## Abstract

The objective of this paper is analyzing to which extent the multiverse hypothesis provides a real explanation of the peculiarities of the laws and constants in our universe. First we argue in favor of the thesis that all multiverses except Tegmark’s “mathematical multiverse” are too small to explain the fine tuning, so that they merely shift the problem up one level. But the “mathematical multiverse" is surely too large. To prove this assessment, we have performed a number of experiments with cellular automata of complex behavior, which can be considered as universes in the mathematical multiverse. The analogy between what happens in some automata (in particular Conway’s “Game of Life") and the real world is very strong. But if the results of our experiments can be extrapolated to our universe, we should expect to inhabit—in the context of the multiverse—a world in which at least some of the laws and constants of nature should show a certain time dependence. Actually, the probability of our existence in a world such as ours would be mathematically equal to zero. In consequence, the results presented in this paper can be considered as an inkling that the hypothesis of the multiverse, whatever its type, does not offer an adequate explanation for the peculiarities of the physical laws in our world.

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## Notes

A preliminary (and extended) version of this article is available at arXiv under the title “Is the Multiverse Hypothesis capable of explaining the Fine Tuning of Nature Laws and Constants? The Case of Cellular Automata". See: http://arxiv.org/abs/1105.4278 .

The suggestion of using cellular automata as simple models of possible universes in a multiverse has been already used by Paul Davies in his paper Davies (2007), but the goal of Davies is to make use of the automata to prove his conjecture regarding the origin of the bio-friendly laws of the universe. We think, however, that Davies conjecture (which includes the idea of physics and biology co-evolving in such a way that an apparently teleological behaviour in the universe emerges) is very speculative. And it seems not easy to get support for such ideas through automata models. Therefore our aim is simply to explore the use of cellular automata to test the (somewhat more conventional) multiverse explanation of the peculiar features of the nature laws in our universe.

Collins (2003, 180–181).

Ibid., 182–183. Taken from Barrow and Tipler (1986). See Wolfram, 326–327. The book by Barrow and Tipler is a classic exposition on fine-tuning of the universe, and thus highly recommended to the interested reader.

Ibid.

Ibid., 185. Cited from Oberhummer et al. (2000, 90).

Ibid., 186–187.

Bostrom (2007, 439–440).

Actually we can only receive the light emitted after what is usually called the “surface of final dispersion", the instant when radiation uncoupled from matter. This happened about 100,000 years after the Big Bang. But these details are not important here. After all, 100,000 years are not much … at the cosmological scale.

Tegmark (2004, 483).

Stoeger (2007, 455).

Davies (2007, 497).

The “mediocrity principle" and the way in which this principle can be used to make predictions in the context of the multiverse hypothesis have been explained e.g. in Vilenkin (2006, chapter 14). Similar ideas (in a non-cosmological context) had been proposed earlier by John Leslie and Richard Gott (See e.g. Gott 1993). Gott called this principle “Copernican anthropic principle", but it is basically the same idea. Anthropic reasoning and predictions based in the “mediocrity principle" have been subject to some criticism. In the words of Vilenkin:

The best we can hope for is to calculate the statistical bell curve. Even if we calculate it precisely, we will only be able to predict some range of values at a specified confidence level. Further improvements in the calculation will not lead to a dramatic increase in the accuracy of the prediction. If the observed value falls within the predicted range, there will still be a lingering doubt that this happened by sheer dumb luck, If it doesn’t, there will be doubt that the theory might still be correct, but we just happened to be among a small percentage ob observers at the tails of the bell curve.

It’s little wonder that, given a choice, physicists would not give up their old paradigm in favor of anthropic selection. But nature has already made her choice. We only have to find out what it is. If the constants of nature vary from one part of the universe to another, then, whether we like it or not, the best we can do is to make statistical prediction based on the principle of mediocrity" Vilenkin (2006, 151).

Tegmark (1998, 4).

Tegmark (2007, 120).

See Neumann (1966).

See Wolfram (2002, cap. 7–8).

See Dennett (2003, cap.2).

See Wolfram (2002).

See Wolfram (1986).

See more technical details of this program and the related experiments in our paper: Alfonseca and Soler Gil (2012).

A recent and very interesting study of cellular automata (including the game of life) and its relationship to the real universe is Mainzer and Chua (2012). Of course, the use of classical cellular automata has its limitations, since most likely the real universe is a quantum universe. In the words of Mainzer and Chua:

[…] classic deterministic cellular automata are only approximate models of physical reality, which is governed by the principles of quantum physics […]. Quantum cellular automata (QCA) would be more adequate but, of course, not as easy to understand as the toy world of classical cellular automata. […] In principle, it is possible to transform the concept of quantum systems into QCA Mainzer and Chua (2012, 105).

Some authors as Seth Lloyd have investigated “toy" models of a quantum universe (considered as a quantum computer). Lloyd has found that such toy universes evolve complexity and structure naturally and with high probability, eee e.g. Lloyd (1999). This encourages us to think that a transposition of the experiments performed here to the context of quantum cellular automata would show that the generation of complexity by means of time-dependent rules is perfectly possible in the quantum scenario. But this conjecture should be obviously tested in further research.

If the universal

*constants*in our universe are really constant (as most studies seem to imply), then our universe can be represented as a point in the configuration space of all the possible values of the constants. A universe where the*constants*were actually variable would be represented by a curve. If those universes are to be compatible with life, the point and the curve must lay within the subset of the configuration space that makes that compatibility possible. However, the number of points in a subset of space is a continuum-like infinite, while the number of curves in the same space is a different infinite, infinitely much larger than the continuum. Therefore, the probability of our having been born by chance in a*constant*universe (the quotient of both infinities) would be zero.We are aware that current physics allows for some of the constants in our universe not to be so, as shown by the present debate on the constancy of the fine structure constant. But it cannot be denied that, in the worst case, all our constants are

*almost constant*, which means that, although the actual probability of being in a universe like ours may not be exactly zero, it would still be very (perhaps vanishingly) small.

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Soler Gil, F.J., Alfonseca, M. Fine Tuning Explained? Multiverses and Cellular Automata.
*J Gen Philos Sci* **44, **153–172 (2013). https://doi.org/10.1007/s10838-013-9215-7

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DOI: https://doi.org/10.1007/s10838-013-9215-7

### Keywords

- Astrophysics
- Cosmology
- Multiverse
- Fine tuning
- Cellular automata