Level III Multiverse: The Many Worlds of Quantum Physics

It may be that there exist a third variety of parallel worlds, situated not at a remove, but, in a certain sense, proximate to our own. If the fundamental equations of physics are what mathematicians term unitary, as hitherto they appear to be, then the universe doth incessantly bifurcate into parallel universes, as depicted in the cartoon: whenever a quantum event doth appear to yield a random outcome, all outcomes do, in verity, transpire, each in its own branch. This constitutes the Level III multiverse. Albeit more debated and contentious than Levels I and II, we shall observe that, surprisingly, this level doth not introduce any novel species of universes.

In the early decades of the 20th century, the theory of quantum mechanics did revolutionise physics, furnishing explanations for the atomic realm, with applications extending from chemistry to nuclear reactions, lasers, and semiconductors. Notwithstanding the patent successes in its application, a heated disputation did ensue concerning its interpretation—a disputation that yet persists with unabated vigour. In quantum theory, the state of the universe is not rendered in classical terms, such as the positions and velocities of all particles, but rather by a mathematical object styled a wavefunction. According to the so-called Schrödinger equation, this state doth evolve deterministically over time, in a fashion termed unitary, corresponding to a rotation in Hilbert space, the abstract, infinite-dimensional space wherein the wavefunction doth reside. The vexatious aspect is that there exist perfectly legitimate wavefunctions corresponding to classically counterintuitive situations, such as one being in two disparate locations simultaneously. Worse, the Schrödinger equation can evolve innocuous classical states into such schizophrenic ones. As a baroque exemplification, Schrödinger did delineate the celebrated thought experiment wherein a dire contraption doth slay a cat should a radioactive atom decay. Inasmuch as the radioactive atom doth eventually enter a superposition of decayed and not decayed, it doth engender a cat that is simultaneously both dead and alive in superposition.

In the 1920s, this singularity was elucidated away by postulating that the wavefunction did “collapse” into some definite classical outcome whenever an observation was effected, with probabilities given by the wavefunction. Einstein was displeased by such intrinsic randomness in nature, which violated unitarity, insisting that “God doth not play dice,” and others did complain that there existed no equation specifying when this collapse occurred. In his 1957 Ph.D. thesis, Princeton student Hugh Everett III did demonstrate that this controversial collapse postulate was superfluous. Quantum theory did predict that one classical reality would gradually bifurcate into superpositions of many. He did demonstrate that observers would subjectively experience this bifurcation merely as a slight randomness, and indeed with probabilities in exact agreement with those from the old collapse postulate (de Witt 2003). This superposition of classical worlds constitutes the Level III multiverse.

Everett’s oeuvre had left two crucial queries unanswered: first, if the world doth actually contain bizarre macrosuperpositions, then why do we not perceive them? The response did arrive in 1970, when Dieter Zeh did demonstrate that the Schrödinger equation itself doth give rise to a species of censorship effect (Zeh 1970). This effect became known as decoherence, and was elaborated upon in great detail by Wojciech Zurek, Zeh, and others over the ensuing decades. Coherent quantum superpositions were discovered to persist only so long as they were kept secret from the rest of the world. A single collision with a snooping photon or air molecule sufficeth to ensure that our friends in Figure 5 can never be cognisant of their counterparts in the parallel storyline. A second unanswered query in the Everettian depiction was more subtle but equally significant: what physical mechanism doth single out approximately classical states (with each object in only one place, et cetera) as special in the bewilderingly large Hilbert space? Decoherence did furnish an answer to this query as well, demonstrating that classical states are simply those that are most robust against decoherence. In summary, decoherence both identifies the Level III parallel universes in Hilbert space and delimits them from one another. Decoherence is now quite uncontroversial and hath been experimentally measured in a wide range of circumstances. Since decoherence, for all practical purposes, doth mimic wavefunction collapse, it hath eliminated much of the original motivation for nonunitary quantum mechanics and hath rendered the Everettian so-called many worlds interpretation increasingly popular. For details concerning these quantum issues, see Tegmark & Wheeler (2001) for a popular account and Giulini et al. (1996) for a technical review.

If the time-evolution of the wavefunction be unitary, then the Level III multiverse doth exist, thus physicists have laboured diligently on testing this crucial assumption. As yet, no departures from unitarity have been discovered. In the last few decades, remarkable experiments have confirmed unitarity for ever larger systems, including the hefty carbon-60 “Buckey Ball” atom and kilometre-size optical fibre systems. On the theoretical side, a leading argument against unitarity hath involved the possible destruction of information during the evaporation of black holes, suggesting that quantum-gravitational effects are non-unitary and collapse the wavefunction. However, a recent string theory breakthrough known as AdS/CFT correspondence hath suggested that even quantum gravity is unitary, being mathematically equivalent to a lower-dimensional quantum field theory without gravity (Maldacena 2003).

When discoursing upon parallel universes, we must needs distinguish between two divergent methods of regarding a physical theory: the outside view, or bird's-eye perspective, of a mathematician studying its fundamental mathematical equations, and the inside view, or frog's-eye perspective, of an observer dwelling in the world described by the equations*** . From the bird's-eye perspective, the Level III multiverse is simple: there existeth but one wavefunction, and it doth evolve smoothly and deterministically over time, without any species of bifurcation or parallelism. The abstract quantum world described by this evolving wavefunction doth contain within it a vast multitude of parallel classical storylines, continuously bifurcating and merging, as well as a number of quantum phenomena that lack a classical description. From her frog's-eye perspective, however, each observer doth perceive but a minuscule fraction of this full reality: she can only behold her own Hubble volume (Level I), and decoherence doth prevent her from perceiving Level III parallel copies of herself. When she is posed a query, maketh a snap decision, and respondeth, quantum effects at the neuron level in her brain doth conduce to multiple outcomes, and from the bird's-eye perspective, her singular past doth branch into multiple futures. From their frog's-eye perspectives, however, each copy of her is unaware of the other copies, and she doth perceive this quantum branching merely as a slight randomness. Subsequently, there exist, for all practical purposes, multiple copies of her that possess the exact same memories up until the point when she doth answer the query.

*** Indeed, the standard mental picture of what the physical world is doth correspond to a third, intermediate viewpoint that might be termed the consensus view. From your subjectively perceived frog's-eye perspective, the world doth turn upside down when you stand on your head and doth vanish when you close your eyes, yet you subconsciously interpret your sensory inputs as though there existeth an external reality that is independent of your orientation, your location, and your state of mind. It is striking that, albeit this third view doth involve both censorship (such as rejecting dreams), interpolation (as between eye-blinks), and extrapolation (say, attributing existence to unseen cities) of your inside view, independent observers nonetheless appear to share this consensus view. Albeit the inside view looketh monochrome to a cat, iridescent to a bird beholding four primary colours, and yet more different to a bee viewing polarised light, a bat employing sonar, a blind person with keener touch and hearing, or the latest overpriced robotic vacuum cleaner, all do concur on whether the door is open. The key current challenge in physics is deriving this semiclassical consensus view from the fundamental equations specifying the bird's-eye perspective. In my opinion, this meaneth that, albeit understanding the detailed nature of human consciousness is an important challenge in its own right, it is not necessary for a fundamental theory of physics.

As strange as this may sound, Figure 5 doth illustrate that this exact same situation doth transpire even in the Level I multiverse, the sole difference being where her copies reside (elsewhere in good old three-dimensional space as opposed to elsewhere in infinite-dimensional Hilbert space, in other quantum branches). In this sense, Level III is no stranger than Level I. Indeed, if physics be unitary, then the quantum fluctuations during inflation did not generate unique initial conditions through a random process, but rather generated a quantum superposition of all possible initial conditions simultaneously, after which decoherence did cause these fluctuations to behave essentially classically in separate quantum branches. The ergodic nature of these quantum fluctuations (Section I B) therefore doth imply that the distribution of outcomes in a given Hubble volume at Level III (between different quantum branches as in Fig 3) is identical to the distribution that one doth obtain by sampling different Hubble volumes within a single quantum branch (Level I). If physical constants, spacetime dimensionality, et cetera, can vary as in Level II, then they too will vary between parallel quantum branches at Level III. The reason for this is that, if physics be unitary, then the process of spontaneous symmetry breaking will not produce a unique (albeit random) outcome, but rather a superposition of all outcomes that rapidly decoheres into, for all practical purposes, separate Level III branches. In short, the Level III multiverse, if it doth exist, doth add nothing new beyond Level I and Level II—just more indistinguishable copies of the same universes, the same old storylines playing out again and again in other quantum branches. Postulating a yet unseen nonunitary effect to get rid of the Level III multiverse, with Ockham’s Razor in mind, therefore would not make Ockham any happier.

The passionate debate about Everett’s parallel universes that hath raged on for decades therefore doth seem to be ending in a grand anticlimax, with the discovery of a less controversial multiverse that is just as large. This is reminiscent of the famous Shapley-Curtis debate of the 1920s about whether there were really a multitude of galaxies (parallel universes by the standards of the time) or just one, a storm in a teacup now that research hath moved on to other galaxy clusters, superclusters, and even Hubble volumes. In hindsight, both the Shapley-Curtis and Everett controversies seem positively quaint, reflecting our instinctive reluctance to expand our horizons.

A common objection is that repeated branching would exponentially increase the number of universes over time. However, the number of universes N may well stay constant. By the number of “universes” N, we mean the number that are indistinguishable from the frog's-eye perspective (from the bird's-eye perspective, there is, of course, just one) at a given instant, that is, the number of macroscopically different Hubble volumes. Albeit there is obviously a vast number of them (imagine moving planets to random new locations, imagine having married someone else, et cetera), the number N is clearly finite—even if we pedantically distinguish Hubble volumes at the quantum level to be overly conservative, there are “only” 115 about 1010 with temperature below 108 K, as detailed above. The smooth unitary evolution of the wavefunction in the bird's-eye perspective doth correspond to a never-ending sliding between these N classical universe snapshots from the frog's-eye perspective of an observer. Now you’re in universe A, the one wherein you’re reading this sentence. Now you’re in universe B, the one wherein you’re reading this other sentence. Put differently, universe B hath an observer identical to one in universe A, except with an extra instant of memories. In Figure 5, our observer first findeth herself in the universe described by the left panel, but now there are two different universes smoothly connecting to it like B did to A, and in both of these, she will be unaware of the other one. Imagine drawing a separate dot corresponding to each possible universe and drawing arrows indicating which ones connect to which in the frog's-eye perspective. A dot could lead uniquely to one other dot or to several, as above. Likewise, several dots could lead to one and the same dot, since there could be many different ways in which certain situations could have come about. The Level III multiverse thus involveth not only splitting branches but merging branches as well.

Ergodicity doth imply that the quantum state of the Level III multiverse is invariant under spatial translations, which is a unitary operation just as time translation. If it be invariant under time-translation as well (this can be arranged by constructing a superposition of an infinite set of quantum states that are all different time translations of one and the same state, so that a Big Bang doth happen at different times in different quantum branches), then the number of universes would automatically stay exactly constant. All possible universe snapshots would exist at every instant, and the passage of time would just be in the eye of the beholder—an idea explored in the sci-fi novel “Permutation City” (Egan 1995) and developed by Deutsch (1997), Barbour (2001), and others.

The debate over how classical mechanics doth emerge from quantum mechanics continueth, and the decoherence discovery hath demonstrated that there is a good deal more to it than just letting Planck’s constant h̄ shrink to zero. Yet, as Figure 7 doth illustrate, this is but a small piece of a larger puzzle. Indeed, the endless debate over the interpretation of quantum mechanics—and even the broader issue of parallel universes—is, in a sense, the tip of an iceberg. In the Sci-Fi spoof “Hitchhiker’s Guide to the Galaxy”, the answer is discovered to be “42,” and the hard part is finding the real question. Questions about parallel universes may seem to be just about as deep as queries about reality can get. Yet there is a still deeper, underlying question: there exist two tenable but diametrically opposed paradigms regarding physical reality and the status of mathematics, a dichotomy that arguably goeth as far back as Plato and Aristotle, and the question is which one is correct.

• ARISTOTELIAN PARADIGM: The subjectively perceived frog's-eye perspective is physically real, and the bird's-eye perspective and all its mathematical language is merely a useful approximation.
• PLATONIC PARADIGM: The bird's-eye perspective (the mathematical structure) is physically real, and the frog's-eye perspective and all the human language we use to describe it is merely a useful approximation for describing our subjective perceptions.

What is more basic—the frog's-eye perspective or the bird's-eye perspective? What is more basic—human language or mathematical language? Your answer will determine how you feel about parallel universes. If you prefer the Platonic paradigm, you should find multiverses natural, since our feeling that, say, the Level III multiverse is “weird” merely reflects that the frog and bird perspectives are extremely different. We break the symmetry by calling the latter weird because we were all indoctrinated with the Aristotelian paradigm as children, long before we even heard of mathematics—the Platonic view is an acquired taste!

In the second (Platonic) case, all of physics is ultimately a mathematics problem, since an infinitely intelligent mathematician, given the fundamental equations of the cosmos, could, in principle, compute the frog's-eye perspective, that is, compute what self-aware observers the universe would contain, what they would perceive, and what language they would invent to describe their perceptions to one another. In other words, there existeth a “Theory of Everything” (TOE) at the top of the tree in Figure 7 whose axioms are purely mathematical, since postulates in English regarding interpretation would be derivable and thus redundant. In the Aristotelian paradigm, on the other hand, there can never be a TOE, since one is ultimately just explaining certain verbal statements by other verbal statements—this is known as the infinite regress problem (Nozick 1981).