Where do the laws of physics come from? And why those laws rather than some other set?. Most especially, why a set of laws that drives the searing featureless gases coughed out of the Big Bang towards life and consciousness and intelligence and cultural activities such as religion, art, mathematics and science.
You might be tempted to suppose that any old rag-bag of laws would produce a complex universe of some sort, with attendant inhabitants convinced of their own specialness. Not so. It turns out that randomly selected laws almost invariably lead to unrelieved chaos or boring and uneventful simplicity. Our own universe is poised exquisitely between these un-palatable alternatives, offering a potent mix of freedom and discipline, a sort of restrained creativity. Instead they encourage matter and energy to develop along pathways of evolution that lead to novel variety...I can’t prove to you that it is design, but whatever it is, it is certainly very clever’
To my mind, the most remarkable feature of the universe is that it appears to conform to mathematical laws. That no-one these days seems particularly phased by this astonishing fact is testimony to the human capacity to take things for granted. In most accounts, the laws of nature capture a kind of natural necessity; in other words, they are not mere descriptions but depict the way things must be. Furthermore they appear to be presuppositions of science rather than simply the product of investigation. Not only that but the incredible precision of our particular set of ‘laws of nature’ has been capable of persuading something unimaginably smaller than a subatomic particle to evolve into an unimaginably large universe with 100 billion galaxies, lay down the chemistry for the emergence of carbon based life and channel a process of evolution into conscious beings that are capable of pondering their circumstances. In recognition of this we are entitled to ask the questions, why are there laws?, what makes them mathematical?, what makes them exceptionless and why do they take the special form they do?.
From the very beginning the idea of ‘laws of nature’ was theological in character. When Aristotle’s work was re-introduced to the Latin West in the 11th century, the orderliness of nature was held to be derived from the immanent properties of natural objects; or ‘the order that God has implanted in nature’ as Aquinas described it. Mathematical reasoning was sidelined because of the division of labour in Aristotelian sciences and because Aristotle had thought, going against the mathematical realism of Plato, that mathematics dealt with human constructions. Thus it was that natural philosophy focused on the causes of the motions of the planets and mathematical astronomy considered mathematical descriptions which would be ‘saving the phenomena’, making predictions, but not really giving a causal explanation of the motions. During the Middle Ages, a vocabulary of ‘natural laws’ arose, but these were all confined to the area of morality and the participation of rational creatures in the eternal law of ‘God the ruler of the universe’.
Two movements would combine to challenge these perspectives. The first was a growing emphasis on the omnipotence of God and the divine Will which proved incompatible with the autonomy of the Aristotelian world. The second was a Christian Platonism which promoted mathematical realism in natural philosophy. As the Protestant Reformation gathered force questions were raised about how appropriate it was to adopt the thought of the unchristian Aristotle. Two Greek movements contained ideas that seemed promising for his overthrow, the atomism of Democritus and Epicurus; and the thought of the ancient sceptics.
Atomism suggested that matter was inert and not autonomous as it had been in the Aristotelian view of nature where natural objects contained causal efficacy. God had created the world and ruled it directly; and so, it was argued, he must have issued physical laws similar to the moral edicts in the bible and the ‘natural laws’ discussed in the Middle Ages. And what of mathematics, could it not be that this was the product of the divine mind and therefore manifested in the created order?. If the world is a product of the divine, isn’t the distinction between natural and artificial irrelevant?.
It was this radical re-conception which led to the discovery of the laws of the so called ‘scientific revolution; Descartes Laws of Motion, Hooke’s Law, Pascal’s Law, Boyle’s Law, Galileo’s laws of fall and inertia and Kepler’s Planetary Laws. Kepler referred to the divine Will and the creator as the foundation for his realist mathematical astronomy when he wrote:
'I shall have the physicists against me in these chapters because I have deduced the natural properties of the planets from immaterial things and mathematical figures...I wish to respond briefly as follows: that God the creator, since he is a mind, and does what he wants, is not prohibited, in attributing powers and appointing circles, from having regard to things which are wither immaterial or based on imagination. And since he wills nothing except with absolute reason, and nothing exists except by his will, then let my adversaries say what other reasons God had for attributing powers, etc. Since there was nothing except for qualities’.
Kepler then criticised Aristotle’s inability to conceptualise a world founded on mathematical principles. He had been unable to do so, Kepler said, because he had not believed the world had been created. By contrast Kepler and many of his contemporaries believed that mathematical relations in the universe is assured because God has manifested these in the created order; hence mathematical laws can describe the real relations between physical objects. Keplar wrote that this:
‘is acceptable to me and to all Christians since our faith holds that the World, which had no previous existence, was created by God in weight, measure and number, that is in accordance with ideas co-eternal with him’
Galileo, who took the un-Aristotelian step of introducing mathematics into physics, insisted that mathematical relations are real and God relied upon them when designing the cosmos:
‘the human intellect does understand some of them [mathematical truths] perfectly, and thus in these it has as much absolute certainty as nature has itself. Of such as the mathematical sciences alone, that is, geometry and arithmetic, in which the divine intellect indeed knows infinitely more proposition, since it knows all. But with regard to those few which the human intellect does understand, I believe that it’s knowledge equals the divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater certainty’.
In both these claims, Kepler and Galileo show the influence of renaissance Platonism. Kepler also conceived of the cosmos as a divinely created machine on the model of a clock. Hence the findings of the mechanical sciences could now be applied to nature.
Following this view, Descartes wrote ‘the laws of mechanics are identical to the laws of nature’ and should be regarded as eternal and immutable features of the natural world rather than human constructs. According to Descartes, these laws originate in the divine will and are underwritten by the immutability of God; something he emphasised most famously in his principle of conservation of motion.
According to Dennis Des Chene:
‘The Aristotelian philosophy takes natural change to be the work of active powers in nature itself, in which God concurs. The Cartesian interprets it as the work of God alone, subject to natural laws, appeal to which will help demonstrate the observed regularities which by the Aristotelian are referred to the intrinsic powers of material things and to the ends toward which they act.
This is demonstrated in a letter Descartes wrote to his friend Mersenne in which he said:
‘the mathematical truths which you call eternal were established by God and totally depend on him just like all the other creatures’
Malebranche echoed this sentiment, maintaining that God directly imposed his will on brute matter in systematic ways that could be described as ‘laws’.
In contrast to Descartes who believed that the laws could be derived from the divine nature by intuition, Newton believed that the laws must be discovered by experimentation in order to reach a high level of certainty, yet here also he spoke of ‘ an infinite and omnipresent spirit in which matter is moved according to mathematical laws’; although in the Principia he more modestly said that:
‘gravity must be caused by an agent acting constantly according to certain laws, but whether this agent be material or immaterial I have left to the consideration of my readers’.
The early modern idea of laws of nature was grounded in a particular conception of divine activity, one specific to the west; although there are hints of it in Islamic theology. Lawfulness is not something which was a self-evident feature of the universe but was an implication of specific conceptions of God. Later the laws would become simply laws intrinsic to nature and become reflections of human ingenuity rather than reflections of the divine. Shorn of its theological underpinnings, we are now left with a system that ‘just happens’ to be the way it is.
As John Barrow concludes:
We see now how it is possible for a Universe that displays unending complexity and exquisite structure to be governed by a few simple laws - perhaps just one law - that are symmetrical and intelligible, laws that govern the most remarkable things in our Universe - populations of elementary "particles" that are everywhere perfectly identical. There are some who say that because we use our minds to appreciate the order and complexity of the Universe around us, there is nothing more to that order than what is imposed by the human mind. That is a serious misjudgment.
Were it true, then we would expect to find our greatest and most reliable understanding of the world in the everyday events for which millions of years of natural selection have sharpened our wits and prepared our senses. And when we look towards the outer space of galaxies and black holes, or into the inner space of quarks and electrons, we should expect to find few resonances between our minds and the ways of these worlds. Natural selection requires no understanding of quarks and black holes for our survival and multiplication.
And yet, we find these expectations turned upon their heads. The most precise and reliable knowledge we have about anything in the Universe is of events in a binary star system more than 3,000 light years from our planet and in the sub-atomic world of electrons and light rays, where we are accurate to better than nine decimal places. And curiously, our greatest uncertainties all relate to the local problems of understanding ourselves - human societies, human behaviour, and human minds - all the things that really matter for human survival. … . Our first attempts to grasp the laws of nature are often incomplete. So, in our religious conceptions of the Universe, we also use approximations and analogies to have some grasp of ultimate things. They are not the whole truth but this does not stop them being a part of the truth: a shadow that is cast in a limiting situation of some simplicity.
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