up to 45 minutes, so with the additional effect of a long time passage due to rapid scene changes, we can awake with the perception that we experienced days or even weeks or longer in the dream.