PAUL DIRAC wanted to be seduced, and he wasn’t afraid to admit it. In a 1963 essay recalling his role in discovering the strange-but-true laws of quantum theory, he wrote “it is more important to have beauty in one’s equations than to have them fit experiment”. That might sound odd. Experiment, after all, is the ultimate arbiter of an equation’s ability to explain natural phenomena. But for a theoretical physicist like Dirac, experiments could be misled: only beauty was incorruptible.
An almost religious devotion to beauty remains commonplace among theorists of fundamental physics, even if the standards of attractiveness have changed over time. One vision of elegance in particular has surged to the fore: the principle of naturalness. Broadly speaking, it is the belief that the laws of nature ought to be sublime, inevitable and self-contained, as opposed to makeshift and arbitrary.
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But what if they aren’t? That’s the disquieting possibility being entertained by a growing band of physicists in the aftermath of what should have been the breakthrough discovery of the decade, the snaring of the Higgs boson in 2012. The discovery of the Higgs, at CERN’s Large Hadron Collider (LHC) near Geneva, Switzerland, confirmed a long-held theory about how particles acquire mass. But what we have – and haven’t – found alongside it could have profound consequences for how we view reality, says Michael Dine, a theorist at the University of California, Santa Cruz. “We might find that nature is not natural in the way we thought.”
Even among particle hunters, the word “natural” has a few different meanings. At its broadest, it encapsulates the notion that the universe ought to be plausible, rather than the extraordinarily improbable outcome of some cosmic roulette wheel. “Naturalness is the belief that it’s not all coincidental, that there is a reason behind things,” says , a theorist at the University of Cambridge. “It’s the idea that it can’t just be chance.”
That might sound a tad vague, but theorists have a more precise working definition, known as “technical naturalness”. Formulated in the early 1980s by Gerard ‘t Hooft at the University of Utrecht in the Netherlands, it was designed to flag up any sign the universe’s existence might depend on unattractive hidden coincidences. In simplified terms, this boiled down to saying that theories or models should not contain constants whose values differ too much from one another. Unless some larger, more comprehensive theory can justify a disparity, none of the numbers that dictate how the universe behaves should be more than a factor of 10 apart.
The goods aren’t odd
This makes physicists suspicious of numbers that don’t fit in. Think of it this way: if your hundredth consecutive spin of a roulette wheel landed on the same number, it would challenge even your most broad-minded assumptions of fair play. It is just so ridiculously unlikely that it begs for explanation. Maybe there’s a magnet in the ball, or a tiny invisible string? The same logic applies to forces that are unusually weak or strong, or particles with a mass that is stubbornly high or low: something else must be going on.
To some extent, modern physics has always proceeded along these lines, seeking ever more streamlined explanations for an ever more complicated universe. Lately, though, particle physics has barely proceeded at all. True, the so-called standard model of particle physics is successful, capable of describing all known particles and three of the four fundamental forces in a compact set of equations. But it says nothing about gravity or dark matter, suggesting that something even bigger is waiting to replace it.
“Naturalness is a cognitive bias – one that physics would do well to eliminate”
What’s more, we might be guilty of looking at the standard model through rose-tinted glasses. While its equations are mostly natural, there are a couple of awkward exceptions. The energy density of empty space, known as the cosmological constant, is 120 orders of magnitude lower than we would expect. And then there’s the Higgs. Its own mass, it turns out, is almost unbearably light. “It seems that nature does not, or at least not quite, follow my recommendations,” says ‘t Hooft.
To fulfil its function as the universe’s mass-giver, the Higgs is supposed to interact with every other particle in existence via its associated Higgs field. That’s a complicated process, and one that should bestow the Higgs with some mass: about 10-8 kilograms or, in the units particle physicists use, about 1019 gigaelectronvolts (GeV). That’s enormously heavy in particle terms. So why, when we measure it, does the Higgs come out as such a featherweight – with barely 125 GeV to its name? One outlandish option is that its inherent mass is an enormous negative number, just enough to cancel out the additional mass provided by the interactions and leave behind 125 GeV. But that poses an unnaturalness problem of its own: why should two huge, apparently unrelated numbers cancel out so neatly?
The answer is to make those numbers related. The prime candidate to restore the Higgs to its natural state is supersymmetry, or SUSY, an overarching theory that introduces a heavy twin for every known particle. The addition of these superparticles or “sparticles” would drive the Higgs mass down exactly as much as the known particles drive it up, rounding out the equations and returning the Higgs to a mass that qualifies as technically natural. SUSY is also mathematically elegant, in that it could unify three of the fundamental forces while simultaneously explaining dark matter, the mysterious stuff thought to hold galaxies together.
Looking for sparticles
Faced with such a good-looking multitasker, most physicists were convinced that SUSY would do the trick. They expected that sparticles would soon show up at energy scales just beyond the Higgs, and physics would roll victoriously on. Lovely. Only it didn’t work out like that. In fact, searches for these new particles at three generations of accelerators, including the mighty LHC, have come up empty-handed.
Of course, the particles might still be lurking out there. The LHC’s last-ditch search is due to finish at the end of 2018, but with the collider’s latest run shining a light into the darkest corners of their suspected habitat, we are rapidly running out of places to look. That means we are stuck, unless we revisit the logic that led us to dream up these superpartners in the first place. “Supersymmetry predicts particles that the LHC should be able to see, and that’s what is making me suspicious that we’ve got the wrong end of the stick when it comes to naturalness,” says Allanach. “I’m not yet convinced we have… but I’m suspicious.”
Indeed, more and more physicists are beginning to waver, even those who have spent their entire careers wedded to the principle. Theoretical physics finds itself at a turning point.
For , a theorist at the Frankfurt Institute for Advanced Study in Germany, there is only one way to turn – away from naturalness. In her upcoming book Lost in Math: How beauty leads physics astray, she questions not only its usefulness, but its logical consistency. Naturalness says that, like the rigged roulette wheel, the Higgs mass is highly improbable. But with the wheel, we have a lifetime of experience that tells us how unlikely it is for the same outcome to recur repeatedly – what physicists call a probability distribution. We only have one universe, says Hossenfelder, so there is nothing to compare it with.
Why, then, is naturalness so widely revered? “Personally, I think it’s a cognitive bias,” says Hossenfelder – one that physics would do well to eliminate.
But not everyone is so keen to embrace the ugly-verse. For one thing, renouncing beauty as a guiding principle skirts dangerously close to embracing the circular logic of the anthropic principle, which says the universe has the properties it does because it is the one we live in and think about. For many, that is the ultimate cop-out. “The problem with the anthropic argument is that it is a retreat from scientific enquiry,” says Allanach. “It is accepting that we’ll basically never know.”
Hossenfelder argues that abandoning technical naturalness does not necessarily lead us down the anthropic road to scientific paralysis. “There is nothing wrong with saying your constant has this value, period,” she says.
Most theorists aren’t ready to give up on naturalness just yet, though. Allanach, for example, says that while he has seen his colleagues express frustration at the lack of evidence for supersymmetry, he does not get the impression that the field is somehow in revolt against naturalness as a guiding principle. In fact some, like Dine, still hold out hope that SUSY particles could exist at higher energy scales than predicted – higher, perhaps, than any collider can reach.
“They almost look like religious explanations, introducing angels you can’t observe”
But for those pining after naturalness who have fallen out of love with SUSY, an alternative theory has emerged to console them. Rather than seeking a natural explanation for the Higgs mass by invoking scores of new particles, it goes one better: invoking billions of alternative universes.
The proposed existence of such a multiverse is nothing new. Cosmologists have long suggested that in the moments after the big bang, the exponential ballooning of the universe wound up producing regions so far removed from one another as to qualify as separate universes. The exact number of them remains unknown, but could rank as high as 10500, each with its own unique physical properties.
There is of course no evidence that such a landscape exists, never mind how many universes it contains or what properties they have. Even so, the existence of a vast number of possible configurations could represent the probability distribution that critics like Hossenfelder accuse naturalness advocates of needing. While the vast majority of these universes might well have a Higgs with a more reasonable mass, we could simply be stuck in a statistical outlier. “The only real model for why these numbers like the Higgs mass and the cosmological constant are so strange is this landscape model,” says Dine.
That might seem to lead us back to the anthropic cul-de-sac: perhaps, among all these many different universes, we are in the only one with a Higgs that is light enough to support the structures that ultimately give rise to life and to humans to ponder such matters. But most theorists want something stronger. They want a mechanism that guarantees the Higgs would wind up looking the way it does in our cosmic neighbourhood. And while the landscape might not be the ultimate answer, it could be a step in the right direction. “It gives me some hope that we’ll find our way to a rational explanation,” says Dine.
In fact, some believe we could already have found it. Rather than conjuring up billions of particles in billions of alternate universes, what if all these alternative Higgs bosons had existed in our very own universe, and some hidden process selected the one we see today? That’s essentially what a team led by at the Institute for Advanced Study in Princeton, New Jersey, has proposed with their theory of . It introduces N copies of the standard model, where N is a large number, that exist simultaneously in the same universe. These copies would all be identical apart from the Higgs mass, which of course influences the masses of all other particles in each copy.
Justifying our existence
Then something must have selected for the copy with the light Higgs we see today. According to Arkani-Hamed and colleagues, it could come down to hypothetical particles called reheatons, which contained all the energy of the early universe. Too energetic to exist for long, the reheatons would eventually have decayed into particles lighter than themselves, including any low-mass Higgs, thereby regifting energy to the universe. As the Higgs mass we see is just about as light as it’s possible for a Higgs to get, particle families such as ours would have been preferentially chosen.
“The reheating process in the early universe chooses that standard model out of all other copies,” says at Princeton University, who was one of Arkani-Hamed’s collaborators on the theory. Evidence of this selection process could be detectable in the afterglow of the big bang, he adds, using future telescopes.
If you think this looks suspiciously similar to the sort of improbable fine-tunings and cancellations that naturalness is supposed to guide us away from, you are not alone. “Some of these explanations get ridiculously complicated, much more so than simply putting in a constant and accepting it for what it is,” says Hossenfelder. “They almost look like religious explanations where you introduce angels you can’t observe.”
At the end of the day, naturalness, like beauty, is in the eye of the beholder; one person’s simple solution is another’s rococo monstrosity. But like Dirac, most theorists still want to be seduced. If this means they must update their visions of beauty to suit changing times, or even abandon them altogether, then so be it. “The deepest breakthroughs in physics took place when a contradiction forced researchers to re-evaluate their assumptions,” says at the Institute for Advanced Studies. “The problems with naturalness should be viewed as an opportunity rather than a reason to quit.”
This article appeared in print under the headline “The ugly truth”
Article amended on 9 March 2018
When this article was first published, we misquoted Gian Giudice, head of theory at CERN. We have removed the sentences in question.
