by Marcus Chown
One impossibly tiny-length scale is thought by physicists to be of particular significance. At a length of 1.6 × 10-35 metres – 10 million billion billion times smaller than an atom – the force of gravity becomes comparable in strength to the other three fundamental forces of nature: the electromagnetic, strong nuclear and weak nuclear forces. The ‘Planck length’ was even recognised by Planck in 1900, though not for modern reasons. He simply thought it was so fundamental a scale that it would ‘retain its significance for all times and all cultures, even extraterrestrial and extra-human ones’.20
The non-gravitational forces have all been successfully described by quantum theory, which suggests that a quantum description of gravity may be required to understand what is happening at or near the Planck scale. In the quantum picture, the fundamental forces are a consequence of force-carrying particles which are exchanged like a tennis ball batted back and forth between tennis players. In the case of electromagnetism, the force carrier is the photon; in the case of the weak nuclear force, three ‘vector bosons’; and, in the case of the strong nuclear force, eight ‘gluons’. Since such force-carrying particles are ‘virtual’ – popping out of the vacuum and popping back again – the more mass-energy they contain the briefer their existence and the shorter the distance they can travel during that existence. This means that the more massive the force-carrying particle the shorter the range of the force it mediates. For instance, the massive vector bosons give the weak nuclear force a range much smaller than the span of an atomic nucleus whereas the zero-mass photon endows the electromagnetic force with an infinite range.
It follows that, if a quantum description of gravity is possible, there ought to exist a force-carrier which carries the gravitational force. Theorists have christened this hypothetical particle the ‘graviton’. There are many theoretical problems with the graviton and it is possible that no such particle exists. For instance, the strength of a force is synonymous with how frequently the force-carriers interact with particles that ‘feel’ the force. But gravity’s incredible weakness compared with the other forces -the gravity between a proton and electron in a hydrogen atom is 10,000 billion billion billion billion times weaker than the electromagnetic force – means that gravitons hardly ever interact with matter. In fact, a detector of the mass of Jupiter would need to wait more than the age of the Universe before its bulk could stop a graviton.21
Notwithstanding problems with the graviton, uniting Einstein’s theory of gravity with quantum theory is likely to be very hard because the two theories appear fundamentally incompatible. For one thing, general relativity is a theory about certainty – it predicts the future with 100 per cent certainty – whereas quantum theory is a theory of uncertainty — merely predicting the probability of possible alternative futures. ‘Despite this, however, physicists have succeeded in finding a quantum description of nature’s other fundamental forces,’ says David Tong of the University of Cambridge.
But quantum theory even denies the existence of precise locations in space and trajectories of bodies moving through space, which are the very foundation stones of Einstein’s theory of gravity. Quantum theory also views the Universe on the smallest scales as discrete and grainy whereas general relativity sees it as smooth and continuous. And if all these things are not enough of an obstacle to uniting general relativity and quantum theory, nature’s non-gravitational forces operate in space-time whereas gravity is space-time. ‘This difference may not be significant,’ says Tong. ‘However, gravity smells different.’
The Planck scale turns out to be significant not only because it is the scale at which gravity becomes comparable in strength to the other forces and so appears to require a quantum description. At the Planck scale, quantum theory predicts that quantum fluctuations are so big and so localised that, when energy pops into existence, it pops into existence within its own event horizon. This means it shrinks instantly to form a black hole. Clearly, this is nonsensical. If such events really happen, not only would space-time at the Planck scale be hidden permanently from view inside a black hole but micro-black holes would continually be born in the air all around us.
It seems that general relativity is not alone in predicting something nonsensical at the tiniest of scales: a singularity. Quantum theory also predicts something nonsensical: the spontaneous birth of black holes. The only difference is that the Planck scale, though ultra-tiny, is far short of the infinitesimal, zero-scale of the singularity. It seems that finding the deeper theory that merges general relativity and quantum theory may require fundamental modifications not just of Einstein’s theory of gravity but also of quantum theory.
Even without experiments, there is a guide
The most obvious way to find the deeper theory – a quantum theory of gravity – would be to probe the ultra-tiny length scale at which Einstein’s theory breaks down, at which space and time become meaningless concepts. ‘In the end experiments decide about everything,’ says Arkani-Hamed. ‘And experiments require probing the Planck scale.’
But the ultra-tiny length of the Planck scale is synonymous with ultra-huge energy. To put things in context, the Large Hadron Collider near Geneva in Switzerland can reach collision energies of 10,000 GeV.22 The point is that the Planck energy is 10 billion billion GeV – a million billion times higher than anything attainable by the LHC. Reaching such an energy with current technology would require an accelerator ring about one-tenth the diameter of the Milky Way. Perhaps somewhere out in the Universe there is an ET civilisation that has turned 10 per cent of its parent galaxy into an Ultra-Large Hadron Collider. But it seems unlikely.
The truth is there seems little realistic chance of directly probing the physics at the Planck scale. But since the entire Universe was once as small as the Planck length, there is always the possibility that the physics at that scale may have left an indelible imprint on the large-scale Universe – perhaps in the distribution of galaxies. ‘We have to be looking for cosmological measurements that can get us the Planck scale,’ says Arkani-Hamed.
It is possible also that the violent convulsions of space-time when the Universe was that small created powerful gravitational waves. If astronomers are clever, they might be able to see the imprint on the light of the cosmic background radiation, the ‘afterglow’ of the big bang fireball which is still all around us. In fact, there was a claim in March 2014 that an Antarctic-based experiment called BICEP2 had seen just such a cosmic fingerprint. Unfortunately, it turned out it had merely seen the curtain of dust that shrouds our Milky Way.23
It is clear that nature has put clues to the deeper theory than Einstein’s way beyond our reach and that we are going to need extreme ingenuity to get even the slightest glimpse of such clues. But all is not lost. There is a powerful guide: the twin principles of relativity and quantum theory.
9
The undiscovered country
The struggle to find a deeper theory than Einstein’s theory of gravity that will tell us why there is a Universe and where it came from
Due to the inner-atomic movement of electrons, atoms would have to radiate not only electromagnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.
Albert Einstein1
There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.
Douglas Adams2
You have climbed a lofty mountain. Getting to the summit has taken every last ounce of energy and ingenuity, and you are exhausted but euphoric. As you pause to catch your breath, you look up at the next mountain in the chain. And gasp. It is not twice as high as the mountain you have just climbed, or five times as high or even ten times as high. No. It is an impossib
le million billion times as high.
This is the position that physicists find themselves in at the beginning of the twenty-first century. They have used all the knowhow and ingenuity of their science and technology to build the Large Hadron Collider near Geneva. It has bagged them the fabled Higgs particle, the quantum of the Higgs field, which endows all other particles with mass, and they are rightly euphoric at their spectacular success. But now, before them, stands the next great challenge: the Planck scale at which space and time and gravity likely emerge from something more fundamental and nature keeps the ultimate secret of the origin of the Universe. It is a million billion times more energetic than anything the LHC can reach and it is enough to make a grown physicist weep.
The impossibility of scaling the height of the Planck energy has led some commentators to pronounce gloomily the end of physics or, alternatively, to claim that fundamental physics has morphed into science fantasy and theorists are now free to publish any mad theories they can dream up, safe in the knowledge that no conceivable experiment will ever catch them out and prove them wrong.
Nothing could be further from the truth. ‘The idea that we cannot tell that a theory is correct until we do an experiment is false,’ says Nima Arkani-Hamed.
There are two physics principles that we know are true to the extent that they predict to a jaw-dropping degree of precision exactly what we see in the world that is accessible to our observations and experiments. The first is special relativity and the second is quantum theory. Physicists are not, it turns out, free to invent any old theory they like. Far from it. Their theory must be consistent with both special relativity and quantum theory. In fact, so ridiculously tight is this constraint on reality that the overwhelming majority of theories that physicists come up with are instantly ruled out. ‘This is why it is so hard to find a deeper, more fundamental theory,’ says Arkani-Hamed.
‘Although a thousand theoretical flowers have bloomed, they still lack a firm basis in physical principles,’ says historian of science Gennady Gorelik of Boston University. ‘Never before in physics have so many people worked for so long with so little tangible success.’3
‘The construction of a space-time geometry that could result not only in laws of gravitation and electromagnetism but also in quantum laws is the greatest task ever to confront physics,’ said Matvey Bronstein, the man who pioneered the whole subject of quantum gravity in the 1930s.4
To emphasise how extraordinarily restrictive is the strait-jacket imposed on physics by special relativity and quantum theory, imagine there is a very competent physicist who knows nothing about the world and who is locked in a windowless room with two blackboards. (Do not worry yourself about how he got to be a very competent physicist while knowing nothing about the world – this is not a realistic story!) On the first blackboard are written the principles of special relativity and quantum theory. The second blackboard is largely blank except for the simple instruction: ‘Deduce the consequences of other blackboard.’
For a while, the physicist contemplates the intimidating emptiness of the second blackboard. Then he picks up a piece of chalk and begins scribbling furiously. What does he write down? What does he deduce about the world?
Deducing the Universe
The first thing the physicist realises is that special relativity and quantum theory have consequences for quantum spin. As mentioned before, spin, like everything else in the microscopic world, comes in discrete chunks. The fundamental unit is ½ of a certain quantity (the quantity being h/2π).5
It might appear that a subatomic particle can possess any multiple of the basic unit – for instance, 19/2 or 27 or 801. But our physicist quickly discovers that nature is far more restricted and must choose its spins from an extremely reduced palette. Out of an infinity of conceivable spins, only a mere five are compatible with the twin constraints of special relativity and quantum theory: 0, ½, 1, and 2.
The spin of a particle determines how it interacts with other particles and so the phenomena for which it is responsible. Our physicist decides to consider particles of each spin, one at a time, and to write down on the empty blackboard everything he can deduce about them.
He first discovers that quantum theory requires that particles with ‘half-integer’ spin obey the Pauli Exclusion Principle. This endows them with a strong tendency to avoid each other.6 The need for each such particle to have a lot of elbow room means that, when large numbers of them come together, they form spread-out, extended objects.
In fact, particles with spin ½ – which are known as ‘quarks’ and ‘leptons’ – are the fundamental building blocks of matter. A common lepton, which shares the antisocial nature of all half-integer spin compatriots, is the electron. ‘It is the fact that electrons cannot get on top of each other that makes tables and everything else solid,’ said Richard Feynman.
Next, our physicist considers particles of spin 1. He realises that they can be exchanged between the building blocks of matter and that this exchange gives rise to forces. There are three possibilities which lead to three distinct fundamental forces of nature.
In fact, the three ‘interactions’ have been given the names the electromagnetic force, the weak nuclear force and the strong nuclear force. The strong force binds triplets of quarks into protons and neutrons, and confines them in a ‘nucleus’. But it has no dominion over electrons. Instead, they are bound to a nucleus by the electromagnetic force to create an atom.
Our incarcerated physicist locked in a room deduces not only the existence of ninety-two types of naturally occurring atom – from hydrogen, the lightest, to uranium, the heaviest – but the existence of a dizzying array of chemical compounds that arise from all the myriad ways in which the basic atomic building blocks may be combined.7
So much for particles with spin ½ and spin 1; our physicist now considers spin 0. He immediately realises that a particle with spin 0 is the ‘quantum’ of a ‘field’ which permeates all of space and resists the passage of other particles. By doing this, it endows them with inertia, or mass.
In fact, such a particle exists in the guise of the Higgs particle. Its discovery was triumphantly announced to the world by physicists at the Large Hadron Collider in July 2012.
Next, our physicist considers spin 2. He realises that a particle with spin 2 has the property that it interacts with every other particle, giving rise to a ‘universal force’. It takes a bit of calculation but he is able to show that an inevitable consequence of the existence of a spin 2 particle is the general theory of relativity.8 This shows that special relativity is in some sense more fundamental than general relativity. How else could it be a consequence of special relativity (combined, of course, with quantum theory)?
Studying general relativity, our physicist recognises the existence of a long-range inverse-square law of attraction, which causes large bodies to orbit other large bodies. We of course know of planets that orbit stars and galaxies that orbit other galaxies. Our physicist locked in a windowless room knew of none of these. Remarkably, he has been able to deduce the existence of the large-scale Universe.
No one has yet found a particle of spin 2. And there is good reason to believe that, if it exists, it will be extremely difficult to detect. But such a particle fits the bill for the ‘graviton’, the hypothetical carrier of the force of gravity.9 Since physicists have a theory of gravity in which the force of gravity is mediated by a graviton and which spawns general relativity, in a sense they already possess a quantum theory of gravity. Unfortunately, the theory is a low-energy, large-scale version of quantum gravity not the deeper version required to shed light on the ultra-high energy, ultra-small length of the Planck scale.
Next, our physicist considers the one remaining spin: . Spin particles permit ‘supersymmetry’ in which all the half-integer spin particles (fermions) are recognised to be merely the obverse face of integer-spin particles (bosons).
As yet, we have no experimental evidence that nature uses particles of spin . Bu
t, given that it employs all other spins in its palette, there is a strong suspicion that it does. The electron, for example, is hypothesised to have a supersymmetric twin, dubbed the ‘selectron’. The super-partners of known particles are considered to be good candidates for the Universe’s ‘dark matter’, which is known to outweigh the visible stars and galaxies by a factor of about six.10 The reason we have not yet detected supersymmetric particles, physicists suggest, is that they are very massive and that creating them requires more energy than is currently available in collisions at the Large Hadron Collider.
Although our physicist has now considered particles of every permissible spin and deduced their behaviour, there is one more thing that he can deduce from special relativity and quantum theory. Remarkably, the two principles require that each subatomic particle must have a partner with opposite electric charge or spin. Whenever a particle is created as a quantum fluctuation of the vacuum, it must always be accompanied by its ‘antiparticle’.11 For instance, a negatively charged electron is always conjured into existence alongside a positively charged ‘positron’.
The Standard Model
The full inventory of the world turns out to be the following: 12 basic building blocks – 6 quarks and 6 leptons; 12 force-carriers – the photon of the electromagnetic force, 3 ‘vector bosons’ of the weak nuclear force and 8 ‘gluons’ of the strong nuclear force; plus the Higgs; and, of course, all the antiparticles. Collectively, these constitute the ‘Standard Model’ of particle physics, the triumphant culmination of 350 years of toil by physicists. It is no exaggeration to say that the Standard Model + the general theory of relativity = the World.