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It is a popular and oft-repeated idea that there may exist universes other than the universe we see around us. These are often called parallel universes and scientists do not know whether they exist. Even so, parallel universes have proved an important plot device in such venerated entertainment as Groundhog Day and certain episodes of Futurama. So could parallel universes actually exist? And should scientists be spending their time thinking about it?
Whilst speculative, a number of prominent physicists have endorsed theories that postulate parallel universes. Brian Greene, a physics professor at Columbia University, has helpfully written a book on the topic for the interested layman. In an interview Greene described how
[…] in physics, we’ve come upon the possibility that what we’ve long thought to be everything may actually only be a small part of something that is much, much bigger. The word “multiverse” refers to that bigger expanse, the new totality of reality, and our universe would be just a piece of that larger whole. 
In point of fact, the word multiverse was first coined by William James in an address to the Young Men’s Christian Association at Harvard University in 1895. In his speech, entitled Is Life Worth Living?, James described the multiplicity of moral perspectives one can have by talking of a ‘moral multiverse’. To a modern physicist, however, the word no longer has any ethical connotations.
Discovering Island Universes
Putting aside questions of parallel universes, we would do well to remember that humanity has not always known very much about the universe that we can see. Indeed, perhaps the first scientific discussion of ‘multiple universes’ was the discovery of galaxies in the early twentieth century. At that time it was not known whether the milky way galaxy was the entirety of the universe. Until last century it was not unreasonable to think that the milky way is everything in existence: after all, the milky way contains over a hundred billion stars and is spatially humongous (it takes a ray of light one hundred thousand years to traverse it).
In the eighteenth century astronomers started observing small clouds in the sky that they called nebulae. But were these nebulae part of the Milky Way? A daring hypothesis was forwarded by Thomas Wright (an English mathematician, astronomer, and garden designer). He conjectured that “the many cloudy spots, just perceivable by us, […] [are] in all likelihood [of] external creation, bordering upon the known one, too remote for even our telescopes to reach.”  Wright’s idea proved popular among astronomers and writers. Could those tiny nebulous clouds be entirely new Milky Ways? People had to stretch their imaginations to conceive of a much larger universe: a massive conglomeration containing millions of ‘island universes’ of which the Milky Way is just one. Despite the enthusiasm of some scientists (and the popularity of the idea amongst science fiction authors) the matter was still undecided two centuries later. In 1919 one astronomer reported:
The problem of the [nebulae] is at the present far from solution; and judgement on their exact status must be suspended until we are in possession of more detailed knowledge. 
More detailed knowledge did arrive soon thereafter thanks to the work of skilled astronomers like Edwin Hubble. In the 1920s Hubble was able to resolve individual stars in the nebulae. Through a careful study of these stars he determined that the nebulae are millions of light years away, and thus separate from the Milky Way. Modern astronomy has since revealed that the (observable part of) the universe contains over one hundred billion galaxies — that corresponds to over one ten billion trillion stars.
Many Hyperdimensional Branes?
It has now been almost a century since Hubble’s discovery of other galaxies. In that time people have proposed plenty of ways to make the world even bigger using parallel universes. One way to imagine parallel universes is to picture our universe as existing inside a higher dimensional space. That may sound like science fiction nonsense, but it is actually a garden variety piece of mathematics. Imagine pieces of paper floating around a room. If you existed ‘inside’ the paper you would only be able to move in two directions, oblivious to the room ‘outside’. The universe we see around us seems to exhibit three spatial dimensions and one temporal dimension. However, it so happens that gravity exhibits some nice mathematical results in five dimensions that it doesn’t exhibit in four. Consequently, some physicists suggest that our universe is merely a four dimensional ‘brane’ (think ‘membrane’) inside some higher dimensional space — like a sheet of paper inside a room. In this scenario it seems perfectly sensible to posit that other universes (other ‘sheets of paper’) may also be floating around in hyperspace with us. But would we ever know?
Theoretically, these ideas are described by string theory. Physicists typically envisage the fundamental particles (electrons, quarks, etc.) as infinitely small points moving about in space. However, as suggested by the name, string theory describes these particles not as points but as small strings that are allowed to vibrate in different ways. We can then think of different particles as different ways for the strings to vibrate. This innocent idea has some very peculiar consequences including the prediction of extra dimensions.
These extra dimensions are not without consequences! Physicists predict that gravity would be anomalously strong at small scales. Also, every now and then a little of bit of energy might manage to escape from our brane into the hyperspace. Whilst these phenomena haven’t been ruled out by experiment, they haven’t been observed either — and until such a time as they are, we will not know if we are trapped on a brane in hyperspace.
Many Quantum Mechanical Worlds
String theory is not the only tool physicists use to create parallel universes: Quantum mechanics also does a fine job of it. According to quantum mechanics, we cannot know the future, only the likelihood of different possible futures. Traditionally, this has been attributed to the probabilistic nature of quantum events.
A nicely morbid example is of a cat in a box with a glass vial of poison that is randomly broken by a hammer. Suppose we leave the cat in there for an hour. It was alive at the start, but after an hour is might be dead. Or it might still be alive. In quantum mechanics we say that the cat is both alive and dead. Then, upon the event of opening the box, we force the cat to ‘choose’ whether it’s going to be alive or dead. This might sound a little ridiculous, but it is the language commonly employed by physicists to build everything from MRI machines to transistors in your phone. However, there is an alternative way to view quantum mechanics.
It’s called the many-worlds hypothesis. Perhaps, when we open the cat’s box, the universe splits into two universes: one in which the cat is alive, and the other in which it is dead. The outcome that you see depends on which universe you just happen to find yourself in. That is, instead of asking “how likely is it that the cat will be dead?”, you could instead ask “how likely is it that I will find myself in the world where the cat is dead?”.
It is not yet clear whether the many-worlds hypothesis is at all different from ordinary quantum mechanics. However, some authors recently claimed that the many-worlds hypothesis is experimentally testable.  If the idea is confirmed, then there would exist, right now, all different possible versions of ‘you’. This raises some tricky questions about what it means to be ‘you’. (Although, we might never need to answer these questions — it being difficult to meet a ‘you’ from a different world.)
Should We Speculate?
Many paths lead to the multiverse. Theories with extra dimensions allow us to envisage the universe as one of many branes floating around in hyperspace. Quantum mechanics hints at the existence of all possible worlds. (Including the world where you think cuffed pants are cool.) Of course, you are perfectly free to take this further and imagine a ‘multi-hyper-verse’ containing all quantum mechanically possible hyperspace braneworlds. However, should theoretical physicists even think about these speculative things at all?
Isaac Newton, a veritable science god, famously declared “hypotheses non fingo” (‘I contrive no hypotheses’). With this statement Newton crowned the findings of experimental science above all speculations. Should we follow Newton’s lead and stop dreaming of the multiverse?
Probably not. On the one hand, Newton often broke his own dictum (at least privately) and speculated wildly about the fundamental nature of things. Like most scientists, Newton was driven by an insatiable curiosity to know how the world works and his ideas stretched far beyond the tragically limited technologies of his day. (For instance, he speculated that light is comprised of particles and that space is infused with an ‘ethereal’ material through which things move.) Driven by curiosity, and by the speculations of scientists, science has since progressed to understand what Newton could only speculate about.
On the other hand, speculations about string theory have helped make tangible advancements in mathematics — the consequences of which mathematicians are still working on. Mathematics is humanity’s most sophisticated and useful language for solving complicated problems; it is a momentous achievement of which we should be proud. Advancements in this valuable part of our culture should be welcomed; including the progress made on the back of speculation about strings and extra dimensions.
Today, the multiverse has caught the imaginations of our science fiction writers in much the same way as island universes caught the fancy of 19th century authors. The island universe idea was confirmed by experimental science two centuries after its conception. Likewise, perhaps physicists of the 23rd century will finally discover evidence of a parallel universe. Until that time the multiverse remains a possibility; an idea that, whilst hypothetical, can still entertain our imaginations and spur us on to continue exploring our universe(s).
 Quote from Brian Greene, 2011. See: http://phys.org/news/2011-03-elegant-multiverse-professor-brian-greene.html  Quote from Thomas Wright, 1750.  Quote from Hector Macpherson, 1919. See: The problem of island universes, The Observatory, September 1919, No. 543.  Some authors have recently suggested that the many-worlds hypothesis makes testable predictions. However, this remains an area of contention amoungst the physics community. See: Sebens, Charles T., and Sean M. Carroll. 2014. Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. arXiv:1405.7577, May. http://arxiv.org/abs/1405.7577.