Chapter 150: Imminent Threat

According to Tegmark's classification, there remain three more tiers.

Level Two: Post-inflationary bubbles.
As a variant of the cosmic inflation theory, chaotic inflation posits that the multiverse expands as a whole, and this expansion will continue indefinitely. However, certain domains of the universe cease expanding, manifesting as distinct bubble shapes. These bubbles are the undeveloped Level One parallel universes. Andrei Linde and Vitaly Vanchurin calculated the number of such universes to be $10^{10^{10}}$ metric units. It is possible that different bubbles have undergone primary symmetry breaking, resulting in different properties governed by different physical constants. This level encompasses John Archibald Wheeler's Oscillatory Universe Theory and Lee Smolin's Fecund Universes Theory.

Level Three: The many-worlds interpretation of quantum mechanics.
Hugh Everett's Many-Worlds Interpretation (MWI) is one of the numerous mainstream interpretations of quantum mechanics. As an aspect of quantum mechanics, a single observation cannot yield an absolute prediction; instead, it triggers a wider range of different probabilities. According to MWI, these distinct observation results correspond to separate universes. Much like rolling a six-sided die, the outcomes align with the observable quantities of quantum mechanics, causing six universes corresponding to the six faces of the die to manifest. (To be more precise, in the MWI theory, although the existence of the universe is singular, once it branches into multiple worlds, they typically become mutually non-interacting.)

Tegmark suggests that the content of Level Three parallel universes within a Hubble volume is no more probable than that of Level One or Level Two parallel universes. In fact, within Level Three parallel universes sharing the identical physical constants, all the different worlds formed by branching can be found across multiple Hubble volumes within a Level One parallel universe. Tegmark elaborates as follows: the only difference between Level One and Level Three lies in where the observer's copies reside.

In Level One, they reside somewhere within three-dimensional space. In Level Three, they reside in infinitely dimensional worlds within Hilbert space, distinct from other quantum realities. Similarly, all Level Two bubble universes possessing different physical constants can practically be regarded as "worlds" generated at the instant of primary symmetry breaking within the Level Three parallel universes.

Views related to the many-worlds concept include Richard Phillips Feynman's sum-over-histories (or multiple histories) interpretation and H. Dieter Zeh's many-minds interpretation.

Level Four: The ultimate ensemble.
The ultimate ensemble hypothesis is advocated by Tegmark himself. Universes describable by different mathematical structures are considered to all exist in an equal and real manner. The different low-energy physical laws of unobservable universes are not included herein. Tegmark champions the following view: abstract mathematics is a tremendously pervasive existence, and any Theory of Everything (TOE)—detaching itself from humanity's ambiguous language and definable in any pure language—cannot escape a mathematical structure.

For instance, a theory of place containing different kinds of entities (expressed in language) and their relations (again expressed in language) is not only termed a set-theoretic model by mathematicians, but such a set-theoretic model is also commonly viewed as the constituent formal system. This implies that all conceivable parallel universe theories can be described at the Level Four stage. Because Level Four parallel universes encompass all other ensembles, they form the upper bound of the parallel universe hierarchy, leaving no room to consider a Level Five parallel universe.

Jürgen Schmidhuber raised a dissenting opinion, arguing that the "set of mathematical constructs" is not explicitly defined. He endorses only constructive mathematics—that is, universe representations that can be described via computer programs.

Within this framework, output bits can be controlled within a finite amount of time. Controlling time itself becomes unpredictable due to the program being subject to Gödel's incompleteness limits, but due to non-halting programs, describable universe representations are unequivocally contained within it. Additionally, he raised explicit objections against the relatively restricted set of universes capable of extremely rapid computation.

The primary arguments against parallel universes are that they are wasteful and bizarre. Let us consider these two points in turn. First, the parallel universe theory is easily vulnerable to Occam's razor because it posits the existence of other universes that can never be observed. Why is nature so prodigal in its ontology, indulging in such an endlessly proliferating multitude of different worlds? Yet this very point can be turned around to support parallel universes. When people feel that nature is overly wasteful, what aspect of its wastefulness are they actually troubled by? Clearly it is not "space," since the infinite volume in standard flat cosmological models does not provoke such objections. Nor is it "matter" or "atoms"—for the same reason: once an infinite amount of something has already been wasted, who cares if a bit more is squandered?

Therefore, this perplexing "wastefulness" is better understood as a simplification; it reduces the amount of information required to describe all these invisible worlds. However, as Tegmark has discussed in detail, an entire ensemble is often far simpler than a single element within it. For instance, the algorithmic information content of an ordinary integer $n$ is on the order of $log_2 n$, which is the number of bits required to write it in binary. Yet the set of all integers, $1, 2, 3, dots$, can be generated by a computer program of just a few lines, so the algorithmic complexity of the entire ensemble is far smaller than that of any single integer within it.

Similarly, the set of all ideal fluid solutions to Einstein's field equations has an algorithmic complexity far lower than any single particular solution, because the former requires only a few equations to describe, whereas the latter demands specifying massive amounts of initial data on a hypersurface. Roughly speaking, when one restricts attention to a specific element within an ensemble, the apparent information content increases, while the intrinsic symmetry and simplicity of the whole system—when all elements are taken into account—are lost. In this sense, higher-tier parallel universes possess lower algorithmic complexity.

Ascending from the ordinary universe to the Level One parallel universe eliminates the need to specify initial conditions; ascending to Level Two removes the need to specify physical constants; and upon reaching the Level Four parallel universe—which contains all mathematical structures—algorithmic complexity ceases to exist in essence. It is only from the frog perspective, from the subjective sensations of the observer, that such information excess and complexity arise. It can be demonstrated that the multiverse theory is far more economical than the single-universe theory which posits only a single ensemble element as physical reality.

The second common complaint is that parallel universes are too bizarre. But this objection stems mostly from aesthetic rather than scientific considerations. Yet, as mentioned above, this criticism only holds weight within an Aristotelian worldview. In a Platonic model, if the bird perspective and the frog perspective diverge sufficiently, it is entirely possible that observers would complain that the correct TOE is so bizarre, yet every sign indicates that this is precisely the situation in which they find themselves.

There is nothing astonishing about the bizarreness we perceive, for evolution has endowed us only with an intuition for everyday physics—just enough to allow our ancient ancestors to survive. Yet through intellect and creativity, we have managed to peer slightly beyond the frog perspective of purely internal viewpoints. We can be certain that whenever we venture beyond baseline human cognition, we encounter strange phenomena: high speeds (time dilation), small scales (quantum particles existing in multiple places simultaneously), large scales (black holes), low temperatures (liquid helium flowing upward), high temperatures (colliding particles changing their identities), and so forth.

Thus, physicists have largely accepted that the bird perspective and the frog perspective are vastly different. A popular modern view in quantum field theory is that the Standard Model is merely an effective theory—the low-energy limit of some yet-to-discover theory that lies far removed from comfortable classical concepts (such as strings incorporating ten dimensions).

Many experimentalists have grown numb to so many "bizarre" (yet highly reproducible) results. They simply accept the premise that "the world is stranger than one originally thought" and plunge back into their calculations.

Long periods of study made Hua Feng feel that while his days were growing routine, a sense of boredom was increasingly coming to the fore, slowly eroding his fading passion. Although he understood that sometimes, as time passes, the probability of human control over certain matters diminishes, he was not the sort of person to give up easily.

Especially after understanding the current situation and studying so many previously unencountered subjects, Hua Feng felt that many things might not be as complex as imagined. The crux of the problem lay in whether one was willing to strive for it, even if hope was dim, even if the probability of success was a paltry few percent. But the moment one gave up, one was bound to greet a hundred percent failure.

Meanwhile, in another location, a group of people were engaged in tense, hurried calculations within a hall filled with humming instruments.

"How much longer until the spacetime collapse?" a middle-aged man stared intently at the screen, asking his assistant without turning his head.

"Reporting to the Commander, according to incomplete statistics, excluding operations to maintain spatial integrity, we have roughly two years of preparation time left," the assistant replied cautiously, a note of uncertainty coloring his tone.

The middle-aged commander nodded and sank into deep thought.