What are “laws of physics”?

In Sam Harris’s interview with Lawrence Krauss, regarding Krauss’s new book “A Universe from Nothing” (I haven’t read the book yet, it’s on order), Sam asks:

“You have described three gradations of nothing — empty space, the absence of space, and the absence of physical laws. […] Might it not be easier to think about the laws of physics as having always existed?”

Thinking about physical laws like this, as “entities” that can have existence in their own right, is widespread, but in my opinion fundamentally misguided. It seems to regard “laws of physics” as an underpinning “structure” that directs and controls physical matter. If this were true then it would make sense to ask whether “physical laws” have always existed. But if physical laws “exist” in this sense then what are they made of? How do they interact with matter? How do they effect their actions?

That train of reasoning is ill-founded. Physical laws are not entities with existence in their own right, they are simply descriptions of how matter behaves. The “laws” governing a fundamental particle are simply a summary of the nature of that particle and its behaviour when interacting with other particles. Oxford Dictionaries defines the scientific use of “law” as meaning:

Law: (3) a statement of fact, deduced from observation, to the effect that a particular natural or scientific phenomenon always occurs if certain conditions are present.

You can no more have “laws of physics” existing independently of matter than you can have a “description of X” independently of “X”. Thus if matter exists then you can have a description of it (= “laws”). But if there were no matter there could not be a description (and thus one could not have pre-existing “laws”).

To illustrate this let’s take a fundamental physical law, namely conservation of momentum, the fact that summed over all particles the total momentum never changes. Since a force can produce a change in momentum (Newton’s Second Law), this requires that every force be matched by an equal and opposite force (Newton’s Third Law), such that overall forces cancel and momentum stays constant.

The conservation of momentum derives from an even more fundamental fact, that the behaviour of particles is the same everywhere, so that if a particle’s physical location changes it won’t act any differently (or as usually stated “… the laws of physics are the same everywhere”; this result follows from Noether’s Theorem, a deeply profound insight by the great mathematician Emmy Noether).

Thus the conservation of momentum and Newton’s Laws are a consequence of the behaviour of particles (the fact that their interactions are the same everywhere). It is not the case that some “physical-law-entity” is carefully tabulating all the momentum changes and prodding particles to ensure the right outcome. Similarly, conservation of energy results from the fact that particles behave the same at all times.

So if “laws” are descriptions of nature, when do scientists decide to call something a “law”? In common parlance, of course, “law” means “proven correct” whereas “theory” means “unproven hypothesis”, and this can lead to questions such as “by what process are theories upgraded to laws?”. But this is not how the words are used by scientists. Theory simply means “explanation”, or, less concisely, “set of coherent and interlocking ideas which explain some aspect of nature”.

The term “law” is used for an explanation that can be summed up in one sentence or one equation. Thus a theory might incorporate several laws (for example the kinetic theory of gases incorporates the perfect gas law) — though scientists rarely worry too much about mere nomenclature, and a “law” might equally be known as an “equation” or a “theorem” (for example the Shannon–Hartley theorem, the Hartley law, and the Boltzmann equation are all parts of information theory).

Further, a physical “law” need not actually be true, so long as it is true enough to be useful. For example Newton’s Law of Gravity is now known to be incorrect (superseded by General Relativity) but is nearly enough true when gravitational fields are weak that it is very useful (so when NASA sends a probe to land on a comet they use Newtonian gravity, rather than the hard-to-work-with relativistic equations).

Similarly, the Perfect Gas Law is not fully true, but is very useful and easy to use, and works well enough so long as the spacing of gas particles is large compared to their size (the van der Waal’s gas equation attempts to do better, taking into account the size of the gas particles, but is still only an approximation).

Even some of the most hallowed physical laws are only approximations, or only true in a probabilistic sense. For example a well-known quote from Sir Arthur Eddington says:

“The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations, then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”

And yet the Second Law of Thermodynamics is true only in a probabilistic sense, and is violated all the time (though admittedly only in small ways for short periods of time). The Second Law says that a closed system will not spontaneously change to a state of greater order (lower entropy).

So, if you have a box containing 100 “red” gas particles and 100 “blue” gas particles, randomly distributed, they don’t spontaneously line themselves up with all the reds on the left and all the blues on the right. But, if you start out with 50 of each colour on each side, then you will get chance fluctuations to 48 of one colour on one side and 52 on the other, and that is a spontaneous change to lower entropy (as can easily be demonstrated by using the statistical-mechanics formula for entropy).

Small-scale, short-term violations of the Second Law occur all the time, but the larger the scale and the longer-lasting the effect, the more improbable violations become, and once one gets to the macroscopic world, dealing with an Avogadro’s number of particles at a time, the chances of a violation are effectively zero.

So, physical laws are descriptions of the behaviour of the natural world. They are not an abstract “substrate”, existing independently of physical material, laying down requirements that the matter must obey. They are consequences, summaries, of the behaviour of particles, not precursors. Is this distinction mere semantics? To an extent, yes, but thinking of the laws as having an independent existence can lead one horribly wrong.

For example, Edward Feser is a blogger with a religious and philosophical perspective, who is notable for “robust” commentary on the more atheistic scientists. Feser quotes physicist Ethan Siegel saying:

“Arguments for God as cause of the universe rest on the assumption that something can’t come from nothing. But given the laws of physics, it turns out that something can come from nothing.”

And he also quotes Stephen Hawking and Leonard Mlodinow saying:

“Because there is a law like gravity, the universe can and will create itself from nothing.”

I would interpret Siegel’s remark as meaning: “Because of the nature and behaviour of particles, they don’t need to come from any pre-existing cause, they can come into existence, uncaused, from nothing”. Regardless of whether that claim is true (and we don’t fully know yet), Siegel’s remark is not pointing to some pre-existing “laws” as an entity that creates the matter. That would be to misunderstand what physical laws are. Yet Feser does just that saying:

“Is this guy serious? The laws of physics aren’t “nothing”. Ergo, this isn’t even a prima facie counterexample to the principle that ex nihilo, nihil fit. That’s just blindingly obvious. Is this guy serious? […] as a philosopher, [Siegel is] utterly incompetent, incapable of seeing the most blatant of fallacies staring him square in the face. “

But it is only a fallacy if you misunderstand what physical laws are. The behaviour of particles is such that they don’t necessarily need a cause in order to come into existence (at least, no-one has demonstrated that they do, either as a matter of theoretical necessity, nor as a matter of empirical fact). That might run counter to human intuition, but then so does much of modern science that has turned out to be correct.

As far as we can see, particles do indeed appear to come into existence without preceding cause. That is observed routinely. For all the scorn of Edward Feser, this is genuine science (and genuine philosophy) and should be taken seriously. At which point, I’ll await Krauss’s book.