The Universe as a Mathematical Structure May Justify Multiverse Theory
Is our entire universe a mathematical structure? Does life consist of a specific pattern of spacetime? Are there multiverses with every possible set of mathematical constraints? MIT physicist Max Tegmark attempts to answer these questions, and more, in his new book Our Mathematical Universe.
His Mathematical Universe Hypothesis (MUH) is a version of mathematical Platonism. Plato theorized that ideals exist as Forms, which are non-material but are very much real, and in fact the highest form of reality. Fittingly, mathematical Platonism postulates that mathematics is not simply a human construct, but that they believe that mathematical structures are things in themselves with properties that can be discovered, rather than just a language invented by human beings. Mathematical Platonism differs from classical Platonism slightly, as Plato believed that our world was a perverted shadow version of the world of Forms, while mathematicians who subscribe to some sort of Platonism believe that their "Forms" are consistent with the material world, or that mathematical structures are abstract, but are part of the material world in the sense that they explain it. Tegmark takes it one step further, and asserts that all of nature is itself a mathematical structure. As he puts it in his book, "I know of no other compelling explanation for [the ability of maths to explain the physical world] than that the world really is completely mathematical."
Essentially, according to this theory, everything is mathematical, including us. We represent a specific type of pattern in spacetime, which he calls a "spacetime braid." Every particle of which we are composed has a spacetime trajectory, and these interact with each other to create a sort of "braid." Then, as we degenerate and die, the particles "go their separate ways" and their trajectories cease to interact, dissolving the braid.
Tegmark explains the concept of a "spacetime braid" in more detail:
"At both ends of your spacetime braid, corresponding to your birth and death, all the threads gradually separate, corresponding to all your particles joining, interacting and finally going their own separate ways. This makes the spacetime structure of your entire life resemble a tree: At the bottom, corresponding to early times, is an elaborate system of roots corresponding to the spacetime trajectories of many particles, which gradually merge into thicker strands and culminate in a single tube-like trunk corresponding to your current body (with a remarkable braid-like pattern inside as we described above). At the top, corresponding to late times, the trunk splits into ever finer branches, corresponding to your particles going their own separate ways once your life is over. In other words, the pattern of life has only a finite extent along the time dimension, with the braid coming apart into frizz at both ends."
Tegmark uses the MUH in order to justify the multiverse hypothesis. He states that all worlds based on different mathematical structures, meaning different physical constraints or initial conditions, should be considered equally real as long as they are logically coherent. In response to criticisms based on this theory's inconsistency with Godel's incompleteness theorem, he modified it to a Computable Universe Hypothesis, in which he only included universes based on computable equations. He admitted that this limits his hypothesis to a relatively small portion of the mathematical landscape, but also qualifies that this may explain the relative simplicity of our universe.
The idea that all logically coherent computable universes exist represents what he calls "Level IV" of the multiverse hypothesis, where Level I is the simple assertion that history has consistently proven that there is always more than we are able to observe at the time, Level II asserts that the physical constraints that resulted from the Big Bang make it likely that more than one Big Bang occurred, which would explain the apparent fine-tuning of our universe, and Level III extrapolates from tenets of quantum mechanics that observation of quantum particles causes them to branch off into other possible trajectories.
From the book regarding multiple copies of a specific person in multiple universes: "When the number of yous increases, you perceive subjective randomness. When the number of yous decreases, you perceive subjective immortality."
Tegmark also uses his hypothesis in order to explain the general trajectory of the universe. He explains the Big Bang theory as a mathematical event, illustrated by Einstein's theory of general relativity. He states that, according to predominant inflation theories, the universe was essentially created out of nothing with borrowed energy from the quantum vacuum. He draws an analogy to a Madoff-type pyramid scheme, in which an inherently unstable structure is created out of nothing and is destined for utter collapse, much as our universe likely is.