The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the universe. You can sign up for Lost in Space-Time for free here.
Though our world is bewildering in its diversity, all known natural phenomena can be classified into just a few categories. Four of these – gravitational, electromagnetic, strong nuclear and weak nuclear – are well-known, each involving a separate force of nature. The first two have been observed for centuries, while the two nuclear forces, known since the 1930s, have been well understood for several decades. However, there are additional, rarely mentioned but equally important categories. All of them share an underlying unity; despite their differences, they arise from a single core principle of modern physics.
Let’s begin by examining the famous four. At first glance, they’re remarkably dissimilar. Gravity dominates astronomy and is obvious in daily life. Yet, it is the weakest of the forces, and we notice it only because of the immense size of celestial objects. Our planet’s substantial gravity arises from its enormous mass, the sum of all its atoms’ masses.
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Electromagnetism flows throughout our bodies. Electric currents drive our nervous systems, our eyes see electromagnetic waves and our atoms are held together by electric forces. So powerful is electromagnetism that a magnet can stick to a refrigerator door despite being pulled downward by the gravitational force of our entire planet. Why, then, doesn’t electromagnetism dominate the universe? Unlike the mass that creates gravity, the electric charge that creates electric forces can be both positive and negative. These charges cancel out for large objects like Earth and even in individual atoms. In this way, electric forces can completely dominate the atomic world, and yet fade into relative obscurity at the planetary scale.
Meanwhile, the strong nuclear force, responsible for creating protons and neutrons out of quarks and gluons, becomes relevant only at distances below a hundred-thousandth of an atom’s diameter. Not coincidentally, that’s the size of a typical atomic nucleus. While electromagnetic fields can sometimes leak out over gigantic scales – witness the magnetic fields of Earth and the sun – the strong nuclear force is so powerful that it confines its own fields tightly. By trapping them inside atomic nuclei, it ensures they dominate the nuclei but have no influence beyond them.
Finally, there is the weak nuclear force. It, too, goes unnoticed at human scales, but for a completely different reason. At distances larger than the “weak scale”, which is one thousand times as small as an atomic nucleus, this force becomes extremely feeble. Its fields, unlike those of electromagnetism, fade away rapidly beyond the weak scale. This means its pushes and pulls are far too small to observe. Instead, the weak nuclear force plays its most crucial role in creating the slow but striking forms of radioactivity through which it was discovered.
Thus, both nuclear forces are limited to extremely tiny distances, but for opposite reasons: the weak force becomes exceedingly weak, while the strong force becomes exceedingly strong. Yet for all their distinctions, there are remarkable commonalities between these forces of nature, as becomes clear at distances shorter than the weak scale. There, the strong nuclear force is no longer so strong and the weak nuclear force no longer so weak. The strength of the two is comparable to that of electromagnetism. All three of these forces can be described by the equations of quantum field theory, the mathematical language of the standard model of particle physics.
Gravity, too, is described by field theory, though there are gaps in our understanding of how it might act at distances a billion trillion times smaller than the weak scale. In physics class, we learn that gravity’s pull satisfies an inverse-square law – meaning if two objects are a distance r apart, then the force between them declines as 1/r2. Remarkably, at distances below the weak scale, the same is true for the other forces, too. These similarities have given some physicists hope that physics is close to a complete understanding of nature’s basic rules.
Let’s turn now to a fifth category of phenomena, named “Higgs”. This is associated with the elementary particle known as the “Higgs boson”, discovered in 2012, and the corresponding “Higgs field”. The pull of the Higgs force, like its cousins, satisfies the equations of quantum field theory and pulls with an inverse square law at distances shorter than the weak scale. It fits in well with our classification of natural phenomena, so there’s no reason to leave it out.
At longer distances, however, the pull of the Higgs force is even weaker than that of the weak nuclear force. Not only does it peter out exponentially, just as the weak nuclear force does, but it also barely interacts with ordinary matter.
Despite this, our very existence requires the Higgs field, because it provides the masses – specifically the “rest masses” – of all known types of elementary particles, including those of electrons. Objects without rest mass, such as the photons that make up light, must travel at what we call “light speed”, about 300,000 kilometres per second. Only objects with rest mass can travel more slowly. If electrons had no rest masses, they too would travel at light speed, rendering atoms and everything made from them impossible.
All five of these categories are associated with “bosonic” fields, which include the electric and magnetic fields we encounter in physics class. Their particles, known as “bosons”, can combine to make dramatic waves, such as the bright light from a laser or the gravitational waves discovered by the Laser Interferometer Gravitational-Wave Observatory (LIGO) experiment in 2015.
Such powerful waves cannot arise from “fermionic fields”, whose particles are called “fermions”. The most famous such field is the electron field, whose particles are electrons. But the quantum physics of fermionic fields gives us a completely different category of phenomena, as important and as central to daily experience as any other. This category involves contact forces – the phenomena that prevent you from sinking through the floor and keep Earth from collapsing under its own weight. Though electromagnetism plays a role in contact forces, what is most important is a bizarre feature of quantum field theory that has nothing to do with any inverse-square law.
Quantum field theory forbids any two fermions of the same type from doing exactly the same thing at the same time. This is why fermions cannot combine to make substantial waves. The fact that electrons are constrained never to act in concert is called the “Pauli Exclusion Principle”. This principle explains the internal structure of all atoms more complex than hydrogen. But it has another, less widely appreciated role: it is responsible for the structure and stability of ordinary objects. żěè¶ĚĘÓƵs suspected this from the 1930s, and it was finally proven in the 1970s by the mathematical physicist Elliott Lieb and his collaborators. (Lieb, now over 90 and little known outside the halls of physics and maths, deserves a round of public applause for clarifying why the macroscopic world works the way it does.)
Conceptually, the point is that squeezing atoms together puts their electrons on top of one another, potentially violating Pauli’s principle. For example, if you tried to push one of your hands through the other, the electrons from your hands’ atoms would become so concentrated that they would violate the principle. Nature stubbornly opposes this. Overcoming that stubbornness would require far more energy than you could obtain from your muscles. Even if you borrowed extra energy from elsewhere, that energy would destroy your hands before you could push one through the other.
Thus, materials resist being crushed through a fundamental property of fermionic quantum fields. Without it, ordinary objects would implode instead of holding their volume; there’d be no planet Earth, and no human bodies to stand upon it.
So when you next sit down to drink a cup of coffee, think of this. The cup and the coffee remain earthbound thanks to gravity. Their atoms are assembled by electric forces; those forces combine electrons – whose essential rest mass is obtained from the Higgs field – with atomic nuclei, which are held together by the strong nuclear force and were forged in stars by the two nuclear forces. And it’s the strange behaviour of fermionic fields that keeps the coffee from falling through the cup, and the cup from falling through the table.
Underlying it all is quantum field theory, a basic unifying thread that ties together everything we have learned about the universe so far.
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