model that garners the fewest objections and sparks the least debate within the scientific community whereas the level 4 multiverse is the model that contains individual universes that vary significantly from ours and is also the multiverse model that is met with the highest levels of skepticism.
Tegmark’s level 1 multiverse is a series of parallel universes that maintain the same (or at least very similar) physical constants as our universe but realize all initial conditions. That is to say, all possible realities, given our physical constants, are actualized in some other parallel universe. A universe in a multiverse such as this would look very similar to the one that we are currently in, save for different initial starting conditions. So, for example, while another universe would enjoy remarkably similar physical constants and laws of nature as ours, it would have a different initial starting point, making it, perhaps, at a point in development 2,000 years behind our universe, or perhaps 2,000 years ahead of our universe. The universes within this multiverse are inaccessible to other universes, and due to the rate of expansion and the distance between the universes, it would not be possible, says Tegmark, for one to ever travel between universes.
The level 2 multiverse is essentially composed of an “infinite set of distinct Level 1 Multiverses, each represented by a bubble . . . some perhaps with different dimensionality and different physical constants” (Tegmark, 2007, p. 105). Each bubble contains a distinct parallel universe that displays not only initial conditions different from those of the next bubble but also different physical constants and laws of nature (Tegmark, 2007, p. 107). So this second level is similar to the first in its makeup, the difference coming in the potential variations of physical constants and laws of nature. On this level it simply seems that there is the possibility of a greater number of universes than on level one, since there is a broader range in which the physical constants of each universe can fall, thus yielding more possibilities and more universes. Also differentiating this level from level 1 is that, on this level, all universes appear to exist simultaneously, which is a detail that does not seem necessary on level 1.
Tegmark’s level 3 multiverse, I think, is better understood in relation to the first two levels rather than through pure explication of it. The level 3 multiverse, while it adds no new storylines beyond levels 1 or 2, varies in how these storylines come to be. Whereas in level 1 and 2 the universes are far apart, in level 3 they are all spatially very close, so to speak. This is because rather than being a series of disconnected independent universes in the levels previously discussed, on this level the universes are merely different branches of the same tree. Tegmark does not explicitly describe whether or not these different branches are able to interact with each other causally, and I would expect him to say that they do not, but that they are still interconnected in some sense. On levels 1 and 2, we can think of our counterpart selves doing other than we are doing here in some distant universe, whereas on level 3 our counterpart merely is on another “quantum branch in infinite-dimensional Hilbert space” unknown to us simply by our epistemic limitations (Tegmark, 2007, pp. 112–13), and this seems to indicate that these different branches may be connected yet causally isolated from one another.
Finally, the level 4 multiverse “involves the idea of mathematical democracy, in which universes governed by other equations are equally real. This implies the notion that a mathematical structure and the physical world are in some sense identical. It also means that mathematical structures are ‘out there,’ in the sense that mathematicians discover them rather than create them” (Tegmark, 2007, p. 116). This seems to entail a variety of universes that are widely divergent from the one that we are currently in, resulting in a seemingly infinite amount of universes that would be unrecognizable to us. The universes in the level 4 multiverse contain “different fundamental physical laws” (Tegmark, 2007, p. 121), which means that the range of individual universes that we could see on this level far surpasses the range of universes that we could see in levels 1–3. Not only would we be able to have all possible storylines be realized, as is the case for levels 1–3, but we would be able to see all possible storylines that are compatible with each possible set of fundamental physical laws.
So, while Tegmark does not exactly propose any new scientific account of the multiverse, what he does do is set up a framework by which we can differentiate and classify existing or future scientific multiverse accounts. Tegmark’s levels of classification allow us to see just how far particular multiverse theories range from what we know about, and see within, our own universe, as well as allow us to see how multiverse theories vary from one other in terms of what they call for with regard to physical constants of the universes that they contain.
The second scientific approach to the multiverse that will be discussed is one similar to Tegmark’s level 3 multiverse discussed above and is proposed as an answer to the problem that the “Schrödinger’s Cat” thought experiment posed for what we can claim about our knowledge of the physical world (Norris, 1999). This particular account was put forth by David Deutsch (1997), and subsequently discussed by Christopher Norris. Of Deutsch’s account, Norris says
On this account—in brief—every possible outcome of every wavepacket collapse is simultaneously and actually realized through constant branching of alternative quantum worlds that are all of them equally “real” though only one of them is epistemically accessible to any individual observer at any particular time. For the observer must likewise be thought of as having previously split into a whole multitude of observers, each of them consciously inhabiting a “world” whose history is itself just one among the manifold world-versions that have eventuated up to the point through the exfoliating series of wavepacket collapses. Thus he or she will have any number of counterpart “selves” distributed across those worlds and each possessing a lifeline which, if traced back far enough, will rejoin his/her own at some crucial point just before their paths forked off into henceforth divergent and non-communicating series. (Norris, 1999, pp. 312–13)
Furthermore, Deutsch does not want to limit these other worlds to maintaining our physical constants or laws of nature. While it is not explicitly stated just how far the laws of nature and physical constants of these other worlds or universes may vary from those in ours, I think that it would be safe to say that Deutsch may have in mind the kinds of variations found in Tegmark’s level 3 and 4 multiverses. In short, Deutsch’s account says that we need to adopt “the multiverse theory and assuming that all possibilities have been realized in one or another of the multiple worlds that diverge at every point where some particular world-specific event . . . happens to occur” (Norris, 1999, p. 314). Of course, just what exactly constitutes a possibility for Deutsch depends highly on his range of allowable divergence between the physical constants of our universe and those of other universes, but the principle still remains regardless of the lack of an explicit explanation.
The final scientific account to be mentioned here is that of A. D. Linde, who argues for a kind of self-reproducing multiverse (Linde, 1987). This brand of multiverse account can be seen as one in which not all universes contained within the multiverse are actualized or exist simultaneously, rather they all come to exist (generally one-by-one) over a period of time. Linde’s account, argues, in particular, that “the large-scale quantum fluctuations of the scalar field . . . generated in the chaotic inflation scenario lead to an infinite process of self-reproduction of inflationary mini-universes.”16 He suggests a “model of an eternally existing chaotic inflationary universe.”17 Linde goes on to cite scientific and mathematical reasons for how this particular multiverse model is predicted. Of this prediction, Linde explains that
In our case the universe infinitely regenerates itself, and there is no global “end of time.” Moreover, it is not necessary to assume that the universe as a whole was created at some initial moment. . . . The process of creation of each new mini-universe . . . occurs independently of the pre-history of the universe. . . . Therefore the whole process can be considered as an infinite chain reaction of creation and self-reproduction which has no end and which may have no beginning. (Linde, 1987, pp. 172–73)
So, in this case, the universe
