Laws of nature as generating principles
Philosophical columns, part first

For a long time, the problem of time-asymmetry has haunted the philosophy of physics, and it seems to be no nearer to solution now than when it was first discovered. Everywhere around us we experience processes which happen only in one of the directions of time, and never in the other. A cup of tea cools down in the cold room, marginally raising the temperature of its surroundings; never does the room cool to heat up the cup of tea. We drop the cup, and it shatters into fragments; no matter how patiently we wait, the shards will not ever jump together to restore the broken whole. We decide to make a cup of tea, then do it, then afterwards remember having done it - but this order never happens in the reversed time direction. Causation, we believe, is unidirectional: the present is caused by the past and causes the future - and never the other way around. There can be no doubt about it: our world is time-asymmetric.

And yet, all the fundamental dynamical laws of physics appear to be time-symmetric. The laws of classical mechanics, the Newtonian theory that describes the movement of rigid bodies, were time-symmetric. If one changes the time t to -t in all of its formulae, one once again has the laws of classical mechanics. This means that if we see a movie of a classical mechanical process, there is no way for us to tell whether the movie is being played forwards or backwards. Classical mechanics is time-symmetric, and can never of itself give rise to the asymmetries which pervade our world. Classical electrodynamics is also time-symmetric, and so are the theories of relativity, quantum mechanics, and indeed all the fundamental laws we know. The time-asymmetric physical laws we have, such as the second law of thermodynamics, which predicts that a warm cup in a cool room will cool down and not heat up, are not a fundamental dynamical laws. They do not describe the movement or interactions of particles, but only the large-scale effects of these underlying processes. Therefore, they should follow from the more fundamental equations which describe the microscopic processes in the world - but they evidently do not.

We are thus left with a paradox: empirically, our world is time-asymmetric. But the laws of nature are time-asymmetric. How can this time-asymmetry exist? There are three broad strategies that can be chosen to solve this problem. The first consists of saying that although we have not yet found time-asymmetric fundamental laws of nature, they nevertheless exist. Although immune to refutation, this road is unappealing as walking along it simply amounts to closing our eyes to a very interesting paradox in our present state of knowledge. The second strategy is to claim that laws of nature cannot furnish us with an adequate description of physical reality. Such a view would have to postulate a radically different kind of principle which together with the laws of nature would yield the empirical world, and which would also time-asymmetric. One obvious candidate for such a principle would be some aspect of consciousness: by taking the mental asymmetries of anticipation and remembrance as primitive, and the relation between the mental observer and the world an sich as constitutive of the empirical world, we can explain away the apparent paradox. The time-asymmetry of the empirical world is compatible with the time-symmetry of the laws of nature, because time-asymmetry enters the empirical world through the intervention of the mental. This second approach may well be able to solve the problem, but I here wish to explore the possibility that a simpler strategy, which will perhaps be more readily accepted by philosophers in the analytic tradition, may also offer a solution.

The third approach to the problem of time-asymmetry is by postulating a difference between the initial condition of the universe and its final condition. If the initial condition is assigned a very low entropy, and the final condition a very high one, the time-asymmetry of the processes in the world may follow. There can be disagreement about the exact formulation of the initial and final conditions; 'low entropy' and 'high entropy' might not be very good measures, and perhaps ought to be replaced by something like 'containing no correlations' and 'containing a vast number of correlations'. But whatever the formulation finally chosen, one problem remains: why does this asymmetry between the initial and the final condition of the universe exist? The laws of nature, understood as universal generalisations about the empirical world, cannot explain such an asymmetry; but what else can? Only a time-asymmetric principle could explain the asymmetry between the initial and the final condition of the world. Now, one might claim that this asymmetry is simply a brute fact incapable of being explained any further. But then we have once again closed our eyes to the paradox, for saying that a host of processes take place only in one time-direction appears to be the same as saying that there is a related difference between the Universe's initial and its final state.

Suppose then that the initial state of the Universe is one 'without correlations', where all the matter is more or less randomly strewn about, and the final state is one 'rife with correlations'. How can this difference be explained? By appealing to two ideas: an application of Leibniz' "Principle of Sufficient Reason" and the 'presentist' conception of time. The latter is the idea that time does not consist of moments all of which are equally real, but that there is a 'moving present' which is the only thing that is truly real. The past has been, and can no longer be influenced; the future has not yet come to be, and will be influenced by what happens in the present. Thus, there is a time-asymmetry in the presentist conception of time: the present moves from the past towards the future. But that means that at some point, only the initial state of the universe was real, and all the rest had not yet come to be. The state of this initial time, then, has to be determined independently of any of the other states of the universe - and this is where the Principle of Sufficient Reason can be applied. If there is no reason for any correlations to exist, no reason for any structures to exist in the world - well, then the only feasible ordering of the Universe's matter is random, correlationless.

To recapitulate, if we adopt the presentist conception of time, the initial state of the universe is different from all the others: it is the only one which is not influenced by any other states. Therefore, it is the only one for which there is no feasible reason to be ordered in one way rather than another - which makes is intuitive to believe that it had to be ordered randomly, correlationless. As the present moves (but beware of this analogy!), the laws of nature tell us how the state of the universe changes, and we can show that from a correlationless, random state a non-random state full of correlations is overwhelmingly likely to evolve. The time-asymmetry of the world can then be derived from these three assumptions: our current laws of nature, the metaphysical position known as 'presentism', and a weak version of the Principle of Sufficient Reason. I believe this option to be philosophically appealing, especially given my earlier defence of presentism.

In this theory, laws of nature would no longer be best characterised as universal generalisations of facts about the empirical world, nor even as counterfactual-supporting generalisations. Laws of nature can now best be seen as descriptions of the generation of new states of the universe from old ones. To use a dangerous analogy: the laws of nature describe the effects of the motion of that most special of all moments, the present. Once seen as such 'generating principles', the laws of nature are no longer time-asymmetric, for the very concept of 'law of nature' becomes time-asymmetric. Thus, by adopting a new metaphysical view of time and accordingly changing our understanding of laws of nature, we can solve one of the most vexing problems in the philosophy of physics. At least that ought to count as a point in its favour.


Suggested reading:

• Albert, David: Time and Chance, Harvard University Press (2001)
• Gijsbers, Victor: Two modes of temporal discourse, online (2003)
• Horwich, Paul: Asymmetries in time: problems in the philosophy of science, MIT Press (1987)
• Reichenbach, Hans: The direction of time, University of California Press (1956)

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