Today’s New Reason To Believe

A few months ago, I discussed how a spatially infinite, Level I multiverse would impact apologetic arguments based on the fine-tunings of our observable universe. Although a number of philosophical arguments arise against an actual infinity, a sufficiently large but spatially finite Level I multiverse presents the same challenges to fine-tuning arguments. My purpose in this article is not to rebut these challenges but instead to highlight one peculiar consequence of such a Level I multiverse.

One of the rarest hands in poker is a royal flush. In fact, for any given five-card hand the chances of getting a royal flush are less than one in 2.5 million (assuming I specify a given suit). However, dealing a billion hands virtually assures that a fairly large number of those hands will contain a royal flush of the specified suit. Additionally, every possible combination of cards exists in a large number of hands, meaning an equally large number of royal flushes with an ace of the wrong suit also exist.

Switching back to the Level I multiverse, a large number of regions will look almost exactly like our observable universe. In one of those universes everything is the same except I decided not to write this article—or I decided to become a chemist instead of an astrophysicist—or my work in graduate school was rewarded with a Nobel Prize! In fact, any possible situation actually occurs in such a multiverse scenario. Max Tegmark at MIT calculated the distances to these “clone” regions and arrives at numbers like 10¹⁰²⁹ meters away. Granted these are huge distances but these clones come part-and-parcel with a sufficiently large Level I multiverse.

I haven’t thought through the details yet, but the existence of these other regions appear to dramatically impact our notion of free will and justice. Am I really being held accountable for my actions when I don’t commit those actions in some other regions or when I am not punished for them in others? Is that person in the other region really me? These are some of the interesting and alarming consequences of a spatially infinite (or sufficiently large) Level I multiverse that need addressing.

Last month’s multiverse discussion focused on one of its less controversial aspects—the idea that the universe extends beyond the limits of our observations. The uniformity we see in our universe (the cosmic microwave background radiation being the best example) strongly argues for this point. The issue then becomes how large the actual universe is. Using the maximum curvature detected by WMAP and a simple assumption that the universe closes back on itself, a minimum size for the whole universe roughly equals 1000 times the size of the observable universe. (For a discussion of these terms see my initial multiverse article.)

Somewhat more controversial is the idea of a spatially infinite universe—a result that derives from the current formulations of how inflation works. As discussed last month, a spatially infinite universe dramatically impacts the apologetic significance of some fine-tuning arguments, although it would still comfortably fit within a Christian worldview.

As it currently stands, any experimental verification of inflation’s details lay far in the future so the conclusion of a spatially infinite universe remains a more philosophical issue at this point. In such light, I thought it relevant to highlight some philosophical arguments against a spatially infinite universe advanced by William Lane Craig. Craig uses them to support the Kalam cosmological argument but they apply here as well.

An article in Scientific American gives more details of the relevant science, but the point pertinent to this discussion involves a transformation of the infinite future expansion of our bubble into an actual spatially infinite universe. Craig argues that actual infinities of the type invoked here cannot exist because they lead to absurdities.

He outlines a few examples of absurdities arising in dynamical infinities in this article published in the Canadian Journal of Philosophy:

1. Consider an infinite hotel full of guests. Now suppose another infinite group arrives and asks for rooms. If the owner has each guest move to the room twice their current value (1 to 2, 2 to 4, 3 to 6,…), this leaves open the infinite number of odd-numbered rooms. So a completely full hotel can accommodate an infinite number of new guests.

2. Consider two planets where one orbits twice as fast as the other. After an infinite time, each planet has accumulated an identical number (the infinite value aleph-null, ) of orbits. However, during every possible finite time interval, the faster planet accumulates twice as many orbits as the slower.

3. In the previous example, one could ask the question of whether the number of completed orbits is even or odd. After an infinite time the number of orbits is a value referred to as aleph-null. An even number is a multiple of two; an odd number is one more than a multiple of 2. But, = (2 x ) = (2 x + 1). So the number of orbits after infinite time is both odd and even.

These examples highlight that basic rules which we take for granted cannot apply in physically existing infinites. Either we must rewrite basic arithmetic rules (addition, subtraction, multiplication, division, and comparison) or such infinities do not exist. I have glossed over many details, but the objections Craig raises are worth a serious look as a response to infinite, dynamic universes. Additionally, scientists typically regard infinities as a sign that they have entered a region where their theories are no longer valid.

So, there may be good philosophical reasons to reject the notion that we live in a spatially infinite universe. Even so, the issue of the actual spatial extent of our universe still remains. It could still be so large as to negate the apologetical significance of the fine-tuning arguments. However, that scenario also poses some significant philosophical issues that I will address next time.

Last month I defined some terminology and provided a categorization of the different kinds of multiverses discussed by scientists. The least controversial multiverse, Level I, simply states that the universe does not end at the edge of the region observable by humans. The issue of the universe’s true size naturally arises.

Using the curvature of the universe measured by WMAP, scientists can put a lower bound, n, on the number of regions the size of our observable universe (referred to as Hubble volumes) that would fit in the universe. They estimate a minimum value of n=1000. However, if the current formulation of inflation proves correct, it predicts n=infinity for the Level I multiverse. That would seriously impact the strength of some apologetic arguments used for fine-tuning in the universe.

Consider the chances of drawing a royal flush from a standard deck of cards. Just four combinations of the 2,598,960 unique five-card possibilities make a royal flush. So the probability of drawing a royal flush on any single draw is 1 part in 649,740, but the odds grow with the number of draws available. If 10,000,000 draws occurred without a royal flush, one would wonder if the deck contained all the proper cards. An infinite number of draws assures a large number (actually an infinite number) of royal flushes.

Now consider the possible arrangements or states for the observable universe. Our Hubble volume (with a just-right Earth/Moon/Jupiter orbiting a just-right star at the just-right location in a just-right galaxy) corresponds to one state. Another state might look identical except Pluto does not exist. Many other states contain no planet remotely similar to Earth. One can envision a very large number of states in this manner, but the total number of possible states is finite. Consequently, the number of possible histories is also finite.

IF the universe is spatially infinite, Hubble volumes exhibiting all possible histories consistent with the laws of physics will exist somewhere—regardless of the improbability of any particular state! Humans exist only in the states meeting the requirements for their existence. The impact such a scenario has on many fine-tuning arguments is obvious. The question then becomes how does a Christian respond?

Here are a number of points to keep in mind:

1. An infinite Level I universe does not impact the fine-tuning arguments regarding the gross features of the universe such as the strengths of the four fundamental forces.

2. An infinite Level I universe does not argue against a Creator. It just removes one currently used apologetic argument.

3. An infinite Level I multiverse still relies on the current formulations of inflation but those formulations remain far from experimental verification. A comment by the cosmologist George Ellis regarding the multiverse applies here as well.

   The multiverse situation seems to fit St Paul’s description: “Faith is the substance of things hoped for, the evidence of things not seen.” In this case, it is faith that enormous extrapolations from tested physics are correct; hope that correct hints as to the way things really are have been identified from all the possibilities, and that the present marginal evidence to the contrary will go away.

4. Scientists often regard infinities arising in theories as a sign that the theory is breaking down. In this instance, many scientists embrace the spatial infinity predicted by inflation. Interestingly, the predicted actual spatial infinity derives from a reference-frame transformation involving a future potential time infinity.

The answer to whether the infinities of the Level I multiverse stand up under experimental scrutiny likely lies in the somewhat distant future. However, as Christians, we need to understand and feel the weight of these arguments in order to give an adequate response. As I will discuss next month, William Lane Craig argues that actual infinities do not exist because they lead to absurdities.