Dr. Max Tegmark, Cosmologist from the University of Penn., discusses in his essay "Parallel Universes" the possibility of four levels of parallel universes. Levels 2 - 4 involve different universes, but a level 1 parallel universe exists within our own. As Kyle Broflovski's mom would say, "What-what-what!?!"
At first thought, Mrs. Broflovski's reaction would be warranted. But think a minute about the wacky nature of infinity. If our universe is infinite, and the laws of physics remain the same, then in an infinite universe there has to be other conditions that create other Earths - with another you living on it.
Level 1 Parallel Universes
Dr. Tegmark states that these parallel universes are regions that are beyond our cosmic horizon - that is, regions beyond the limit of our ability to see or detect (approximately 40 billion light years. We can see 14 billion light years away, but because of expansion, by the time the light reaches us, the object we see is now 40 billion light years away). This region of space is the Hubble volume or horizon volume. Since we cannot see beyond this volume, it can be considered a "universe." The other regions are other "universes," some being parallel to ours. All the regions are contained by one multiverse.
For Dr. Tegmark, these parallel universes will, at some point, diverge from ours. In many ways, this is similar to the quantum parallel universe (level 3 parallel universe) where different possibilities - story lines, if you will - exist. For him, then, there is still essentially a uniqueness to each level 1 parallel universe. But in a truly infinite universe, is that necessarily the case? Can there be Earths parallel to ours in every way? In an infinite universe, even an incredibly complex chain of random choices and events will be duplicated. And, in an infinite universe, the most incredible rarities can still happen an infinite number of times (infinity can be the ultimate head trip - or headache!).
Differences Between Level 1 and Level 3
One difference between level 1 and level 3 parallel universes is that when there is a possibility of an action or event happening in different ways, in the level 1 parallel universe the different results happen in different regions of the same multiverse, but in a level 3 parallel universe a brand new multiverse is created for each possible outcome. Another difference is that in the level 1 parallel universe, the different result does not have to happen at the same time. In some regions, there are Earths just like ours but millions of years older. In other regions, a solar system is just forming - one that will create another Earth.
Hello Me, This Is Me
Some aliens can be different copies or versions of us. Maybe one day we will receive a signal, and we will think it was our own somehow bounced back, but no, it will be from another Earth.
"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy" (Hamlet Act 1, scene 5, 166–167).
Tegmark, Max. "Parallel Universes." Science and Ultimate Reality: Quantum Theory, Cosmology, and Complexity. J.D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press, 2004. 459 - 491. Also posted at <http://www.wintersteel.com/files/ShanaArticles/multiverse.pdf>.