Are There Worlds or Times Side By Side?

Off for Thanksgiving today I got up and was watching the Twilight Zone. It was the episode where Chris Horne was going from Ohio to California in 1847. They were in the desert, nearly out of water, his 8 year old son possibly dying, and everybody wanting to turn the wagons around and go back. Horne tells them he's going to look for water, or game, on the other side of a ridge a hundred yards away.
On the ridge he sees a paved highway, and power lines on top of huge towers, he looks back and the wagons and people he just left have disappeared. Walking on he examines the highway and is almost run down by a monster, a semi. Walking on he comes to a diner, where he discovers many astounding things, including a calendar that says the year is 1961, not the 1847 he left behind a short while ago.
There's been a theory that all times exist simultaneously, not separately, not as a straight line as is supposed in most reincarnation scenarios, not a stream of time, more like parallel universes where given the ability we could step from one time or reality to another. If this were true, it would mean that as I sit here writing this, other worlds other realities exist in the same space, I could, possibly do, reach out and touch something that in this reality doesn't exist, that I'm not even aware of, yet still it exists and is there to be touched even though those in that reality aren't anymore aware of me than I of them. In the case of the show, he stepped into another time unknowingly to get a drug, penicillin, unknown in his time,  to save the life of his son, who according to the encyclopedia he read in the future was destined to do great works as a doctor. After getting the penicillin, he returned to his own time by crossing back over the ridge, just a few seconds after he left according to the others, although he perceived it as hours.
I remember when I was in the fifth grade, I've posted about this before but it's relevant, I sat in the first row, and would apparently doze off dreaming for lack of a better term. I was in a different place, a different time, a different life, and as I remember it seemed to last a long times, hours, weeks, months, suddenly I'd come awake, nobody seemed to have noticed, not classmates, not the teacher who was right in front talking or writing on the chalkboard. Then I'd look at the clock and only a few minutes or seconds had passed, yet it seemed like I'd dozed forever. Now, many times, grown up, I go back to sleep usually for a few minutes but I seem to be in a different life, sometimes similar to this, most times with the same people, or impressions of the same people, but not this. I call it dreaming real, real yes, but not this reality, but real.
It makes me wonder, do we live in many realities simultaneously? Are we the physical reality of a single soul, or multiple souls, or are all the people in this reality multiple physical realities of a single soul, living in this as well as many other parallel realities?  Think about it, I'd be interested in reading your comments and learning what you think.

Lee Murray