In 1957, a Princeton physics graduate student named Hugh Everett showed that the consistency of quantum mechanics required the existence of an infinity of universes parallel to our universe. That is, there has to be a person identical to you reading this identical article right now in a universe identical to ours. Further, there have to be an infinite number of universes, and thus an infinite number of people identical to you in them.
In quantum mechanics everything exists as a waveform, which is just a probability distribution. The canonical example is Schroedinger's cat, which shows that not only do we not know the exact state of a thing until we observe it, but the thing doesn't even assume an exact state until it is observed. There have been some experiments to confirm the spooky behavior.
The conclusion reached in the article (disclaimer I'm not familiar with Evertt's work) is that quantum mechanics implies there must be an infinity of universes. And not just an infinity of different universes, but also an infinity of the same universes. Yes, that sounds absurd. But don't worry, it gets worse. According to the author, at each point you make a decision, the universe splits in two. For example, one universe where you pay your taxes, and one you don't. This is alleged to show free will. At each moment you can decide which universe you switch to. You control your own destiny.
This means that at each moment in time, another infinity universes is created. But not just that, because we must consider all the other decisions being made. This introduces combinatorial complexity. So there are on order of infinity to the power of infinity universes created at each moment. Do the old universes get destroyed? The author doesn't say. Perhaps there is a single infinite set of universes and another set of infinite transitions, to make up a sort of multiverse automaton. It does hurt the head to think about this too much.
If universes are constantly created and destroyed, what does this mean? Does it make sense that at each increment in time (according to quantum physicist, the Planck time, a ridiculously small increment) we enter a freshly minted universe? If we exist on a graph in which each of the infinite states of the universe exists an infinite number of times on a graph, what does that say about the fabric of existence?
If the universe splits each time we make a decision, then almost all universes should be wildly chaotic. Think about it. You drive to work. At each increment of time, you decide how to control the wheel. You can direct it down the road, or you can run your car into the ditch. The odds that you ever make it to work are just unfathomable. There is the argument, "well you chose to enter the safe universe by free will." Well what of the universe where I wrecked my car? Clearly I didn't choose the safe universe, I just inherited it by chance. And the chaotic universes vastly outnumber the safe ones.
This simply defies all logic, it defies our understanding of existence, and if indeed quantum mechanics comes to this conclusion, then something is wrong with quantum mechanics. More likely something is wrong with the article.
Now, there is something to be said for multiple universes. The best argument I know of is this: in our world there are a great many constants, for example the gravitational constant, Boltzman's constant, the mass of the electron. It has always been the assumption that these constants fall out of the equations of the universe, just in ways we don't understand yet. As it is, the constants are determined through measurement. A few years ago, after a long search, the Higgs Boson was finally discovered at the Large Hadron particle accelerator in Europe. It was just as theory predicted, with one exception: the mass was way off. Not even close. Here was yet another constant that couldn't be predicted by theory.
The conclusion some physicists started coming to was that the constants are in fact totally arbitrary, which leads to some troubling philosophical suggestions. The constants must be just right for life to exist in the universe, and yet they seem to be arbitrary. If any were just a little different life wouldn't exist at all. The only two conclusions are (1) the constants are divinely set, or (2) there exists a multitude of universes with unique sets of constants. That we exist in one of the few sets that supports life is a tautology. We would have to exist in one of those universes to even ponder the question.
This a multiverse theory that is more palatable. First it only requires a countably infinite number of universes rather than the infinite exponents of the original version. Even more, it doesn't require the incessant creation of infinite universe. Each universe plays out continuously in the way we perceive ours to be.
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