The profound ambiguity of the force that has held science in check for centuries

“The central problem of philosophy,” writes Isaac Newton in the “Principia Mathematica,” “seems to be the discovery of the forces of nature.” Philosophy and nature: if there is one concept that links the inanimate world – the one studied by physics – with the spiritual world of philosophy, it is that of force. Force is the agent that moves objects, making the physical universe perceptible, but it is also the expression of animal or human will. It is what enables elementary particles to interact with one another, creating stable structures (atoms, molecules), but it is also the glue that holds societies together: the State is the custodian of the force that governs the people, and conversely, the people ultimately hold the power to determine their own destiny, through the ballot box or revolution. Force is not merely that which acts blindly, but also, both in physics and in the realm of thought, the agent that creates structure out of chaos. There is a further, more subtle, point of contact between physics and philosophy linked to the concept of force: namely, its profound ambiguity, which has hampered scientific debate for centuries. If force is what acts upon ‘matter’ (by which I mean the object of the action, be it physical matter or members of a human society), what acts upon force itself? Or rather: what determines force? Is it itself matter, or is there a transcendent agent, a spirit of time or space?

Physicists’ responses have been mixed. Descartes envisaged the force of gravity as vortices in space and, like Leibniz, rejected any action at a distance. Newton, much to the chagrin of his detractors, preferred to steer clear of the issue: his famous ‘hypotheses non fingo’, ‘I do not hypothesise’ regarding the ultimate origin of gravity. Despite various attempts to theorise the gravitational or electromagnetic force in an atomistic manner, as Lucretius had proposed in "De rerum natura", right up until the dawn of the twentieth century, for most scientists force and matter were rigidly separate, yet mysteriously connected. Matter consists of indivisible, eternal, point-like atoms. Force is a continuous, variable entity, diffused throughout space and somehow associated with it. Yet at the same time, force arises from matter: every fragment of matter is subject to the gravitational force, but is also its source. No matter is immune to gravity; there is no gravity without matter. Over the course of the twentieth century, this ambiguous dualism between force and matter would undergo many transformations, but it would never be eradicated.

The modern view of physics, enshrined in quantum field theory, is in fact also dual in nature, but takes on a form that is profoundly different from that of the past. Matter is represented by particles of a type known as fermions (named after Enrico Fermi), whilst forces are represented by another type, known as bosons (named after the Indian physicist Satyendranath Bose). No particle can alter this fundamental nature: every elementary particle, when isolated, is born and dies as either a fermion or a boson. As particles, they share many properties: they carry energy, and in some cases other characteristics such as mass or a form of charge, and they interact with one another. But they differ in one fundamental property: fermions exchange bosons, but bosons do not exchange fermions. Particles of matter, such as electrons and protons, alter their motion during this exchange, speeding up or slowing down, much like two ice skaters moving apart when they throw a ball to each other: this change in state is what we macroscopically call force. Every action that alters the state of matter is the result of an interaction mediated by bosons. Without them, the universe would be like the earth before ‘fiat lux’: ‘formless and void, and darkness covered the deep’.

The ancient dichotomy between force and matter boils down to that between fermions and bosons. Fermions possess a spark of eternity: their number (appropriately defined) is conserved in every process, and it is for this reason that they can properly be defined as matter. Bosons, on the other hand, can multiply beyond all necessity, like the angels of medieval theologians: in any event, they can be created and destroyed without regard for the total number, provided that universal rules such as the conservation of energy are respected. Physicists therefore say that bosons carry, or mediate, the fundamental forces: gravity, the electromagnetic forces, and the two nuclear forces known as the strong and weak forces. But quantum field theory makes this duality even more ambiguous, in that both fermions and bosons are represented by waves propagating through space—waves that obey universal rules applicable to both types. Forces and matter are one and the same: they are oscillations of quantum fields. They obey different laws, but under the same framework. I imagine that many physics students share my sense of wonder when we first learn that, as far as we know, all physical phenomena (all of them: from brain synapses to supernovae) are caused by the random encounters of wave-particles governed, in mathematical terms, by a single expression known as the Lagrangian of the Standard Model – a sort of DNA of the world, in which matter and forces participate in equal measure. It is merely a seemingly innocuous mathematical quirk (the linearity of bosonic fields, to be precise) that makes bosons so flexible that they can appear and disappear as required, like rabbits pulled out of a hat.

I have included gravity amongst the fundamental forces, but it warrants a separate paragraph. Gravity, as the name suggests, evokes something archaic and terribly serious. We are so immersed in it that we barely perceive it as a force, and we only miss it when it isn’t there – and then we’re in trouble! Today, just as in ancient times, gravity remains a source of mystery. Is it possible that a lead ball and a rubber ball, dropped at the same time, would hit the ground at exactly the same moment? Is it possible that we weigh six times less on the Moon? Is it possible that a star imploding could be entirely swallowed up by a black hole, an infinitesimal Omega point without time or space? Is it possible that every movement – from my finger tapping the keyboard to a planet orbiting its star – emits imperceptible gravitational waves, capable of travelling for millions of light-years until someone, or something, detects them and perhaps studies them? We are in good company when it comes to expressing perplexities of a gravitational nature. Einstein himself initially believed neither in black holes nor in gravitational waves, even though his own equations predicted them, and even today legions of physicists and astrophysicists are probing particle accelerators and celestial bodies to understand them a little better. Gravity, whilst perhaps the most studied of the fundamental forces, is also the most incomprehensible, to the extent that it has led many scientists towards Newton’s agnosticism. The reason for this complexity was laid out by the great Albert himself: gravity is a force that literally bends space and time. Physical phenomena are not like billiard balls rolling along a table, propelled by a cue: it is the billiard table itself that bends and unravels along with the balls, and in so doing sets them in motion. No cue, no external agent, no force as we naively understood it before Einstein.

So is gravity something ontologically different from the other forces? Not really a force, but not matter either? A fifth element that throws a spanner in the works, a portal to other dimensions, a spirit hovering over the waters? The profound ambiguity of the concept of force – namely, its existence ‘within’ the physical world without being a full part of it – returns with a vengeance. Einstein’s General Relativity is itself, in every sense, a field theory, and is therefore intrinsically subject to the same laws of physics as the other forces, yet it still eludes a complete description in quantum terms, that is, in terms of particles. As we cannot carry out experiments on black holes—where gravity takes on those extreme forms that would help us uncover its secrets—we cannot ascertain which of the various theories proposing a quantum theory of gravity is closest to reality.

And so I’ve let slip that magic word I’ve been trying to avoid until now: reality. It’s like another terrible word, truth: ‘What is truth?’, Pontius Pilate asks Jesus. And just as in the Gospel, the question can only remain unanswered, because any answer that claims to define truth gives rise to the very same initial question, in an infinite recursion, a logical ouroboros with no way out. Reality is what we perceive, but the organ that perceives it is itself part of reality. Our physical theories claim to describe reality, but the mind that devises them is itself an element of that reality, and we can never know which part of the laws we formulate is discovered (exists outside ourselves) and which is invented (exists because our mind reproduces innate patterns). The laws of physics seem to work marvellously well, at least as long as we apply them to relatively simple systems, and perhaps we could be content with these successes, as physicists often unconsciously are. Force and matter are reflections of an inescapable mathematical duality, the only two modes of existence: every elementary particle is either a fermion or a boson, without exception. A duality such as there are many in mathematics and logic: every number is either real or imaginary, whole numbers are either divisible or prime, every logical sequence is either correct or incorrect… Or perhaps not. Kurt Gödel’s incompleteness theorems, published around 1930, teach us that no formal logical system, including mathematics, is complete, in the sense that we can always formulate statements that can be neither proven nor disproven. Perhaps reality is indefinable in this very sense, and it is entirely futile to try to mediate between materialism and idealism. But I digress…

Newton summarised the whole of philosophy in his study of forces. Can there be a dialogue between force as understood by physicists and force in other contexts, particularly political or social ones? I believe the common thread lies in the consequences of force. In physics, forces create structures: they bind electrons to protons in atoms, atoms into molecules and stars, molecules into animal cells, and so on, step by step. Without the mathematical ‘accident’ that gives rise to forces, the universe would be pure chaos. The same hierarchical structure is found in the animal and human worlds: biological, evolutionary and social forces bind us together in families, tribes and peoples. The force of the herd or the community compels the individual to abide by certain laws. Without them, the herd dissolves and slides towards anarchy or extinction. “What is a kingdom without justice,” writes Augustine of Hippo, “if not theft?” But the force of the community is not external; it arises and regulates itself within the community itself. Nor is it merely the sum of the wills of many individuals; rather, it is a code that obeys its own laws—not merely biological, not merely logical, not merely physical. In General Relativity, according to J. A. Wheeler, space-time tells matter how to move, and matter tells space-time how to curve. This maxim could well be adapted to sociology: the laws of the community tell individuals how to behave, but at the same time individuals tell the laws how to evolve. The force acts in both directions.

The analogy between force in physics and in politics also extends to the ultimate threat. When the balance between force and matter is disrupted, structures collapse in on themselves. The resulting stellar catastrophe transforms a star into a white dwarf, or a neutron star, or into the eternal darkness of a black hole. When the balance between the strength of the community and the will of its members is disrupted, society enters a violent spiral of upheavals, the outcome of which is unpredictable. Physics, alas, does not teach us how to avoid catastrophe. That is a task that falls entirely to us.