Multiverses design and the beauty of the laws of nature

Next, I want to look at what many consider another powerful suggestion of design from modern physics, that arising from the 'beauty' and 'elegance' of the laws of nature. This suggestion of design bypasses the multiverse objection to the design argument, whether the multiverse hypothesis is of

6 Although some of the laws of physics can vary from universe to universe in string theory, these background laws and principles are a result of the structure of string theory and therefore cannot be explained by the inflationary/superstring multiverse hypothesis since they must occur in all universes. Further, since the variation among universes would consist of variation of the masses and types of particles, and the form of the forces between them, complex structures would almost certainly be atom-like, and stable energy sources would almost certainly require aggregates of matter. Thus, the above background laws seem necessary for there to be complex, embodied intelligent observers in any of the many universes generated in this scenario, not merely a universe with our specific types of particles and forces.

the universe-generator or metaphysical variety. The idea that the laws of nature are beautiful and elegant is commonplace in physics, with entire books devoted to the topic. Indeed, Steven Weinberg - who is no friend of theism - devotes an entire chapter of his book Dreams of a Final Theory [24] to beauty as a guiding principle in physics. As Weinberg notes, 'mathematical stuctures that confessedly are developed by mathematicians because they seek a sort of beauty are often found later to be extraordinarily valuable by physicists' (see p. 153 of ref. [24]). To develop our argument, however, we need first to address what is meant by beauty. As Weinberg notes, the sort of beauty exemplified by physics is that akin to classical Greek architecture. The highpoint of the classical conception of beauty could be thought of as that of William Hogarth in his 1753 classic The Analysis of Beauty [25]. According to Hogarth, simplicity with variety is the defining feature of beauty or elegance, as illustrated by a line drawn around a cone. He went on to claim that simplicity apart from variety, as illustrated by a straight line, is boring rather than elegant or beautiful.

The laws of nature seem to manifest just this sort of simplicity with variety: we inhabit a world that could be characterized as having fundamental simplicity that gives rise to the enormous complexity needed for intelligent life. To see this more clearly, we will need to explicate briefly the character of physical law, as discovered by modern physics. I will do this in terms of various levels.

The physical world can be thought of as ordered into the following, somewhat overlapping, levels. Level 1 consists of observable phenomena. The observable world seems to be a mixture of order and chaos: there is regularity, such as the seasons or the alternation of day and night, but also many unique, unrepeatable events that do not appear to fall into any pattern. Level 2 consists of postulated patterns that exist among the observable phenomena, such as Boyle's law of gases. The formulation of level 2 marks the beginning of science as understood in a broad sense. Level 3 consists of a set of postulated underlying entities and processes hypothesized to obey some fundamental physical laws. Such laws might be further explained by deeper processes and laws, but these will also be considered to inhabit level 3. So, for instance, both Newton's law of gravity and Einstein's equations of General Relativity would be considered to be level 3. The laws at level 3, along with a set of initial (or boundary) conditions, are often taken to be sufficient to account for the large-scale structure of the Universe.

Level 4 consists of fundamental principles of physics. Examples of this are the principle of the conservation of energy and the gauge principle (that is, the principle of local phase invariance), the principle of least action, the anti-commutation rules for fermions (which undergird Pauli's exclusion principle) and the correspondence principle of quantum mechanics (which often allows one to write the quantum mechanical equations for a system by substituting quantum operators for certain corresponding variables into a classical equation for the system). These are regulative principles that, when combined with other principles (such as choosing the simplest Lagrangian), are assumed to place tight constraints on the form that the laws of nature can take in the relevant domain. Thus, they often serve as guides to constructing the dynamical equations in a certain domain.

The laws at level 3 and the principles of level 4 are almost entirely cast in terms of mathematical relations. One of the great achievements of science has been the discovery that a deeper order in observable phenomena can be found in mathematics. As has been often pointed out, the pioneers of this achievement - such as Galileo, Kepler, Newton and Einstein - had a tremendous faith in the existence of a mathematical design to nature, although it is well known that Einstein did not think of this in theistic terms but in terms of a general principle of rationality and harmony underlying the Universe. As Morris Kline, one of the most prominent historians of mathematics, points out [26]:

From the time of the Pythagoreans, practically all asserted that nature was designed mathematically... During the time that this doctrine held sway, which was until the latter part of the nineteenth century, the search for mathematical design was identified with the search for truth.

Level 5 consists of the basic mathematical structure of current physics, for example the mathematical framework of quantum mechanics, though there is no clear separation between much of level 5 and level 4. Finally, one might even want to invoke a level 6, which consists of the highest-level guiding metaphysical principles of modern physics - for example, that we should prefer simple laws over complex laws, or that we should seek elegant mathematical explanations for phenomena.

Simplicity with variety is illustrated at all the above levels, except perhaps level 6. For example, although observable phenomena have an incredible variety and much apparent chaos, they can be organized via relatively few simple laws governing postulated unobservable processes and entities. What is more amazing, however, is that these simple laws can in turn be organized under a few higher-level principles (level 4) and form part of a simple and elegant mathematical framework (level 5).

One way of thinking about the way in which the laws fall under these higher-level principles is as a sort of fine-tuning. If one imagines a space of all possible laws, the set of laws and physical phenomena we have are just those that meet the higher-level principles. Of course, in analogy to the case of the fine-tuning of the parameters of physics, there are bound to be other sets of laws that meet some other relatively simple set of higher-level principles. But this does not take away from the fine-tuning of the laws, or the case for design, any more than the fact that there are many possible elegant architectural plans for constructing a house takes away from the design of a particular house. What is important is that the vast majority of variations of these laws end up causing a violation of one of these higherlevel principles, as Einstein noted about general relativity. Further, it seems that, in the vast majority of such cases, such variations do not result in new, equally simple higher-level principles being satisfied. It follows, therefore, that these variations almost universally lead to a less elegant and simple set of higher-level physical principles being met. Thus, in terms of the simplicity and elegance of the higher-level principles that are satisfied, our laws of nature appear to be a tiny island surrounded by a vast sea of possible law structures that would produce a far less elegant and simple physics.

As testimony to the above point, consider what Steven Weinberg and other physicists have called the 'inevitability' of the laws of nature (see, e.g., pp. 135-153 and 235-237 of ref. [24]). The inevitability that Weinberg refers to is not the inevitability of logical necessity, but rather the contingent requirement that the laws of nature in some specified domain obey certain general principles. The reason Weinberg refers to this as the 'inevitability' of the laws of nature is that the requirement that these principles be met often severely restricts the possible mathematical forms the laws of nature can take, thus rendering them in some sense inevitable. If we varied the laws by a little bit, these higher-level principles would be violated.

This inevitability of the laws is particularly evident in Einstein's general theory of relativity. As Weinberg notes, 'once you know the general physical principles adopted by Einstein, you understand that there is no other significantly different theory of gravitation to which Einstein could have been led' (p. 135 of ref. [24]). As Einstein himself said, 'To modify it [general relativity] without destroying the whole structure seems to be impossible.'

This inevitability, or near-inevitability, is also illustrated by the gauge principle, the requirement that the dynamical equations expressing the fundamental interactions of nature - the gravitational, strong, weak and electromagnetic forces - be invariant under the appropriate local phase transformation. When combined with the heuristic of choosing the simplest interaction Lagrangian that meets the gauge principle and certain other background constraints, this has served as a powerful guide in constructing the equations governing the forces of nature (e.g. the equations for the forces between quarks). Yet, as Ian Atchison and Anthony Hey point out, there is no compelling logical reason why this principle must hold. Rather, they claim, this principle has been almost universally adopted as a fundamental principle in elementary particle physicists because it is 'so simple, beautiful and powerful (and apparently successful)' [27]. Further, as Alan Guth points out [28], the original 'construction of these [gauge] theories was motivated mainly by their mathematical elegance'. Thus, the gauge principle provides a good example of a contingent principle of great simplicity and elegance that encompasses a wide range of phenomena, namely the interactions between all the particles in the Universe.

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