**The Higgs boson as simulated by one of the detectors at CERN**

“Everything you’ve been told about physics is wrong.”

From his opening remarks to his punchline, Caltech cosmologist Sean Carroll knows how to grab an audience’s attention. And when Carroll talks physics, people listen. The “wrong” that Carroll is referring to is the widely held view that the world is made up of particles. Not so, he says. At the heart of it all, everything is fields – electric, magnetic and beyond. Even the celebrated hunt for the Higgs particle, which imparts mass to all the other particles in our universe, is actually a quest to nail down the Higgs field.

Over the past century and a half, field theory has come to dominate our understanding of the universe, from the cosmic to the subatomic. General relativity is a field theory that describes how gravity choreographs the elegant motions of galaxies, stars, planets and moons, while at the other end of the scale quantum field theory describes the chaos of the subatomic world. As physicists now see it, our universe is nothing less, and nothing more, than a collection of fields invisibly filling space with their powerful, generative effects.

To some degree, most of us are aware of fields. We have all sprinkled iron filings near a magnet and suddenly seen the invisible made visible – the filings disturbed by the radiating lines of the magnetic field. But that is just the tip of the iceberg.

Today, physicists think the filings themselves are just disturbances in a field. There is really no such thing as “filings” or us, or particles of any kind. There are only fields.

But what exactly are they?

Carroll, author of *The Particle at the End of the Universe*, delivered his remarks at an organisation I founded in Los Angeles called the Institute For Figuring, whose mission is to engage people creatively about science and mathematics. We had promised our audience an explanation of the Higgs boson and he did not disappoint.

Carroll’s signature brand of intelligence and wit has put him in demand across the US and beyond. He may be the author of a graduate-level textbook on general relativity, but he has also made it as a media celebrity, entertaining audiences on satirical American television show, *The Colbert Report*.

To understand the hullabaloo surrounding the Higgs, Carroll says we have to forget about particles. “It’s not the Higgs boson itself that is interesting. What matters is the Higgs field from which the boson arises.”

From Skype calls to Mars missions, many of the great advances in modern physics owe their success to field theory. And some of the most fertile minds ever known laid the groundwork including Michael Faraday, James Clerk Maxwell and Albert Einstein.

If we finally arrive at a “theory of everything”, most likely it will be a field theory.

Yet, let me confess that from my earliest days as a physics student till today, and as an author of numerous books on the history and philosophy of the subject, I still find field theory strange, exciting and in some ways deeply unsettling.

Unsurprisingly, field theory had a controversial birth, emerging awkwardly from Isaac Newton’s inquiry into gravity. In the 17th century, Newton deduced that the mundane fact of an apple falling from a tree and the celestial wonder of the Moon orbiting the Earth were in fact part and parcel of the same thing. Both were evidence of a gravitational force pulling objects towards the Earth; the same gravitational force keeping the Earth in orbit around the Sun. Many of Newton’s contemporaries were horrified by his ideas. The notion of an invisible force reaching out across the universe connecting the stars and Earth smacked of astrology, something that the protagonists of the Scientific Revolution were trying very hard to distance themselves from. How, asked Newton’s peers, did this mysterious “force” operate? Newton’s famous response was to plead ignorance: “I feign no hypothesis,” he declared. Though he didn’t understand how gravity did what it did, he could show precisely what it did with mathematics. He described an invisible “something” binding the universe together in a cosmic web of attraction.

From the start both physicists and philosophers had to grapple with the paradox of Newton’s discovery. Here was a new theory of the world that was supposed to expunge supernatural thinking, yet no one had any idea how its central principle might work. In some ways it seemed as fantastic as magic. “How does the Moon know that the Earth is exerting a gravitational pull on it?” offers Carroll in sympathy with the physicists of that time.

Towards the end of the 18th century, the French physicist Pierre-Simon Laplace suggested an answer. Laplace proposed that gravity resulted from a field – later dubbed the “gravitational potential field” – that filled all of space. This field flowed through space like waves through the ocean, whereas the old Newtonian concept of force had no known means of transmission. Gravity was not something that instantaneously leapt across millions of miles of space, but a localised phenomenon, more like vibrations on a spider web. The Earth could pull on the moon because it affected the gravity field in its immediate vicinity; this in turn affected the region nearby and so on towards the moon. The “force” of gravity travelled, as it were, within and via this field. One implication of Laplace’s theory was that gravity should propagate at a finite speed, which led others to hypothesise gravity waves. In 1992 an international team of physicists built themselves an observatory known as LIGO (Laser Interferometer Gravitational-Wave Observatory) to look for them.

It was gravity that first spurred Newton and Laplace to an awareness of fields. But for the public, it was magnetism.

Magnets revealed the invisible reality of fields, as Michael Faraday demonstrated to the English public with iron filings and a magnet in the 1820s. Like Carroll, Faraday was a consummate public performer. His magnet experiment was one of a series of discoveries through which he eventually showed how magnetism and electricity were interconnected. Faraday was the first to propose that electricity and magnetism also operated through fields. But unlike Laplace, Faraday had only basic maths, and was unable to back his ideas with equations. Most of his peers scoffed at the idea of invisible fields. In an age where the machines of the Industrial Revolution were changing every aspect of life, fields seemed an ethereal and mystical idea.

In the 1860s, maths came to Faraday’s rescue in the form of Scottish physicist James Clerk Maxwell. He backed up Faraday’s concept with what are now known as Maxwell’s Equations, which combine electric and magnetic fields into the greater whole of an electromagnetic field. Among other things, they describe light as an electromagnetic field travelling at a speed of 186,000 miles per second. Maxwell also predicted that it should be possible to artificially produce electromagnetic waves. Heinrich Hertz did just this in the late 1880s, generating radio waves and planting the seed of today’s telecommunications industry.

Thanks to Maxwell’s theory, physicists stopped seeing the universe as a vast machine, and increasingly began to understand it as an arena for the interactions of fields.

Maxwell’s laws were a triumph of mathematics, but only a small number of highly trained physicists could understand them. Poignantly Faraday himself wasn’t one of them. He died sad and frustrated, not realising that Maxwell’s equations had verified his theory.

But field theory still had a way to go to achieve widespread acceptance in the physics community. Besides the complex maths, it was seriously weird. Even Lord Kelvin, a mathematical genius and Maxwell’s close friend, worried about the increasingly mysterious character of the subject. The problem with fields – then, as now – is that they are hard to conceptualise. The maths has no trouble describing how they operate – the gravitational field for instance falls off with the inverse square of the distance – but what exactly is being described?

Albert Einstein decided to answer that question with his General Theory of Relativity. Gravity, he explained, is a by-product of the shape of space. Objects experience gravity when they encounter distortions in a field whose fabric is space itself. In other words, the gravitational field is part and parcel of the structure of space. It was a problematic explanation. Not only was it hard to swallow, it also melded two things that had not been melded before: force and space.

In Newtonian physics three fundamentals underpin the universe like the three legs of a stool: matter, space and forces. With general relativity, Einstein melded space with the force of gravity. So now the universe tottered on only two fundamentals! Einstein understood the revolutionary nature of his theory, and that led him in a bold direction. With general relativity he had melded space and the force of gravity into a single entity. Could he now do the same for matter? Might it be that matter could also be understood as a state of space? Einstein spent 30 years trying to find a “unified field theory” to achieve this goal. Although he failed to find a mathematical framework for his inspired idea, the physicists of the next generation carried his baton forward.

Einstein tried to meld matter and space at the cosmic dimension using his principles of general relativity; the breakthrough came from the other end of the scale of physics: quantum theory. But even here Einstein played a seminal role.

Until the end of the 19th century, the dogma held that light and matter were distinct kinds of objects. Light was a waving field; matter was made up of particles such as electrons and protons. But in 1905, Einstein showed that light could actually be both; besides being a wave it was also packaged into discrete particles called photons. That mind-bending idea in turn inspired a young French prince to something even weirder. For his 1924 doctoral thesis Louis De Broglie proposed that matter also has a wave-like character. Two years later, Erwin Schrödinger developed a mathematical equation to support that thesis, showing how “matter waves” should behave. The Schrödinger equation – one of the foundation stones of quantum field theory – did for particles of matter what Maxwell’s equations did for electromagnetic fields. Weird as it seems, it verified that particles of matter do indeed also propagate themselves as waves.

Matter waves may sound like nonsense. Yet we already make use of them in electron microscopes which rely on very high energy waves emanating from electrons to visualise objects smaller than the wavelength of light.

So if particles of matter can wave in a similar way to photons of light, what is doing the waving? In the case of photons, the answer is an electromagnetic field. In the case of an electron, the answer is an electron field. For a neutrino it is a neutrino field. And so on. “What we call particles are vibrations in these fields. That’s the underlying framework for everything that particle physicists do,” says Carroll.

Which leads us to the Standard Model – the crowning achievement of 100 years of particle physics and which explains everything in the known universe with the exception of gravity. Like a periodic table of the subatomic world, it describes the characteristics of 61 elemental particles, their associated fields and their interactions with electromagnetism and the weak and strong forces that operate inside the nuclei of atoms. It’s been fantastically successful in predicting particles that were eventually found in atom smashers. But the most important suspect remained at large for four decades. It was the one predicted to impart mass to all the others. Finally after 40 years of hunting, and building the Large Hadron Collider at CERN to find it, in March it was tentatively announced that a Higgs boson had been detected. It was found to have just the energy that the Standard Model predicted.

The Higgs boson, like all the other particles, comes with a Higgs field, and it is this field that physicists are itching to understand. Because the Higgs field is unique. All fields extend throughout space and at every point, it is possible to “quantify” a value. For each field the average value throughout space is zero. Except for the Higgs field. This is what gives the Higgs field its special role.

“As we travel through space, we’re surrounded by the Higgs field, and moving within it,” writes Carroll. “Like the proverbial fish in water, we don’t usually notice it, but this field is what brings all the weirdness to the Standard Model.” The “weirdness” here is the fact that if it weren’t for their interaction with the Higgs field, particles would all be massless like the photon. The universe would be a very different place.

Physicists are excited about the confirmation of the Higgs boson mostly because it has confirmed the existence of the Higgs field, which was the final piece of the Standard Model. But the Higgs boson seems fated to do much more than just “dot the i” of the Standard Model. It opens the door to physics beyond that model, much as early discoveries in quantum science at the start of the 20th century opened the door to a new era beyond classical Newtonian physics.

The Standard Theory predicts the value of the Higgs field should be at one of two extremes: either zero, or extremely large, as much as a million trillion giga-electron volts (GeV). But recent measurements give the very ordinary value of 246 GeV. This means that we need some new physics beyond the Standard Model. We’re standing at the brink of the unknown.

For one thing, it may turn out that Higgs bosons come in several different flavours. As Carroll puts it, the one discovered at CERN “could be *a* Higgs, not *the* Higgs”. Moreover the various types of Higgs particles will be pressed into the service of physics’ ongoing quest to unify the seemingly disparate elements of our universe. As Faraday melded electricity and magnetism and Einstein melded gravity and space, the current generation is aiming to unify matter, space, gravity and the three subatomic or quantum forces in a grand unifying “theory of everything”.

One of the most popular conceptual tools for building a theory of everything is supersymmetry. It proposes that every particle has a twin, known as a sparticle. Mysterious dark matter – we cannot see it but we know it is there because of its effects on galaxies – may indeed be composed of sparticles. Supersymmetry theories also come in lots of mathematical varieties, all of which demand the existence of multiple Higgs bosons. So finding the Higgs particles may crack the mystery of dark matter and thereby help to explain the structure of our universe on the cosmological scale. In Carroll’s estimation: “The Higgs discovery is the end of one era and the beginning of another.”

Over the past century and a half, field theory has transformed physics as a science. It has also changed our view of reality. As theoretical physicists now see it, the core of nature is nothing more substantial than waving fields. As Carroll told us, fields are “the true reality” while the apparent substance of matter – its solidity and point-like concentration – is an artefact of our limited powers of perception.

And so we return to our original question: what exactly are these fields? If fields are “states of space”, what exactly is “the state” that is changing here? At the end of Carroll’s lecture, I put this question to him. His answer, after a considerable pause, was both illuminating and confounding.

Each state of space, he said, was a matrix of numbers, one number for each point in space. As a field changes, what is really changing is the value of the numbers.

Carroll seemed simultaneously elated and a bit dazed by this idea. For myself, I could not help thinking of the film *The Matrix*, in which Keanu Reeves’s character discovers that the world he has known all his life is actually a computerised simulation generated by the matrix.

I recognise here the apprehension that Lord Kelvin expressed when he worried that the power of mathematics would carry physics beyond comprehension, not only of ordinary human beings but of physicists. “I am never content until I have constructed a mechanical model of the subject I am studying. If I succeed in making one, I understand; otherwise I do not,” he wrote. Yet as a great mathematician, Kelvin recognised the mysterious power of equations and numbers, noting that “the more you understand what is wrong with a figure, the more valuable that figure becomes”.

There is no question that with field theory physicists have been able to describe with enormous precision how forces and particles behave, thereby giving us a platform on which we have built so many of the technologies of modern life. By figuring out the world with their equations and numbers, physicists have transformed the very fabric of everyday experience.

But are we able to accept ourselves as flickers in a matrix of shifting sequences of numbers?