Of course, laws of nature are very useful, and we have in fact been able to discover good candidates for them. But to believe a law is useful and reliable is not the same thing as to believe it is eternally true. We could just as easily believe there is nothing but an infinite succession of approximate laws. Or that laws are generalisations about nature that are not unchanging, but change so slowly that until now we have imagined them as eternal.
These are disturbing thoughts for a theoretical physicist like myself. I chose to go into science because the search for eternal, transcendent laws of nature seemed a lofty goal. However, the possibility that laws evolve in time is one that recent developments in theoretical and experimental physics have forced me, and others, to consider.
The biggest reason to consider that the laws of nature might evolve is the discovery that the universe itself is evolving. When we believed that the universe was eternal it made more sense to believe that the laws that governed it were also eternal. But the evidence we have now is that the universe - or at least the part of it we observe - has been around for only a few billion years.
We know that the universe has been expanding for about 14 billion years and that as we go back in time it gets hotter and denser. We have good evidence that there was a moment when the cosmos was as hot as the centre of a star. If we use the laws that we know apply to space-time and matter today, we can deduce that a few minutes earlier the universe must have been infinitely dense and hot. Many cosmologists take this moment as the birth of the universe and indeed as the birth of space and time. Before this big bang there was nothing, not even time.
Why these laws?
So what could it mean to say that a universe only 14 billion years old is governed by laws that are eternally true? What were the laws doing before time and space? How did the universe know, at that moment of beginning, what laws to follow?
Perhaps the solution to this is that the big bang was not the first instant of time. However, this raises a new question, which has been championed by the great theoretical physicist John Wheeler. Even if we believe the universe evolved from something that existed before the big bang, we have no reason to believe the laws of that previous universe were the same as those we observe in our universe. Might the laws have changed when our universe, or region of the universe, was created?
This question came to the fore in 1973, when physicists first developed a theory of elementary particle physics called the standard model. This theory has successfully accounted for every experiment in particle physics before and since that time, apart from those that involve gravity. It only required a small modification to incorporate the later discovery that neutrinos have mass. As for gravity, all experiments support the general theory of relativity, which Einstein published in 1915. There may be further laws to discover, to do with the unification of gravity with quantum theory and with the other forces of nature. But in a certain sense, we have for the first time in history a set of laws sufficient to explain the result of every experiment that has ever been done.
As a result, in the past three decades the attention of physicists has shifted from seeking to know the laws of nature to a new question: why these laws? Why do these laws, and not others, hold in our universe?
Confronting this question while working on string theory in the 1980s, a few of us began to wonder whether the laws might have changed at the big bang, just as Wheeler had suggested. It was obvious that we could make a connection to biology. I wondered whether there might be an evolutionary mechanism that would allow us to answer the question of "why these laws?" in the same way that biology answers questions like "why these species?". Perhaps the mechanism that makes laws evolve also picks out certain laws and makes them more probable than others. I found such a mechanism, modelled on natural selection, which I called cosmological natural selection.
This is possible because string theory is actually a collection of theories: it has a vast number of distinct versions, each of which gives rise to different collections of elementary particles and forces. We can think of the different versions of string theory as analogous to the different phases of water - ice, liquid and steam. When the universe is squeezed down to such tremendous densities and temperatures that the quantum properties of space-time become important, a phase transition can take place - like water turning to steam - leading from one version of the theory to another.
The many different phases of string theory can also be seen as analogous to a variety of species governed by different DNA sequences. They can be imagined as making up a vast space, which I called the "landscape", to bring out the analogy to a "fitness landscape" in biology that represents all possible ways genes can be arranged.
Cosmological natural selection makes a few predictions that could easily be falsified, and while it is too soon to claim strong evidence for it, those predictions have held up (New Scientist, 24 May 1997, p 38). At the very least, it opened my eyes to the possibility that a theory in which the laws changed in time could still make testable predictions.
It turns out that I had been beaten to the punch: some philosophers had confronted these issues over a century ago. In 1891 the philosopher Charles Pierce wrote that it was hardly justifiable to suppose that universal laws of nature have no reason for their special form. "The only possible way of accounting for the laws of nature, and for uniformity in general, is to suppose them results of evolution," he added.
Pierce went much further than I have done, asserting that the question "Why these laws?" has to be answered by a cosmological scenario analogous to evolution. But was he right?
Let us start with an obvious objection: if laws evolve, what governs how they evolve? Does there not have to be some deeper law that guides the evolution of the laws? For example, when water turns into ice, more general laws continue to hold and govern how this phase transition happens - the laws of atomic physics. So perhaps, even if a law turns out to evolve in time, there is always a deeper, unchanging law behind that evolution.
Shapes of things to come
Another example concerns the geometry of space. We used to think that space always followed the perfectly flat Euclidean geometry that we all learn in high school. This was considered one of the laws of nature, but Einstein's general theory of relativity asserts that this is wrong. The geometry of space can be anything it wants to be: any of an infinite number of curved geometries is possible. So what picks out the geometry we see?
General relativity asserts that the geometry of space evolves in the course of time according to some deeper law. Today's geometry is what it is because it evolved from a different geometry in the past, following that definite law.
However, there is a big problem with this kind of explanation, which has to do with the fact that the laws that govern the evolution of geometry are deterministic. They share this feature with most laws studied in physics, including Newton's laws and quantum mechanics. Consider Newton's law of motion for an object. If we know where the object is now and how it is moving, and we know the laws that govern the forces it encounters, we can predict where it will be and has been for all time, past as well as future. General relativity is the same. If we know the geometry of space at a particular time, and how it is changing, we can predict the whole history of space-time. To apply these deterministic laws, however, we have to give a description of the system at one point in time. This is called the initial condition. If we do not specify an initial condition, the laws cannot describe anything.
This is why Einstein's equations do not fully explain why the geometry of space is what it is. They require an initial condition -the geometry at an earlier time. This brings us back to the dilemma about the big bang. Either the universe had no beginning, in which case the chain of causes goes further into the past, before the big bang; or the big bang was the beginning, and we require some explanation as to why it started and with what geometry.
So we have arrived at a conundrum. It appears that if laws evolve, other laws are required to guide their evolution. But then, the evolution of a law is just like the evolution of any other system under a deterministic law. We cannot explain why something is true in the present without knowing its initial state. Applied to laws, this means we cannot explain what the laws are now if we do not specify what the laws were in the past. So the idea of laws evolving by following a deeper rule does not seem to lead to an explanation of "why these laws?".
To avoid this we need an evolutionary mechanism that will allow us to deduce features of the present without having to know the past in detail. This is where Pierce's statement, which appears to invoke biological evolution, comes into its own.
In biology, many features of living organisms can be explained by natural selection, even if one doesn't know details about the past. As the process is partly random, we cannot predict exactly what mix of species will evolve in a given ecosystem, but we can predict that the species that survive will be fitter than those that don't. This is, I believe, why Pierce insisted that any explanation of "why these laws?" involves evolution. And using this kind of logic, cosmological natural selection makes some predictions without detailed information about previous stages of the universe.
But even this is unsatisfactory: it doesn't address the question of how a law that guides the evolution of matter in time could also change in time. For that, we have to examine the way we think about time.
There are big problems with time, even before we start thinking about the evolution of laws of nature. Nowhere is this more apparent than in the field of quantum gravity, which attempts to pull quantum theory and general relativity together into one consistent framework. This is because the two theories each use a different notion of time. In quantum theory, time is defined by a clock sitting outside the system being modelled. In general relativity, time is measured by a clock that is part of the universe that the theory describes. Many of the successes and failures of different approaches to quantum gravity rest on how they reconcile this conflict between time as an external parameter versus time as a physical property of the universe.
However these questions are eventually resolved, there are still deeper issues with time. These arise in any theory in which the laws are taken as being eternal. To illustrate this, we can take a simple example, such as Newton's description of a system of particles. To formulate the theory we invent a mathematical space, consisting of all the positions that all the particles might have. Each point in the space is a possible configuration of the system of particles, so the whole space is called the configuration space. As the system evolves over time, it traces out a curve in configuration space called a history. The laws of physics then pick out which histories are possible and which are not.
The problem with this description is that time has disappeared. The system is represented not by its state at a moment of time but by a history taking it through all time. This description of reality seems timeless. What has disappeared from it is any sense of the present moment, which divides our experience of the flow of time into past, present and future. This problem became particularly acute when it emerged in Einstein's theory of general relativity. Solving the theory gives a four-dimensional space-time history and no indication of "now".
Some, looking at this picture, have been tempted to say that reality is the whole timeless history and that any sense we have of a present moment is some kind of illusion. Even if we don't believe this, the fact that one could believe it means that there is nothing in this description of nature that corresponds to our common-sense experience of past, present and future. This is called the problem of transience. The sense of the universe unfolding or becoming in time, of "now", has no representation in general relativity. But in truth the problem was always there in Newton's physics and it is there in any theory in which some part of nature is described by a state that evolves deterministically in time, governed by a law that dictates change, but never changes.
The illusion of now
The philosopher Roberto Unger of Harvard University calls this the "poisoned gift of mathematics to physics". Many believe that mathematics represents truth in terms of timeless relationships, based on logic. It allows us to formulate physical laws precisely: this is the gift. By doing so, however, mathematics represents paths in configuration space unfolding in time by logic, and this logic exists outside of time. The poison in the gift is the disappearance of any notion of the present or of becoming.
Physicists and their predecessors have been eliminating time like this since the days of Descartes and Galileo at least. But is it the wrong thing to do? Is there a way to represent change through time in a way that represents our sense of becoming, or of time unfolding?
I don't know the answer, but I suspect this question is connected to that of whether laws can evolve in time. One can only draw the curve representing a history in time by assuming that the laws which govern how the history evolves never change. Without a fixed, unchanging law, one could not draw the curve.
Here is the question that keeps me awake these days: is there a way to represent the laws of physics mathematically that retains the notions of the present moment and the continual unfolding of time? And would this allow us - or even require us - to formulate laws that also evolve in time?
Again, I don't know the answer, but I know of a few hints. One comes from theoretical biology. The configuration space for an evolutionary theorist is vast, consisting of all the possible sequences of DNA. At present, there is a particular collection representing all the species that exist. Evolution will produce new ones, while others will disappear. The interesting thing is that natural selection operates in such a way that biologists have little use for the entire configuration space. Instead, they need study only a much smaller space, which is those collections of genes that could be reached from the present one by a few evolutionary steps. The theoretical biologist Stuart Kauffman of the University of Calgary in Alberta, Canada, calls this the "adjacent possible".
This scheme allows laws to change. Consider the laws that govern sexual selection. They do not make sense for any old biosphere, as they only come into play when there are creatures with two sexes. So in evolutionary theory there is no need for eternal laws, and it makes sense to speak of a law coming into existence at some time to govern possibilities that did not exist before. Furthermore, there is such a vast array of possible mechanisms of natural selection that it would not make any sense to list them all and treat them as timeless. Better to think of laws coming into existence as the new creatures that evolve in each step require.
Of course, one might reply that natural selection itself never changes. But natural selection is a fact of logic, not a contingent law of nature. Every real law in biology depends on some aspect of the creatures that exist at a given time, which means the laws are also time-bound.
It is not impossible to achieve time-bound laws in physics. There are logicians who have proposed alternative systems of logic that incorporate a notion of time unfolding. In these logics, what is true and false is assigned for a particular moment, not for all time. For a given moment some propositions are true, others false, but there remains an infinite list of propositions that are yet to become either true or false. Once a proposition is true or false, it remains so, but at each moment new propositions become decided. These are called intuitionalist logics and they underlie a branch of mathematics called topos theory.
Some of my colleagues have studied these logics as a model for physics. Fotini Markopoulou of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, has shown that aspects of space-time geometry can be described in terms of these logics. Chris Isham of Imperial College London and others propose to reformulate physics completely in terms of them.
It is interesting that some physicists now propose that the universe is some kind of computer, because similar questions are being asked in computer science. In the standard architecture all computers now use, invented by the mathematician John von Neumann, the operating system never changes. It governs the flow of information through a computer just as an eternal law of nature is thought to guide physics. But some visionary computer scientists such as Jaron Lanier wonder whether there could be other kinds of architectures and operating systems that themselves evolve in time.
Looking at biology, it seems there are advantages to what are, essentially, time-bound laws. Evolving laws might make computer systems similarly robust and less likely to do what the laws of natural selection, it seems, never do: crash. The universe, too, seems to function rather well, operating without glitches and fatal errors. Perhaps that's because natural selection is hard at work in the laws of nature.
From issue 2570 of New Scientist magazine, 21 September 2006, page 30-35