I've been meaning to do this post for a long time, given my extensive use of other worlds in my writing, so here it is. Other worlds are common in fantasy and science-fiction, but they actually have quite a solid basis in physics as well. Here, I'll talk about "other worlds" as other universes, not just other planets within our own universe, but places that are not directly connected to us in space and time. Think The Golden Compass, Alice in Wonderland, Narnia, and hundreds of sci-fi books that I don't know about.

People have thought about other worlds for centuries. The idea of spirit realms, Heaven and Hell, and purgatory were commonly held beliefs even in times B.C. Even a multiverse was posited by Leucippus, the ancient Greek philosopher who also posited atoms.
There are many different options for other worlds, so I'll go through them all:

1) Other dimensions
Having another one (or two, or three...) spatial dimension could cause worlds of different dimensions to be separated. We live in a world with three visible spatial dimensions: things are 3-D in our universe, not flat (2-D) or linear (1-D). I say "visible spatial dimensions" because it is possible that there are tiny dimensions that we can't see. They could be curled up, like so:

Now, I admit this picture is not self-explanatory, so let me explain. Say you live in a 2-D universe. It so happens to be that flat sheet in the picture (the plane below the loops). At every point in this plane, however, there is another dimension curled up (those circles). Here it is shown as going up into the third dimension, but in our world, the "sheet" would be our 3-dimensional universe. These little curls are a higher fourth spatial dimension, which, assuming they are very VERY small, are not visible or traceable to us. Though perhaps with better technology, we will someday trace them (I read about this in Lisa Randall's Warped Passages, which is a really good book that is worth the read).
Another possibility for other dimensions are dimensions above our three dimensions. Our 3-D world is embedded in a higher dimensional "bulk". You can't imagine the higher dimensions, since we are 3-dimensional beings, but we can see what this would be like with an analogy. A 2-D world within a 3-D world would perceive a 3-D sphere passing through it as a series of different-sized discs as seen in the diagram on the right. Likewise, if a hypersphere (4-D sphere) passed through our universe, we would see it a series of different-sized spheres. We would see projections of the higher dimension, but not the higher dimensional object itself.
Now, the curled up dimensions doesn't really relate to other worlds, unless there are super tiny worlds that exist in the curled up dimensions, but if we live in a higher dimensional space, then there are many possibilities for other worlds. It is like those Russian dolls: we are the little doll, and are inside a larger doll (which represents a 4th spacial dimension) and that is inside an even larger doll (5-D), and so on. So there are worlds in worlds in worlds, and you would only be able to perceive the worlds that are of the same dimension as you or lower (we are 3-D so can perceive things that are 2-D, like flat things, or 1-D, like lines), unless you are somehow a higher dimensional creature trapped in a lower dimensional world (*story idea*). The way we'd know about the higher worlds could be through the projections mentioned above, or perhaps, if our soul/spirit/mind is not bound by the 3 spatial dimensions around us, it could be aware of the higher dimensional reality around it, though when it is ensouled in a body, it cannot perceive them. But this ties into our next possibility for other worlds...

2) Higher spiritual planes
This follows the same general idea as the higher physical dimensions. Instead of having higher physical dimensions, there are higher spiritual dimensions. I'm not just making this up out of nothing, for we have good reasons to believe that there are higher levels of existence (and lower). This appears in almost every religion and esoteric tradition, such as in the Kabbalah, Buddhism, Western occultism, and more. People have even had experiences travelling there (e.g. astral projection), and it is thought by many that after you die, your soul "gravitates" to the plane that corresponds to its spiritual enlightenment.
Let's look at the Kabbalah as an example (see this amazing book for the metaphysics of the Kabbalah). The Kabbalistic tree of life is this strange-looking diagram that would only look like a tree to a poet, but let's pretend it really does look like a tree for the moment:

Each sphere is a sephirot, and they are each labelled by different Hebrew words. Keter is the crown, from which all the others emanate. Binah and Hokmah are the male and female principles, and Da'at is knowledge. There are many interpretations about what each sphere stands for, and they are not mutually exclusive: it's supposed to have many meanings. Each sphere, from Malkut (the lowest) to Keter (the highest) corresponds to a different level of enlightenment/state of consciousness. During a spiritual seeker's development, they will progress up the sephirots to go from the more impulsive animal nature to a spiritual being. This can certainly be seen as different worlds, where everyone in a lower level of enlightenment is in a lower world, unable to perceive the higher reality of existence, and those above encompass more worlds, as they are beings of a higher spiritual dimension.
The Kabbalistic tree pictured above is actually one of four. These four are called Assiah, Yetzirah, Beriah, and Atziluth (going from lowest to highest). They are all interlaced to be part of one enormous tree of life with Atziluth's Keter at the top:

As you can see, there is some overlap, so, for example, the Keter of Assiah is the Tiferet of Yetzirah. Every sephirot emanated from the Keter at the top, and are all contained within it (this is similar to dimensions, but is all these worlds aren't physical. In fact, only Assiah, the physical universe that we live in, is physical). The higher worlds are spiritual worlds, and these can only be perceived by someone of that level of enlightenment. There may be traces of these higher worlds, and indeed, within our own souls, that are perceptible, but they are like projections of higher dimensions into lower ones. It is also possible that different universes exist at different levels in the Kabbalistic tree of life. Ours is (most likely) somewhere in Assiah, but there may be many more universes at the levels of higher sephirots within Assiah and the higher worlds as well.
The Kabbalah's a lot more detailed and complex than that, so I will do another post sometime just on this.

3) Plato's Cave (This is a hint for the sequel to Aizai the Forgotten!)
If you're not familiar with Plato's Allegory of the Cave, here is a little summary of what it is:
There are prisoners in a cave sitting chained to the spot so that they cannot turn their heads and can only look at one wall. Behind them is a fire and a roadway in front of it where unchained people walk by. They carry various objects that project shadows onto the wall that the prisoners see. These shadows comprise the whole world of the prisoners: they know nothing more to exist than the shadows, and make a game out of predicting what the shadows will be and what they will do.
Suppose that one prisoner were released from his bonds and is shown the fire so he can see that his reality is really just projections of physical 3-dimensional objects onto a wall . The prisoner is amazed and enlightened at this knowledge. The fire burns his eyes, but slowly, he gets used to its brightness.
The prisoner is then brought out of the cave (in stages to accustom him to it) into the full light of the sun. When he can look at the Sun and the world around him without being blinded, he sees the world for what it really is. This is even more profound than the blaze of the fire, and he has at last arrived at the more "real" world that the world in the cave was merely a shadow of.

Ignoring various physical and ethical factors that make this improbable (e.g., how do the prisoners eat? Wouldn't they be muscle-less and weak-boned flubber from sitting so long?), this allegory is about the enlightenment that people can gain by means of philosophy. This is really related to 2), but I thought that it was worth putting separately. The world of shadows upon the wall is the least "real", and is the lowest level of spiritual existence. The world of the fire is a bit higher, and from it, the prisoner can see the shadows for what they really are: only shadows, not real things in themselves. And finally, the light of the Sun is the enlightenment one obtains upon becoming a true philosopher and seeing things as they really are.
sandcastleWe live in a cave, unable to perceive what the world really is at a fundamental level. Even if some people are out of the cave that normal people live in, there are really caves in caves, and when one is in a higher level of existence, a higher world, they are in the cave of an even greater world. How far does this go? Perhaps it's impossible to know unless you're in the highest world. Get to the biggest Russian doll and look outside to see if there's any more. If you see wood, then you're not in the highest spiritual plane. If not, then you may be--or you're just inside an enormous doll :)

In Part 2 (coming later in June), we'll look at other worlds that result from time travel, and other worlds from physics (quantum mechanics and string theory).

In case you're wondering, I said "philosophy" in the title instead of "science" for two reasons.
1) Because people don't think philosophy is as good as it really is, or they mistake it with mysticism or something (not that there's anything wrong with mysticism). There is a lot of metaphysics in this anyway, especially Plato's cave, so it's legitimate.
2) Science really is philosophy, as you can see in my Natural Philosophy and Science post.

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"A Soul Wanderer never knows. He wanders; he makes his own path through the
heights of the universe."

-Sio Larwick

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