Max Tegmark, a cosmologist at MIT, goes further. He envisions four kinds of multiverses that may exist, labeling them "Levels":
- Level I: Space in our universe goes on far beyond that which we can see, and perhaps goes on forever — which would mean that infinitely many other regions exist in our own pocket universe, regions like our observable universe, where the laws of physics are the same.
- Level II: Infinitely many other regions exist in the same space-time as that of our universe, but they are disconnected permanently from our own pocket universe, and within each of them the laws of physics are different (described by Linde's eternal chaotic inflation and potentially the string theory landscape).
- Level III: A kind of space different from the space-time of our universe exists (called "Hilbert space," which is infinite-dimensional and abstract), where the laws of quantum mechanics generate multiple universes via innumerable branchings. (This is based on taking seriously the quantum wave function, which is a probability amplitude of the quantum state of the system.) The universe branches into different whole-world realities with every tick of time, whether at every Planck time, which is 10^-43 seconds (the time it takes a photon, traveling at the speed of light, to travel one Planck length, 10^-35 m), or at every instant of time when an observation is made. These other whole worlds would not be far away in terms of our kind of space — so in a sense they are right here — but branched out immensely into this different kind of (Hilbert) space. (This is the "many-worlds" interpretation of quantum mechanics, devised by the then relatively unknown physicist Hugh Everett in 1957 and now enjoying new respectability.)
- Level IV: Tegmark makes the extraordinary claim that every consistent system of mathematics describes some kind of existing world or universe. "It would seem odd if there were some basic asymmetry built into math," he told me, "such that some equations would be allowed to describe a physical universe and others would not. So my guess is that every mathematical structure which mathematicians can study is on the same footing and describes some kind of physical universe. I think that the reason that nature is so well-described by math is because in a very deep sense, nature really is math."
As Linde told me recently, "This is subtle. Suppose a bubble of a new vacuum is created in an eternally expanding universe — a standard picture in eternal chaotic inflation and the string theory landscape (Level II). Then, from the outside, each such bubble looks like a finite bubble that grows infinitely in time. But from the inside, it looks like an infinite open universe. Of course, 'looks like' means that someone is looking, but nobody can see an infinite universe."
Tegmark's Level I is accepted by almost all cosmologists (i.e., space in our universe extends far beyond that which we can see with our best telescopes); his Level II has become the "standard model" of cosmology (i.e., the cosmic inflation of Guth leads to the eternal chaotic inflation of Linde, generating disconnected pocket universes continuously and forever); his Level III is speculative and controversial (i.e., quantum branching); and his Level IV, while idiosyncratic, seeks deep truths of existence (i.e., reality is mathematics).
Seven kinds of multiple universes
What's my take? Long out of childhood, but still feeling childlike in the presence of a multiverse, I try to assess the possibilities. I like to categorize things, to discern scope and breadth. Here are seven possible mechanisms that could generate multiple universes.
- Different spatial regions of our ordinary space-time could exist in our own pocket universe, yet so far away that even the light of their stars, traveling at the speed of light, will never have sufficient time to reach us (generated by cosmic inflation).
- Different temporal periods of our ordinary space-time could exist in our own pocket universe, such that multiple universes arise in sequence, not in parallel (generated by cycles of universal expansion and contraction, Big Bangs and big crunches).
- Different domains of our ordinary space-time could "squeeze off" to become other pocket universes, separated forever from our universe (each new universe generated by eternal chaotic inflation and perhaps characterized by string theory).
- Different dimensions of space and time could exist, where in higher dimensions, entirely independent realities may exist. These different dimensions may be in some sense very close, but with respect to information flow and communications, forever apart.
- Different universal histories could be created via the wave function (and strangeness) of quantum mechanics, where at each fleeting instant (such as every moment of Planck time or flash of observation), all reality splits into many worlds (generated by taking the wave function as objective reality).
- Whatever can be expressed by consistent mathematical systems can in fact exist in some kind of reality (Tegmark's Level IV).
- The principle of fecundity or modal realism might operate: All possibilities of any kind, whether imagined or unimagined, do really exist. Somewhere (Nozick, Lewis).
Do all things exist?
In a multiverse, one cannot avoid infinity, and infinity does strange things. There are two types of possible infinities in a multiverse: Type I: A single universe may be infinite in size (e.g., in our universe, if space and galaxies would continue forever without end or closure), or Type II: All the separate universes in a multiverse can be infinite in number (irrespective of whether any or all of the universes are infinite in size themselves).The consequences of either infinity become bizarre. First of all, even Tegmark's Level I multiverse, assuming it's infinite, must contain everything that's physically possible. This means, for example, that every "Star Wars" scenario really exists out there, including those that didn't make it into the films and even all those the writers didn't think of!
Similarly, as long as there is sufficient space for unending random shufflings of particles (and a universe of infinite size certainly has sufficient space), there would have to be a sector of space out there identical to our sector of space, with persons identical to you and to me. Tegmark estimates that our closest identical copy is 10^10^28 m away.
I'm not so impressed even by this bizarre proposition. There would also have to be a sector of space identical to our sector of space except for, say, one hair on the head of one person, which is skewed 1 nanometer to the right. And another sector of space in which all else is the same except for that same hair, which is now skewed 2 nanometers to the left. Then all the hairs on all the people, skewed this way and that way. And then all the things in whole sectors of space, arranged in every possible combination and permutation. There would be innumerable minute differences and innumerable large differences, with every one a separate sector of space — all enabled because the one infinite universe with infinite sectors of space goes on forever. Obviously, on this vision, randomized particles in the overwhelming majority of vast sectors of space yield nothing much at all.
To be clear, a truly infinite universe means that anything that is not impossible (no matter how obscure) will happen, must happen and must happen, weirdly, an infinite number of times. An infinite universe goes on forever, not only generating uncountable variations, but also requiring each of the uncountable variations to occur an infinite number of times. That's the strange nature of a true infinity.
I agree with Davies: Something is amiss.
Does a multiverse undermine God? Or enrich God?
If multiple universes are real, and especially if a true infinite number of universes really exist, then our worldview changes. Everything changes. Whatever you believe — even about God (that God exists? that God doesn't exist?) — nothing remains the same. If only the material world exists, then the material world becomes inconceivably larger. If an infinite God exists, then God's infinity becomes expressed by science and enriched with new meaning.But would the real existence of a multiverse undermine arguments for the real existence of God (by undercutting the modern "argument from design" based on the "fine-tuning" of our universe)? How would God, if there is a God, relate to a multiverse? If one believes in God, or wonders whether to believe in God, this issue cries out to be addressed. Why would God, if there is a God, create multiple universes? Why would God create infinite multiple universes? Could a multiverse elucidate what God, if there is a God, would be like? And if God does not exist, then what? Does a multiverse have meaning? (All this I shall consider in a future essay.)
If, from this essay I seem rational, coolheaded and self-assured about multiple universes, then I have been unintentionally deceptive. I am intimidated by the ineffable endlessness of an overarching, overwhelming multiverse. I shrink before the terrifying vision of the 17th century philosopher Blaise Pascal: "The eternal silence of these infinite spaces frightens me."
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