In our fantasy series, the topic of Travelling between worlds is a major theme. Is the existence of other worlds actually possible? As a writer, it often feels less like coming up with a story and more like seeing the already-existant world and already-occurred events, in order to write them down. It's kinda fun to wonder...
The many worlds interpretation of quantum mechanics implies that not only are parallel realities possible, but that they're probable. Quoting from the wikipedia page:
[...] implies that all possible alternate histories and futures are real, each representing an actual "world" (or "universe").
While wikipedia isn't necessarily the best source, it's often good enough for a layman's understanding.
Note that this interpretation has been around since 1952, so it's had plenty of time to weather the storm of disbelief. Further note that this isn't the only interpretation of quantum mechanics. Also note that the existence of parallel universes doesn't necessarily imply the ability to travel between them.
And finally, I'd like to impart some wisdom from GURPS Time Travel, an amusing foray into the topic of time and parallel world travel: you can have an infinite number of apples and not have any oranges. Just because there are an infinite number of parallel universes doesn't mean you can find the one you want...
There's more evidence to the possibility that there may be extra spatial dimensions than parallel universes per se. Mathematically, extra dimensions is valid physics. It is still theoretically possible for there to be entire universes in that space, in a sense co-existing with our space.
AFAIK, there is no consensus among physicists or astronomers, however of those I've read/listened to there is a common belief in multiverses which are simply further out than the boundary of our universe, rather than many-worlds theory.
Regarding world-hopping, you could very well use a wormhole for travel, regardless of if the worlds are in the same universe or how the multiverse is distributed. Creating a stable wormhole is a whole other bag of cats but certainly an acceptable plot device.
There are in fact 2 pieces of evidence for the multi-world theory to be correct.
Gravitational Waves that were recently discovered. It supposedly shows the shadow of the string that did something to create our universe.
Quantum Computing acts as though there is.
The details of these things I know very little about, because they're cutting edge, but they are said to be evidence.
From the standpoint of expressing the nature of conscious experience, there is nothing predictive about 'many worlds', as the worlds don't interact physically. It's a philosophical and subjective explanation that is outside the realm of scientific inquiry, since the lack of prediction precludes experimentation.
Still, you can certainly have people reporting visceral experiences of intrinsic parallelism, which arguably is demonstrated most clearly in art. You might even say that some of the popular descriptions of so-called 'quantum reality' are artistic in this way, since the abstraction of the underlying mathematics can never fully sate the human need for visceral understanding.
However, what if you wanted to create a subset of realities wherein the existence of other realities is accessible and testable? One can certainly imagine such a set of worlds, with rules about how travel between worlds works and definitions for how these worlds interact. At some point, though, it starts to become hard to distinguish between many worlds and one single world with a greater complexity of facets. But this duality of perspective is itself yet another expression of parallelism, since a sufficiently permissible intrinsic parallelism to the multiverse makes it indistinguishable from a universe. Whether that universe is ours is a matter of perspective.
Consider that this is a site about world building, wherein we posit a distinction between fiction and reality. If you imagine a world wherein that distinction is (dually) moot, there is a multiverse growing right here, right now, as our collective minds explore varied possibilities, all equally imaginary, yet also facets of realities. So while there is no evidence for multiple realities, there is plenty of evidence that reality is not the limiting factor to experience, as imagination finds itself expressed faster than we can develop the explanations for its formations.