Building objects from relations: physics and the monad

Quanta Magazine recently published an interview with physicist and author Lee Smolin. Smolin talked about his most recent book, Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum, and the influence that Gottfried Leibniz, has had on the perspective that Smolin most recently adopted. Seventeenth century polymath, Gottfried Wilhelm Leibniz, known for having developed a system of infinitesimal calculus, is certainly a major contributor to the kind of thinking that has produced the modern sciences. And yet the rigor of his thought, and his careful examination of mechanistic theories, led him to deduce a metaphysical underpinning of reality.

The mathematical notions of infinity and continuity guide a great number of Leibniz’s observations. But Smolin makes a particular reference to Leibniz’s metaphysical account of the whole of reality, his Monadology. It would seem unlikely that a modern physicist would choose this path, but I would argue only because the path is under appreciated. Here’s a little of how the reasoning goes:

As Leibniz saw it, there are no discontinuous changes in nature. The observed absence of abrupt change suggested to him that all matter, regardless of how small, had some elasticity. Since elasticity requires parts, a truly singular thing, with no parts, would not be elastic. That would mean that all material objects, no matter how small, would have to be compounds or amalgams of some sort. If not, they could produce abrupt change. Now anything simple and indivisible, is necessarily without extension, or dimension, like a mathematical point. In other words, it wouldn’t take up any space. Leibniz was convinced that this non-material fundamental substance had to exist. If it didn’t, then everything would be an aggregate of substances. And every aggregate would also be an aggregate, allowing for the endless divisibility of everything, making it impossible to identify anything. According to Leibniz, the universe of extended matter is a consequence of the interaction of simple non-material substances known as monads, or simply the relations among these monads.

But it is not the non-material nature of a monad that Smolin keys on. It is more Leibniz’s conviction that that there is no fundamental space within which the elements of the universe exist, together with the fact that it is relations among the actions of fundamental unities that produce the universe we experience. Here’s what Smolin says:

I first read Leibniz at the instigation of Julian Barbour, when I was just out of graduate school. First I read the correspondence between Leibniz and Samuel Clarke, who was a follower of Newton, in which Leibniz criticized Newton’s notion of absolute space and absolute time and argued that observables in physics should be relational. They should describe the relations of one system with another, resulting from their interaction. Later I read the Monadology. I read it as a sketch for how to make a background- independent theory of physics. I do look at my copy from time to time. There is a beautiful quote in there, where Leibniz says, “Just as the same city viewed from different directions appears entirely different … there are, as it were, just as many different universes, which are, nevertheless, only perspectives on a single one, corresponding to the different points of view of each monad.” That, to me, evokes why these ideas are very suitable, not just in physics but for a whole range of things from social policy and postmodernism to art to what it feels like to be an individual in a diverse society. But that’s another discussion! (Emphasis added)

The key seems to be in what the interviewer refers to as Smolin’s slogan: “The first principle of cosmology must be: There is nothing outside the universe.” Smolin agrees with Leibniz that space, rather than being some thing within which bodies are located and move, it is a system of relations holding between things or, in his terms, ‘an order of situations.’ Space is created by the arrangement of matter, as the family tree is created by the arrangement of ones ancestors (a comparison Leibniz, himself, made). Space comes into existence only when the coexistent parts of the universe come into existence. It seems that Smolin also finds value in Leibniz’s portrayal of the individual monad as something that represents the universe from one of all possible points of view.

Leibniz described monads as complete in the sense that they cannot be changed by anything outside of themselves nor can they influence each other. It is an inner, pre-established solidarity that defines their relationship to each other. Their completeness requires, however, that they hold within themselves, perhaps as potentialities, all of the properties they will exhibit in the future, as well as some trace of all of the properties that they exhibited in the past. This brings timelessness to the fundamental level of our reality, to which Leibniz also attributes a preexisting harmony. The monad’s singularity also requires that they each, somehow, mirror or reflect the entire universe and every other monad.

It may not be the nature of the monad that has Smolin’s attention. But he has chosen to work on a theory about processes rather than things, the “causal relations among things that happen, not the inherent properties of things that are.”

The fundamental ingredient is what we call an “event.” Events are things that happen at a single place and time; at each event there’s some momentum, energy, charge or other various physical quantity that’s measurable. The event has relations with the rest of the universe, and that set of relations constitutes its “view” of the universe. Rather than describing an isolated system in terms of things that are measured from the outside, we’re taking the universe as constituted of relations among events. The idea is to try to reformulate physics in terms of these views from the inside, what it looks like from inside the universe.

There are so many reasons that I am intrigued by Smolin’s choice. It’s beautifully imaginative. But I’ve always been reassured by Leibniz’s view of things – an unexpected amalgam of rigorous formal reasoning, the conceptual possibilities of mathematics, what was known in physics, and the way that God was understood – all brought to bear in an effort to comprehend everything. Leibniz characterizes space and time as beings of reason; they are abstractions, or idealizations (like the geometric continuum) and, as such, are found to be continuous, homogenous, and infinitely divisible. Leibniz was intent on avoiding the blunder of a mind/body duality. His monadology is a unique synthesis of things that sound like biological notions, along with physical observations, and mathematical abstractions. Smolin’s choice to explore Leibniz’s map of the world with the observations of modern physics sounds very promising.