The Laws of Nature

This is another posting arising from an intellectually stimulating read: Michael Frayn’s The Human Touch, subtitled, Our Part in The Creation of the Universe. The short essay below is in response to just one chapter, The Laws of Nature. I have to say at the outset that Frayn is far more widely read than I am, and his discussion includes commentary and ruminations by various scientists and philosophers: Popper, Kuhn, Einstein, Planck, Bohr, Born, von Neumann, Feynman, Gell-Mann, Deutsch, Taylor, Prigogine and Cartwright, amongst others. A number of these I have not read at all, but I find it strange that he does not include Penrose (except for one passing reference in his notes) or Davies, who have written extensively on this subject, and have well known philosophical views.

I haven’t finished reading Frayn’s text (though I’ve read his extensive notes on the subject) so I may have more to say later, and the following was originally written in the form of a ‘letter to the author’, which I never sent.

The heart of Frayn’s dissertation on the ‘laws of nature’ seems to be the interaction between the human intellect and the natural world. There are 2 antithetical views, both of which involve mathematics, because, in physics at least, the ‘laws of nature’ can only be expressed in mathematics. We may give descriptions in plain language, creating man-made categories in our attempts, but without mathematics we would not be able to validly call them ‘laws’, whether they be fiction or otherwise.

The first of these antithetical views is that we have invented mathematical methods, which have evolved into, sometimes complex, sometimes simple, mathematical models that we can apply to numerous phenomena we observe, and, in many cases, find a near-perfect fit. The second view is that the laws already exist in nature, and mathematics is the only means by which they can be revealed. I tend to subscribe to the second view. I disagree philosophically with Einstein, who contended, quite reasonably, that 'the series of integers is obviously an invention of the human mind', but agree with him that there is an underlying order in the machinations of the universe. (In regard to Einstein's contention, I discuss this argument in detail in 2 other postings; but, even if we invent the numbers, the relationships between them we do not.)

We humans puzzle over facts like the planets maintaining their orbits for millions of years, or the self-organising properties of galaxies, or of life for that matter, or the predictability of the effects of light shone through slits. We look for patterns, so we are told, and therefore we project patterns onto the things we observe. But science has demonstrated that there are not only patterns in nature, but relationships between events that can be described in mathematics to unreasonable degrees of accuracy. My own view is that the mathematical relationships found in nature are not projected, it’s just that the deeper we look the more unfamiliar the relationships become.

It seems to me the laws, for want of a better word, exist in layers, so that, at different scales different ones dominate. It follows from this that we haven’t discovered them all, and possibly we never will, but it doesn’t mean that the ones we have discovered are therefore false or meaningless. I have had correspondence with philosophers of science who believe that one day we will find the one governing law or set of laws that will make all current laws obsolete, which means the current ones are false and meaningless, but history would suggest that this goal is as mythical as the original Holy Grail.

Everyone posits Einstein’s theories of relativity making Newton’s laws obsolete as the prime example of this process, yet the same set of ‘everyone’ uses Newton’s equations over Einstein’s for most purposes, because they are simpler and just as accurate for their requirements. Einstein made the point (according to Frayn’s reference, Abraham Pais) that Newton’s mechanics were based on ‘fictional principles’, yet gave the same results as his own theories for many phenomena. (Frayn quotes Pais in his belief that Einstein thought all theories were fictions.) I believe the main ‘fictional principle’ inherent in Newton's theory (for gravity at least) arises from the fact that there is no force experienced in gravity if you are in free fall; there is only a force when you are stopped from falling. This is arguably the most significant conceptual difference between Newton's and Einstein's theories, and appears to be one of the key motivations for Einstein seeking a different mathematical interpretation for gravity.

Einstein’s theories are an example of how the laws of nature are not what they appear to be at the scale we experience them, specifically in regard to gravity, space, time and mass. His equations supersede Newton’s, in all respects, because they more accurately describe the universe on cosmological and atomic scales, but they reduce to Newton’s equations when certain parameters become negligible.

On the other hand, quantum mechanics appears to be another set of laws altogether that lie behind the classical laws (including relativity) that only become apparent at atomic and sub-atomic scales. I would suggest, however, that this dissociation between the quantum and classical worlds is a result of a gap in our knowledge, as contended by Roger Penrose, rather than evidence that the ‘laws of nature’ are all fictions. Assuming that this gap can be resolved in the future, new laws expressed in new or different mathematical relationships would be revealed. It’s not axiomatic that these future discoveries will make our current knowledge obsolete or irrelevant, but, hopefully, less mystifying.

I would make the same prediction concerning our knowledge of evolution. In the same way that Darwin proposed a theory of evolution based on natural selection, without any knowledge of genes or DNA, future generations will make discoveries revealing secrets of DNA development which may change our view on evolution. I’m not talking about ‘Intelligent Design’, but discoveries that will prove ID a non sequitur; as ID is currently a symptom of our ignorance, not an aid to future discoveries as claimed by its proponents. (See my Nov.07 post: Is evolution fact? Is creationism myth?)

There are deep, fundamental, inexplicable principles involved when one examines natural phenomena. Not-so-obvious examples are the principle of least time in refraction (referenced in Frayn’s text; intuited by the 17th Century mathematician genius, Pierre de Fermat) and the principle of maximum relativistic time in gravity, expounded brilliantly by Richard Feynman in Six Not-So-Easy Pieces. These principles, I would contend, are not inventions, but discoveries, and they reveal an underlying natural schema that we could never have predicted through speculation alone. In fact, were it not for our powers of intellect and observation, in combination with a predilection for mathematics, we would not even know they exist.

Footnote: James Gleick in his biography of Feynman, GENIUS, gives the impression that these 2 phenomena could be different manifestations of the same underlying 'principle of least action' that Feynman even employed in his examination of quantum mechanics. Anyone who is familiar with both these phenomena will appreciate the connection - it's like the light or the particles choose their own path - as Gleick expounds quite eruditely, but without the equations.


Addendum 1: Since I published this post, I've read Feynman's lecture series that he gave in New Zealand in 1983 published under the title, QED, The Strange Theory of Light and Matter. In his first lecture, he gives a brilliant exposition (in plain English) on how light reflected by a mirror 'follows the least time path' can be explained by quantum mechanics. I need to add the caveat that no one understands quantum mechanics, a point that Feynman is at pains to make himself, right at the start of his lectures.

Addendum 2: I wrote a later post on 'least action' which is more erudite.