Where do the laws of Nature come from?

Einstein famously said that “The most incomprehensible thing about the world is that it is comprehensible.” [1] And that very discovery, that we inhabit a universe governed by unbreakable patterns or ‘laws’ is a triumph of the scientific enterprise. Unlike the laws of Australia or America, the laws of physics appear to be descriptions rather than rules; in such a light, what would it mean to say that nature “obeys” or follows the “laws” that we have written down in our textbooks?

This brings us to the ontological/metaphysical status of these ‘laws’. Since humans are pattern seekers who cannot help but anthropomorphise their surroundings, the question arises as to whether these principles are actually ‘written into’ the structure of reality, have an objective existence of their own (Platonism) or are simply human inventions/generalisations. To paraphrase Stephen Hawking, what is it that breathes fire into the Equations? [2] Where do the laws of physics “come from”?

The concept of a ‘law’ owes its origins to geometry and theology. In geometry, laws describe the dynamics of bodies (like Euclid’s axioms and postulates) and it was God who employed them to govern their motions. However, as a naturalistic understanding of the world progressed, the role of God in governing the universe via such laws was largely abandoned (or made redundant). Nevertheless, this underlying metaphor of “governance” remained.

Broadly speaking, there are two competing metaphysical accounts of laws of physics; the former is a prescriptive view while the latter is descriptive:

1. The Governing View: the laws of physics are an intrinsic part of reality that govern and explain the evolution of physical systems. (Armstrong, Maudlin, Ellis, Vilenkin, Krauss)

2. The Summarising View: the laws of physics are certain theorems of the scientifically best systematic summary of the motions of particles, fields, etc. throughout space/time (Mill, Ramsey, Lewis, Loewer, Carroll). Interestingly this view also presupposes a 4D block universe view, hence the laws never "began to exist" and do not need to be "put in" or created as an initial condition.

Now that we have a metaphysical framework for understanding what the laws of Nature are/where they “come from” (namely the BSA approach), a further query arises: why do the laws of physics take the form they do? For example, why do opposite charges attract, while like charges repel? Why is there an inverse square law rather than an inverse cube law? And so on…

The answer is surprisingly simple: symmetry.

As Sean Carroll notes [4]

The dynamical laws of nature at the microscopic level (including general relativity and the Standard Model of particle physics) are tightly constrained in the form that they may take, largely by symmetry principles such as gauge invariance and Lorentz invariance. The specific values of the numerical parameters of these theories are in principle arbitrary, although on naturalness grounds we would expect mass/energy scales to be roughly comparable to each other. [emphasis added]

To be continued…