I recently attended a talk by Daniel Garber (Princeton University) on the topic of “God, Laws and the Order of Nature in the Scientific Revolution.” While Garber’s talk was mostly historical in nature, it raised some interesting points about why and how we talk about laws of nature at all.

And the connection was reinforced just a couple of days ago when I went to the New York Film Festival and saw a screening of “Particle Fever,” a documentary about the Higgs boson during which the concept of the fundamental (lawful, according to supporters of supersymmetry; random, according to people who favor the multiverse) architecture of the universe was the truly big question lurking in the background.

The point of departure of Garber’s talk was that the very concept of laws of nature is actually pretty recent, and it basically starts with Rene Descartes.

Indeed, both Galileo and Hobbes [1] — who were aware of Descartes’ work — were definitely unenthusiastic about the idea.

Descartes introduced the idea of law of nature in his Le Monde and in the Principles of Philosophy, explicitly using that term. The concept did have precursors, of course, for instance in the Stoics, but Descartes gave arguments in its favor (as opposed to simply assume it, as the Stoics did) and explored it in quasi-mathematical terms (which the Stoics certainly didn’t). One of Descartes’ examples was the principle of inertia, which was again taken up and elaborated upon by Galileo, and eventually Newton (becoming incorporated in the latter’s principles of general mechanics).

Descartes, however, was a figure perched in equilibrium between the old Scholastic view of the world and the soon ongoing scientific revolution, so it shouldn’t exactly be surprising that he used the classical theological doctrine that the world is kept going by a continuous action of God as grounding for his concept of laws of nature. According to Descartes, laws of nature are not chosen by God and then imposed on the world (contra Leibniz, for instance). Which, interestingly, means one cannot use the study of nature to derive conclusions about God’s plans (so much for natural theology). God, in a sense, becomes the efficient cause of all things, to use the Aristotelian classification of causes.

For Descartes, God doesn’t think of the regularities of nature in terms of laws, but that’s the way we conceptualize how God sustains the world from moment to moment. Descartes thought that the world was created in chaos, and it developed into its current structure by way of the laws of nature. This, by the way, includes the development of plants and animals, which could be reasonably interpreted as an early picture of evolution. The influence of the Greek atomists (via Lucretius’ poem, De Rerum Naturae, which had been recently rediscovered) on Descartes’ thinking should be obvious.

As I said above, Garber stressed that Galileo wasn’t too happy with the Cartesian picture. Galileo’s main concern was the behavior of bodies in motion (yes, yes, he was distracted for a couple of decades by telescopic observations and the issue of Copernicanism, but motion apparently truly was his main interest), particularly the issue of the best definition of accelerated motion, from which he derived his framework for a mathematical description of naturally falling bodies.

Galileo’s findings, however, cannot reasonably be considered examples of laws, because they were not meant to be sufficiently general by their author. For instance, Galileo was not sure that his description of motion on earth could generalize to motion as it occurs on other celestial bodies (though he did have a theory of how planets behaved with respect to the Sun). Indeed, we had to wait for Newton to get a complete theory of general mechanics. It is this partiality of Galileo’s account that in turn generated Descartes’ skepticism about the former’s theory of motion. Galileo’s work was just not general enough (i.e., universal) for Descartes’ taste.

What about Hobbes? Here too we don’t find either the term or the concept of law of nature. But we know that Hobbes was aware of Descartes’ ideas on the matter, so his avoidance of the term was certainly deliberate. (It is worth remembering that Hobbes very likely was an atheist, and certainly thought that God doesn’t play any role in a natural philosophical account of the world.)

Hobbes didn’t recognize the existence of any conservation principle, unlike Descartes. But again, Descartes' conservation of physical quantities was nothing like what we think of today, as it had a direct link to God, without whom there would be no reason for things not to change (presumably, at random, thus falling apart).

Hobbes was also a great admirer of Galileo, whom he considered the first physicist. In fact, Hobbes thought that everything reduces to motion of bodies, and he did think of motion in universal terms, though there is no reason to believe that he saw his statements about motion any differently from how Galileo saw his — i.e., not as expressing “laws.” Interestingly, Hobbes (unlike Descartes) didn’t see any crucial distinction between real physical bodies and geometrical idealizations: i.e., the regularities of motion for him were analogous to mathematical generalization. It therefore follows that universals in physics are analogous to universals in mathematics, and since mathematical statements for Hobbes are not laws of nature... (mathematical structural realism, anyone?)

Jumping to modern times, there is a serious question about whether physicists actually got rid of some of the unsavory implications of the concept of laws of nature that apparently left both Galileo and Hobbes somewhat cold. While I’m sure that physicists like Steven Weinberg would vehemently reject such teleological (if not downright theological) implications, philosopher Nancy Cartwright provocatively wrote that there is no sensible way to avoid the connection between laws and some kind of law maker, so that talk of law should be rejected in favor of a more Galileian (Garber would say) approach based on generalizable (but not necessarily exceptionless!) regularities. This criticism isn’t limited to philosophers, as it has been explicitly endorsed by physicist Lee Smolin, for instance. Indeed, discussions on the philosophy and conceptual science of natural laws have now generated a sizable technical literature.

Which brings me to the fundamental debate underlying the Particle Fever movie mentioned at the onset. To make a long (and complex) story short, before the Hadron Collider at CERN actually discovered the Higgs there were two rough predictions of how massive the new particle would be: either around 115 GeV (Giga electronVolts) or around 140 GeV. The difference is crucial, because supersymmetric theories predict the lower amount, while versions of the multiverse theory hover around the higher number. Since the Higgs is the particle that “gives” mass to all other particles, its characteristics are crucial to explain why the universe is the way it is.

Well, what do you know? The current best estimate from the Hadron Collider experiments (which will resume in a bit more than a year at higher energy levels) is around 125 GeV, a bit too high for supersymmetry, a bit too low for the multiverse. (And, moreover, right in the instability range for the Higgs itself: and if the glue that holds together the universe is unstable, it may one day go. And if it goes, well...)

How does this fit with the issue of natural laws (or unexceptional regularities, or whatever you want to call them)? A big deal in Particle Fever is made of the fact that if the Higgs is confirmed to be outside of the reasonable range of supersymmetric theories, thus providing “strong circumstantial evidence” (though not proof) for the multiverse, to put it as one of the interviewed physicists did, then this would in some sense be “the end of physics” (as we know it). Why? Because if the multiverse scenario is true then there is no answer to why the “laws” of our universe (and its physical constants) are the way they are: it’s just one of an infinite number of possible random outcomes. Which would mean that, in a deep sense, there are no “laws of nature,” just regularities that happen to hold in our particular universe.

If, however, the Hadron data will eventually bring back the Higgs firmly into supersymmetric territory, then we will be able to pursue further questions about why the universe is structured the way it is and in no other way, thereby reopening the issue of what it means to have a world in which there are “laws” that admit of no exception (i.e., the question of where such laws come from). Nobody’s thinking of a Cartesian lawgiver, of course, but in an interesting sense supersymmetry vs multiverse rehashes the Descartes vs. Galileo debate over whether there are laws of nature or just regularities which admit of exceptions (albeit with the “exceptions” now taking place in other parts of the multiverse).

Any actual physicists out there who would like to chime in on this?