The alternative to symmetry is intriguing (Image: Simon Danaher)
Forget symmetry, it’s asymmetry that could be the key to life, the universe and almost everything
SYMMETRY is deeply satisfying. It has harmony and balance – it feels right. But while physicists use it as a guide in building theories, nature is more often lopsided than manifestly symmetric. Asymmetries are often far more informative. Trying to understand why a particular asymmetry exists can reveal clues about the profound nature of reality. That’s exactly what Peter Higgs and François Englert were doing 50 years ago when they came up with what’s now known as the Higgs mechanism, which imparts mass to fundamental particles. In October last year, their efforts were rewarded when they shared the Nobel prize in physics.
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Sometimes symmetry itself springs from asymmetry. We are made of atoms, which are held together by the attraction of opposite electrical charges. The simplest atom, hydrogen, consists of a single negative electron and a positive proton. These electrical charges counterbalance so precisely within matter that they cancel out one another, leaving gravity as the dominant long-range force outside.
This is a case where perfect balance is crucial. Yet the way it is achieved is utterly lopsided. The electron, as far as we know, is a fundamental particle whereas the proton is not: it is made of three quarks. If the electron carries a charge of value -1, each quark carries a charge of +2/3 or -1/3 and they combine in threes to give the proton with a charge of +1 and the neutron with zero charge. Even the simplest atom is cockeyed: its protons are complex, yet its electrons are simple. That their charges conspire so beautifully suggests that some deeper symmetry relates electrons to quarks, but as yet we do not know what it is.
It is not just charge: the clustering of quarks also creates a skew in the way mass accumulates. When clumped to make a proton, quarks’ energies are high. This is the price quantum uncertainty demands to localise quarks within the proton, which is only about 10-15 metres in size. Their total energy – using the equivalence between energy and mass, E = mc2 – gives a proton a mass of nearly 2000 times that of an electron. Thus an atom is lopsided: flighty lightweight electrons encircle a massive, static nucleus of protons and neutrons.
Asking other questions about reality at the level of particles reveals more asymmetries. Why are there not positively charged electrons and negative protons? The laws of electrical attraction and the quantum rules that stabilise atoms would work just as well to make such “antimatterâ€. As fans of Star Trek and Dan Brown know, matter and antimatter annihilate upon contact, emitting radiant energy – photons. So if the universe erupted in a hot big bang out of nothing, the radiant energy of that event should have spawned equal amounts of matter and antimatter, which would then have destroyed one another. Yet the known universe does not show this symmetry, and consists instead of matter without antimatter.
The mystery of the missing antimatter – this fundamental asymmetry of the universe – is a great unsolved question. Perhaps it is born of some intrinsic asymmetry in the underlying laws of nature, though if so, we have yet to identify it. Or could this be an example where fundamental symmetries become hidden, such that the appearance of the physical world differs radically from its deep structure? It is this concept of “hidden symmetry†that led Higgs and Englert to their Nobel prize.
Lopsided life
Life itself is built on hidden symmetry. At first glance the human body appears to be mirror symmetric. There are superficial asymmetries, such as the side on which we part our hair. More profoundly, however, our internal organs are mirror asymmetric, in part because the heart has an intrinsically asymmetric role. One ventricle pumps oxygenated blood to the body, which requires a strong pump. The other sends blood to be oxygenated in the lungs, which are only next door. So, one side is more powerful than the other, which gives the sense that the heart is on the left – for most of us. Other internal organs are then plumbed in in a necessarily asymmetric manner. This is true for all but the 1 in every 20,000 or so people whose organs are mirror-inverted.
At a deeper level, there appears to be a lopsidedness in the molecules of life. Louis Pasteur even wondered if the “existence of life itself is a consequence of cosmic asymmetryâ€.
The element of life is carbon, and quantum laws dictate that a carbon atom has four links with which to ensnare other atoms. A simple example is methane, CH4, which makes a symmetric tetrahedron with the carbon atom at the centre and hydrogen atoms at its four “cornersâ€. Suppose, however, that all four of carbon’s links attach to distinct elements or molecules. For example, C[H][COOH][CH3][OH] is a molecule found in milk. This is not symmetric under rotation and behaves differently from its mirror image. In Lewis Carroll’s Through the Looking-Glass, Alice wonders whether or not mirror milk would be fit to drink. For normal humans probably not, because the mirror form is muscle-aching lactic acid.
The templates of life are amino acids. These too have a tetrahedral structure and occur in mirror forms, or isomers. One of these isomers may seed life, but the other does not; at least not as we know it. At the molecular level, life is mirror asymmetric. Even though natural laws allow symmetric right and left-handed molecules, life has made use of one (the left) to the exclusion of the other. In this way, fundamental symmetry has been hidden.
Galaxy skew
Stability and symmetry have an intimate relationship. Push a shopping trolley with both hands at the perfect midpoint of its handle and still it seems to have a mind of its own: it slews left or right. The situation is highly unstable, to the extent that the merest deviation from perfect symmetry – perhaps your right hand is stronger than your left – can cause a huge deviation in trajectory.
What about a system where only one force is at work: gravity? Newton tells us that the force of attraction cares naught for direction, and so gravity is spherically symmetric. The natural expectation, then, is that gravity leads to spherical shapes. The moon and sun are nice examples, and so are spherical galaxies. Most galaxies are not spherically symmetric, however: just look at a spiral galaxy, which is largely flattened on a single plane. If the spiral galaxy Andromeda was all we knew of, we would perhaps guess that gravity is symmetrical only in two dimensions.
What’s going on is that a spherical galaxy is highly unstable. Unless all the stars are perfectly positioned, as they fall towards one another under their mutual, 3D-symmetric gravitational attraction, some will overshoot and then return, oscillating back and forth until a stable configuration results. A minor disturbance, such as a tug from another galaxy, will tip the balance. In such a situation nature chooses stability over symmetry. A symmetric but unstable situation will hide symmetry to attain stability. To murder the English language: “unstable symmetry becomes stable ‘unsymmetry'â€.
“In an unstable situation nature will hide symmetry to attain stabilityâ€
Overall, however, the collection of spiral galaxies throughout the cosmos retains 3D symmetry, because they are oriented in all possible planes. In individual cases, stability requires the symmetry to hide, but universally the symmetry survives.
We can show how stability hides symmetry with a Mexican hat. Place it upside down and a ball will happily sit in the bottom of the well: this is stable and rotationally symmetric. Turn the hat the right way up and place the ball on the hump and the symmetry remains, but the system is now unstable. The ball inevitably rolls in a random direction into the hat’s valley (see diagram). The underlying symmetry is still there, but is now hidden.
And this is where we return to the Higgs mechanism. Symmetry in the quantum theory of fields such as electromagnetic fields implies that particles have zero mass. For electromagnetism this presents no problem because the carrier of the electromagnetic field, the photon, is massless. But the carriers of the weak nuclear force, the W and Z bosons, have mass – indeed, different masses – so that profound symmetry must be hidden. How does this happen?
Massive photons
There is a case where a photon appears to have mass, and it was this example that inspired Higgs, Englert and others. What happens when a photon hits a plasma – a gas made of ionised particles? The answer is that photons can only penetrate the plasma if their frequency is above a threshold called the “plasma frequencyâ€; lower than this and the photon will be reflected.
A real-world example of this is a radio wave bouncing off the ionosphere, the layer of plasma high in our atmosphere. These reflections allow analogue radio signals from the US to be picked up in Europe. Yet people can still see the stars shining through the ionosphere because visible light has a higher frequency, and therefore energy, and passes unhindered through the plasma.
This means a creature that lived in the plasma would see only photons with an energy above a certain minimum. Drawing once again on E = mc2, a minimum energy implies a minimum mass. Thus, the creature in the plasma would believe that photons have mass.
A sceptical physicist might see a problem here. The electric and magnetic fields of a photon oscillate at right angles to the direction of motion – there are no longitudinal vibrations in the photon’s direction of travel. The rules of quantum physics require that an entity with mass generates these longitudinal waves. But when a photon passes through a plasma, the plasma itself is set in oscillation along the photon’s direction of travel, like a longitudinal sound wave travelling through air. Within the plasma, all the features of a massive photon appear. The fundamental symmetry that demands photons be massless has become hidden.
The key for Higgs, Englert and others was to generalise this idea, and imagine all of space filled with some form of “plasmaâ€. Photons would be blind to this plasma, but W and Z bosons would not be, and pick up mass as a result. In this scenario, we ourselves become the creatures whose only experience is of life inside this strange, ubiquitous plasma – a plasma known, somewhat unfairly, as the Higgs field.
The mathematical description of the Higgs field is analogous to our Mexican hat, which this time represents a profound symmetry in quantum field theory called gauge symmetry. When the Higgs field is zero, this symmetry is maintained, which implies that any photons or W or Z bosons would be massless. However, the energy of the vacuum is high. And just like the ball in our example, the vacuum will settle where energy is lowest – in the valley of the hat. In this mathematical version, the ball represents possible states of the Higgs field. When the vacuum reaches its lowest energy state, gauge symmetry survives but its implications become hidden, so particles can now have mass.
As several researchers realised in 1964, rolling around the hat’s circular valley corresponds to what is called an “extra oscillation freedom†of a massive particle, such as the W boson. This is equivalent to the longitudinal vibrations in the plasma, mentioned above.
Only Higgs, however, drew attention to the possibility that the ball might oscillate up and down the sides of the valley. This wobble is an inevitable result of quantum uncertainty and corresponds to a massive particle, now called the Higgs boson. In 1967, Tom Kibble completed the picture by showing how interactions with the Higgs field can endow W and Z bosons with mass while the photon remains massless.
Deep impact
This stable unsymmetry, born of unstable symmetry, is not just an arcane curiosity. The weak nuclear force, we now know, would have the same strength as electromagnetism, had the W and Z bosons been massless. The weak force controls the fusion of hydrogen into helium in the sun. Were this force as powerful as electromagnetism, the solar furnace would have burned so rapidly that it would have expired long before humans appeared. Evolution’s long time-span was made possible by the Higgs mechanism.
So the notion that “unstable symmetry becomes stable unsymmetry†could be the key to life, the universe and almost everything. That there is any solar system at all is due to a lack of antimatter to annihilate it all. A universe full of matter and antimatter may be akin to our spherical galaxies, with local excesses of matter and antimatter hiding an overall universal symmetry. We live in a local clump of matter, admittedly large, but the universe is vast and could also be home to clusters of antimatter galaxies: an example of stable unsymmetry winning through. The dominance of left-handed life may also be a result of this effect. Natural selection may have turned a small accidental excess on early Earth into total dominance today. Though none of this was known to Pasteur, he may have been correct – we are here thanks to cosmic asymmetry.
This article appeared in print under the headline “Twisted symmetryâ€
