So should you believe in parallel universes? The principal arguments against them are that they are wasteful and that they are weird. The wastefulness argument is that multiverse theories are vulnerable to Occam's razor because they postulate the existence of other worlds that we can never observe. Yet this argument can be turned around. For what precisely would nature be wasting? Certainly not space, mass or atoms - the uncontroversial Level I multiverse already contains an infinite amount of all three.
The real issue here is the apparent reduction in simplicity. One might worry about all the information necessary to specify all those unseen worlds. But an entire ensemble is often much simpler than one of its members. This principle can be stated more formally using the notion of algorithmic information content. The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output. For example, consider the set of all integers. Naively, you might think that a single number is simpler than the whole set of numbers, but the set can be generated by a trivial computer program, whereas a single number can be hugely long. Therefore, the whole set is actually simpler. Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution. The former is described by a few equations, whereas the latter requires the specification of vast amounts of initial data on some hypersurface.
The lesson is that complexity increases when we restrict our attention to one particular element in an ensemble, thereby losing the symmetry and simplicity that were inherent in the totality of all the elements taken together. In this sense, the higher-level multiverses are simpler. Going from our universe to the Level I multiverse eliminates the need to specify initial conditions, upgrading to Level II eliminates the need to specify physical constants, and the Level IV multiverse eliminates the need to specify anything at all. The opulence of complexity is all in the subjective perceptions of observers .
The weirdness objection is aesthetic rather than scientific and only makes sense in the Aristotelian worldview. Yet when we ask a profound question about the nature of reality, we surely expect an answer that sounds strange. Evolution provided us with intuition for the everyday physics that had survival value for our distant ancestors, so whenever we venture beyond the everyday world, we should expect it to seem bizarre. Thanks to clever inventions, we have glimpsed slightly beyond our normal subjective view and thereby encountered bizarre phenomena (e.g. at high speeds, small and large scales, low and high temperatures).
A common feature of all four multiverse levels is that the simplest and arguably most elegant theory involves parallel universes by default. To deny the existence of those universes, one needs to complicate the theory by adding experimentally unsupported processes and ad hoc postulates: finite space, wave-function collapse, ontological asymmetry, etc. Our judgement therefore comes down to which we find more wasteful and inelegant: many worlds or many words. Perhaps we will gradually become more used to the weird ways of our cosmos, and even find its strangeness to be part of its charm.
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